Vacated in part, and remanded with instructions by published opinion. Judge GREGORY wrote the opinion, in which Judge KEENAN joined. Judge AGEE wrote the dissenting opinion.
*898GREGORY, Circuit Judge:This case concerns the certification of a class of black steel workers who allege endemic racial discrimination at a South Carolina plant owned by Nucor Corporation and Nucor Steel Berkeley (collectively, “Nucor”). Plaintiffs-appellants (“the workers”) accuse Nucor of both discriminatory job promotion practices and a racially hostile work environment under Title VII of the Civil Rights Act of 1964 and 42 U.S.C. § 1981. The district court originally denied class certification for both claims, and this Court reversed. See Brown v. Nucor Corp., 576 F.3d 149 (4th Cir.2009) (“Broum I ”).
The district court has revisited certification and decertified the promotions class in light of the Supreme Court’s opinion in Wal-Mart Stores, Inc. v. Dukes, — U.S. -, 131 S.Ct. 2541, 180 L.Ed.2d 374 (2011).1 We thus again confront the question of whether the workers’ have presented a common question of employment discrimination through evidence of racism in the workplace. Despite Wal-Mart’s reshaping of the class action landscape, we hold that the district court has for a second time erred in refusing to certify the workers’ class, where (1) statistics indicate that promotions at Nucor depended in part on whether an individual was black or white; (2) substantial anecdotal evidence suggests discrimination in specific promotions decisions in multiple plant departments; and (3) there is also significant evidence that those promotions decisions were made in the context of a racially hostile work environment.
Against that backdrop, the district court fundamentally misapprehended the reach of Wal-Mart and its application to the workers’ promotions class. We thus vacate the district court’s decision in part and remand for re-certification of the class.
I.
The Nucor plant encompasses six production departments that work together to melt, form, finish, and ship steel products to customers. See Brown I, 576 F.3d at 151. At the start of this litigation, 611 employees worked at the plant. Seventy-one (11.62%) were black.2 There was, however, at most one black supervisor in the production departments until after the Equal Employment Opportunity Commission (“EEOC”) initiated charges that preceded the putative class action.
The workers’ promotions claim rests on alternative theories of liability under Title VII, which prohibits employment discrimination because of an individual’s “race, col- or, religion, sex, or national origin.” 42 U.S.C. § 2000e-2. The promotions claim first alleges a pattern or practice of racially disparate treatment in promotions decisions. See Teamsters v. United States, 431 U.S. 324, 336, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977). Second, it charges that Nucor’s facially neutral promotions policies and procedures had a racially disparate impact. See Griggs v. Duke Power Co., 401 U.S. 424, 431, 91 S.Ct. 849, 28 L.Ed.2d 158 (1971); Wal-Mart, 131 S.Ct. at 2554.
Both theories are grounded in a statistical analysis of racial disparities in job pro*899motions at the plant combined with anecdotal evidence of discrimination. The workers’ statistical evidence spans the four-year period preceding the litigation, between December 1999 and December 2003. Because Nucor destroyed and/or ■discarded the actual bidding data for the period before 2001, the workers’ experts established an alternative benchmark using ‘change-of-status’ forms filed by the company whenever a promotion took place at the plant. The experts extrapolated comparative statistics for that period using an assumption that the racial composition of the bidding pool for those jobs was the same as for the post-2001 jobs analyzed (when Nucor retained actual bidding records).
The workers also presented abundant direct and circumstantial anecdotal evidence of discrimination in promotions, including:
* Anecdotal evidence provided by the1 - seven named plaintiffs and nine other
putative class members, claiming discrimination in specific promotions decisions in the Nucor production departments;
■ * A description of complaints, contained in affidavits and depositions, made to plant General Manager Ladd Hall, who the workers allege failed to meaningfully respond;
* Descriptions of retaliation against those who complained to management;
* A written copy of Nucor’s promotions policy and testimony that the policy was largely ignored in favor of giving unbridled discretion to supervisors; and
* Testimony by a white supervisor that his department manager told him that “I don’t think we’ll ever have a black supervisor while I’m here.”
The facts undergirding the workers’ separate hostile work environment claim, not directly at issue in this appeal, also bear on the promotions analysis. Those facts are disquieting in their volume, specificity, and consistency. Supervisors allegedly routinely referred to black workers as “nigger” and “DAN (dumb ass nigger),” with one supervisor reportedly stating “niggers aren’t smart enough” to break production records, while others tolerated the routine use of epithets like “bologna, lips,” “yard ape,” and “porch monkey.” These epithets and others were broadcast over the plant-wide radio system — comprising a network of walkie-talkies used to communicate — along with monkey noises and the songs “Dixie” and “High Cotton.” The workers’ declarations and depositions further suggest that departmental supervisors and the plant’s general manager consistently ignored racial harassment carried out by white, workers, including the circulation of racist emails, the prominent display of a hangman’s noose, the commonplace showing of the Confederate flag, and an episode when a white employee draped a white sheet' over his head with eyes cut out in the form of a KKK hood.
In 2007, the South Carolina district court denied the workers’ motion for class certification for both the promotions and hostile work environment claims. In 2009, a divided panel of this Court reversed, concluding that the workers satisfied the threshold requirements of Federal Rule of Civil Procedure 23. We remanded the case “with instructions to certify the appeí- . lants’ class action.” Brown I, 576 F.3d at 160.
On February 17, 2011, the district court followed our instructions to certify the class, concluding that the workers satisfied Rule 23(b)(3)’s requirements that common questions predominate and that the class, action was superior to other litigation de*900vices to resolve the dispute. The district court later declined to stay the case pending a ruling in Wal-Mart, and it declined to reconsider its order certifying the class.
The Supreme Court decided Wal-Mart in June 2011, decertifying an unprecedented nationwide class of approximately 1.5 million female employees spread over 3,400 stores. Wal-Mart held that the plaintiffs had failed to present a “common contention” of employment discrimination capable of “classwide resolution,” as required by Rule 23(a)(2). Wal-Mart, 131 S.Ct. at 2551. Given the diffuse class and number of employment decisions at issue, the Supreme Court observed that “[without some glue holding the alleged reasons for all those decisions together, it will be impossible to say that examination of all class members’ claims for relief will produce a common answer to the crucial question why was I disfavored.” Id. at 2552 (emphasis in original). The plaintiffs, Wal-Mart concluded, failed to meet that standard when they premised liability on a company policy of decentralized subjective decision-making by local managers, combined with statistics showing gender-based employment disparities, limited anecdotal evidence, and expert testimony about a corporate culture that allowed for the transmission of bias. See id. at 2551, 2554-55.
On September 11, 2012, the district court relied on Wal-Mart to decertify the workers’ promotions class, invoking the court’s authority under Rule 23(c)(1)(C) to amend a certification order at any time before final judgment. Wal-Mart, the court observed, clarified and heightened the commonality requirement of Rule 23(a)(2), requiring the workers to present “significant proof’ that Nucor “operated under a general policy of discrimination” and that they suffered a common injury. J.A. 10934 (quoting Wal-Mart, 131 S.Ct. at 2553).
Under that standard, the district court concluded that decertification of the promotions class was required because: (1) this Court’s examination of the workers’ statistical analysis in Brown I was not sufficiently “rigorous” to assess whether it raised questions common to the class under Rule 23(a)(2); (2) the workers’ statistical and anecdotal evidence failed to establish such commonality because it did not provide “significant proof’ that there existed both a “general policy of discrimination” and a “common injury”; (3) the delegation of subjective decision-making to Nucor supervisors was not, without more, a sufficiently .uniform policy to present “ ‘common’ issues appropriate for resolution on a class-wide basis”; and (4) even if the workers had identified a common question of law or fact satisfying Rule 23(a)(2), they failed to independently satisfy Rule 23(b)(3)’s requirements that common issues predominate and that the class action is a superior litigation device.
Although the court decertified the class for the promotions claim, it refused to do so for the hostile work environment claim. The district court reaffirmed that the workers had demonstrated that the “landscape of the total work environment was hostile towards the class.” J.A. 10964 (quoting Newsome v. Up-To-Date Laundry, Inc., 219 F.R.D. 356, 362 (D.Md. 2004)). Unlike the promotions claim, the court determined that the hostile environment allegations required no showing of a company-wide adherence to a common policy of discrimination. Still, the court found that “there is significant evidence that management ignored a wide range of harassment” and that the workers “met their burden to present significant proof of a general policy of discrimination.” J.A. 10968.
*901On September 30, 2013, the workers appealed the district court’s decertification of the promotions class.
II.
We typically review a district court’s certification order for abuse of discretion. Doe v. Chao, 306 F.3d 170, 183 (4th Cir.2002), aff'd on other grounds, 540 U.S. 614, 124 S.Ct. 1204, 157 L.Ed.2d 1122 (2004). We review de novo, however, whether a district court contravenes a pri- or express or implicit mandate issued by this Court. United States v. Bell, 5 F.3d 64, 66 (4th Cir.1993); S. Atl. Ltd. P’ship of Tenn. v. Riese, 356 F.3d 576, 583 (4th Cir.2004) (‘We review de novo ... whether a post-mandate judgment of a district court contravenes the mandate rule, or whether the mandate has been ‘scrupulously and fully carried out.’ ” (quoting 2A Fed. Proc., L.Ed. § 3:1016)).
Determining the appropriate standard of review thus requires a two step approach. First, we examine de novo whether the district court’s decertification order violated our mandate in Brown I to certify the workers’ class. Second, if no such violation occurred, we must determine anew whether the district court abused its discretion in decertifying the promotions class.
As to the first question, an “extraordinary” exception to the mandate rule exists when there is “a showing] that controlling legal authority has changed dramatically.” Bell, 5 F.3d at 67 (alteration in original). Moreover, Rule 23(c)(1)(C) provides a district court with broad discretion to alter or amend a prior class certification decision at any time before final judgment.
Against that backdrop, the parties disagree about whether Wal-Mart provided sufficient justification for the district court to invoke its powers to revisit certification: Nucor maintains that Wal-Mart represents a “sea change” and that “class actions may proceed only in the most exceptional of cases.” Resp’ts’ Br. 15, 20. The workers suggest, however, that the Supreme Court instead largely reaffirmed existing precedent. Appellants’ Br. 34.
The truth has settled somewhere in between. See Scott v. Family Dollar Stores, Inc., 733 F.3d 105, 113-14 (4th Cir.2013) (discussing limitations on the scope of Wal-Mart’s holding); McReynolds v. Merrill Lynch, Pierce, Fenner & Smith, Inc., 672 F.3d 482, 487-88 (7th Cir.2012), cert. denied, — U.S.-, 133 S.Ct. 338, 184 L.Ed.2d 157 (2012) (finding that Wal-Mart provided the basis for a renewed class certification motion); DL v. District of Columbia, 713 F.3d 120„ 126 (D.C.Cir.2013) (surveying how Wal-Mart has changed the class action landscape); Elizabeth Tippett, Robbing A Barren Vault: The Implications of Dukes v. Wal-Mart for Cases Challenging Subjective Employment Practices, 29 Hofstra Lab. & Emp. L.J. 433 (2012) (using an empirical analysis to predict Wal-Mart’s likely impact on class certifications in the future). At the very least, Wal-Mart recalibrated and sharpened the lens through which a court examines class certification decisions under Rule 23(a)(2), an impact plainly manifested by the number of certifications overturned in its wake. See, e.g., EQT Prod. Co. v. Adair, 764 F.3d 347 (4th Cir.2014); Rodriguez v. Nat’l City Bank, 726 F.3d 372, 376 (3d Cir.2013); M.D. ex rel. Stukenberg v. Perry, 675 F.3d 832, 839, 841-44 (5th Cir. 2012); Ellis v. Costco Wholesale Corp., 657 F.3d 970, 974 (9th Cir.2011).
In that light, we find that the district court’s decision to reconsider the certification of the workers’ class did not itself violate our mandate in Brown I. Per this Court’s original remand instructions, the district court certified both the promotions *902and hostile work environment classes. Although the court had no discretion to then reconsider questions decided by this Court under then-existing facts and law, WalMart provided a sufficiently significant change in the governing legal standard to permit a limited reexamination of whether the class satisfied the commonality requirement. of Rule 23(a)(2).3 There are, however, instances described below when the district court unnecessarily revisited other discrete determinations made by this Court in Brown I, such as whether the Nucor plant should be treated analytically as a single entity, and whether the class independently met the requirements of Rule 23(b)(3). The reconsideration of those determinations was not compelled by Wal-Mart and contravened our mandate in Brown I.
Because the district court could reexamine whether the workers met the requirement of commonality, we review those findings under the abuse of discretion standard that typically applies to certification orders. See Amchem Prods., Inc. v. Windsor, 521 U.S. 591, 630, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997) (“The law gives broad leeway to district courts in making class certification decisions, and their judgments are to be reviewed by the court of appeals only for abuse of discretion.”); Brown I, 576 F.3d at 152; Thorn v. Jefferson-Pilot Life Ins. Co., 445 F.3d 311, 317 (4th Cir.2006). A district court abuses its discretion when • it materially misapplies the requirements of Rule 23. See Gunnells v. Healthplan Servs., Inc., 348, F.3d 417, 424 (4th Cir.2003); Thorn, 445 F.3d at 317-18 (“A district court per se abuses its discretion when it makes an error of law or clearly errs in its factual findings.”). The decisive question here is whether the district court materially misapplied Rule 23(a)(2) to the facts at hand in light of Wal-Mart.4
III.
Rule 23(a)(2) establishes that a class action may be maintained only if “there are questions of law or fact common to the class.” The district court determined that Wal-Mart required decertification of the workers’ promotions class insofar as the Supreme Court’s interpretation of the rule (1) emphasized the analytical rigor required to evaluate a plaintiffs statistical evidence of commonality at the class certification stage, (2) placed the' burden on plaintiffs to provide “significant proof’ of a “general policy of discrimination” and “common injury,” and (3) relatedly established that a company’s policy of discretionary decision-making cannot sustain class certification without a showing that supervisors exercised their discretion in a common way.
Each of these arguments is considered in turn.
*903A.
Wal-Mart reaffirmed existing precedent that courts must rigorously examine whether plaintiffs have met the prerequisites of Rule 23(a) at the certification stage, an analysis that will often overlap with the merits of a claim. Wal-Mart, 131 S.Ct. at 2551 (citing Gen. Tel. Co. of Sw. v. Falcon, 457 U.S. 147, 160-61, 102 S.Ct. 2364, 72 L.Ed.2d 740 (1982)). But as the Court later clarified, “Rule 23 grants courts no license to engage in free-ranging merits inquiries at the certification stage.” Amgen Inc. v. Conn. Ret. Plans & Trust Funds, — U.S. -, 133 S.Ct. 1184, 1194-95, 185 L.Ed.2d 308 (2013). Instead, the merits of a claim may be considered only when “relevant to determining whether the Rule 23 prerequisites for class certification are satisfied.” Id. at 1195.5
This Court’s precedent and its approach in Broum I are consistent with Wal-Mart and Falcon. See Gariety v. Grant Thornton, LLP, 368 F.3d 356, 366 (4th Cir.2004) (observing that “while an evaluation of the merits to determine the strength of the plaintiffs’ case is not part of a Rule 23 analysis, the factors spelled out in Rule 23 must be addressed through findings, even if they overlap with issues on the merits”). In Broum I, this Court expressly invoked Falcon’s requirement of a rigorous analysis to determine compliance with Rule 23. 576 F.3d at 152. More important, of course, we actually conducted such an analysis, providing a detailed evaluation of the workers’ anecdotal and statistical evidence to ensure that it presented a common question under Rule 23(a)(2). Id. at 153-56.
Contrary to the dissent’s assertion, we do not (and Broum I did not) suggest that Rule 23 is a mere pleading standard. See post at 933. Far from it. It is true that’ Broum I cautioned that “an in-depth assessment of the merits of appellants’ claim at this stage would be improper.” Id. at 156. Such a statement, however, is consistent with the Supreme Court’s dictate in Amgen that a court should engage the merits of a claim only to the extent necessary to verify that Rule 23 has been satisfied. Amgen, 133 S.Ct. at 1194-95. Broum I did precisely that.
1.
Even evaluated in a still more painstaking manner, the workers’ statistical evidence is methodologically sound while yielding results that satisfy Wal-Mart’s heightened requirement of commonality discussed below. The parties’ central dispute concerns the data used to analyze the period from December 1999 to January 2001, when Nucor failed to retain actual bidding records. For that period, the workers’ expert developed an alternative benchmark that uses 27 relevant ‘change-of-status’ forms — filled out when an em*904ployee changes positions at the plant — to extrapolate promotions data because actual bidding information was unavailable.
■ Of course, it belabors the obvious to observe that the alternative benchmark is a less precise measure than actual bidding data. It is also clear, however, that plaintiffs may rely on other reliable data sources and estimates when a company has destroyed or discarded the primary evidence in a discrimination ease. More than two decades of this Court’s precedent affirm as much. See Lewis v. Bloomsburg Mills, Inc., 773 F.2d 561 (4th Cir.1985); United States v. County of Fairfax, 629 F.2d 932, 940 (4th Cir.1980); see generally Ramona L. Paetzold & Steven L. Willborn, The Statistics of Discrimination: Using Statistical Evidence in Discrimination Cases' § 4.03 (2014) (describing the use of proxy data when actual data is unavailable or unreliable). In Lewis v. Bloomsburg Mills, Inc., this Court approved the use of Census data to establish a hypothetical available pool of black female job applicants after a company discarded employment applications for the relevant period. 773 F.2d at 568.6 Plaintiffs then compared the “observed” annual rate of hires of black women with the “expected” rates based upon the proportional availability of black females in the labor pool. Id. We endorsed a similar use of proxy data in United States v. County of Fairfax, involving a county government that had destroyed three years of employment applications. 629 F.2d at 940. To analyze hiring during that time, plaintiffs assumed that the proportion of black and women applicants for those years was the same as in the first year for which the county retained records. Id. This Court approved, concluding the alternative benchmark was “the most salient proof of the County’s labor market.” Id7
2.
The critical question is thus not whether the data used is perfect but instead whether it is reliable and probative of discrimination. To that end, a court must examine whether any statistical assumptions made in the analysis are reasonable. See Paetzold & Willborn, supra, § 4.16. The district court here identified two assumptions made by the workers’ experts as problematic. ■
The district court first questioned the assumption that the job changes described on the 27 forms represent promotions. See J.A. 10942. As an example of clear factual error committed by the court, it quoted at length from the dissent in Brown I to argue' that the forms may represent job changes unrelated to promotions. J.A. 10942 (quoting Brown I, 576 F.3d at 167-68 (Agee, J., concurring in part and dissenting in part)). The forms cited in Judge Agee’s original dissent, however, are plainly not among the 27 *905relied upon by the workers’ experts in constructing the alternative benchmark. Compare J.A. 10942 (the district court’s decertification order quoting the dissent in Brown I), with J.A. 11005-11032 (copies of the actual change-of-status forms used in the expert analysis). Worse still, the dissent in Brown I reached the question of whether the 27 forms represented promotions without the issue having been raised, much less analyzed, by the district court in its original order denying certification, see J.A. 8979, or by Nucor itself in its briefing before this Court in Brown I.8 The dissent in Brown I thus both engaged in sua sponte fact-finding to divine which forms were used, and then got the facts wrong.9 Using the flawed data, the dissent concluded in Brown I that “[o]n this record, it is difficult, if not impossible to discern whether the 2000 data based on the nebulous change-of-status forms proves those positions were promotion positions available for employee bidding and thus relevant to the formulation of statistical evidence for the appellants’ claims.” Brown I, 576 F.3d at 168 (Agee, J., concurring in part and dissenting in part). The district court expressly embraced that conclusion in decertifying the promotions class after Wal-Mart. J.A. 10942.
Upon examining the correct change-of-status forms, discerning whether they represent promotions is a relatively straightforward enterprise. Nineteen of the 27 forms expressly state they are for a promotion, for a “successful bidder” on a “higher position,” or for a new position that was “awarded” or “earned.” Two of the forms describe changes in job classification accompanied by an increase in pay. One form notes that an inspector was a “successful bidder” on a mill adjuster job — a move referred to on another change form as a promotion. Two forms are for a “successful bidder” on a new position where no new pay grade is noted. The remaining three forms appear to involve changes in positions or training that involved a decrease in pay, but there is no indication, or argument by Nucor or the district court, that the exclusion of those forms would substantially undermine the probativeness of the expert analysis.
The second assumption criticized by the district court was that the bidding pools for the 27 positions filled between December 1999 and January 2001 had the same average racial composition as the- pools for similar jobs analyzed from 2001 to December 2003, when the company retained actual bidding data. Because of discovery limitations imposed by the district court, the information available regarding the 2001-2003 promotions was restricted to positions similar to ones bid on by the named plaintiffs, where there was at least one black bidder. However, because Nucor failed to retain bidding records for 1999-2000, the data from that period could not *906be limited to positions where there was a known black bidder. Instead, the alternative benchmark had to assume that there was at least one black worker applying for each promotion analyzed — an assumption that the district court concluded helped render the statistical analysis unreliable. But as we already determined in Brown I, the assumption does not fatally undermine the probativeness of the experts’ findings. The workers’ experts limited the records they analyzed to the same positions identified in the later period when bidding data was available, positions for which there was a black bidder. J.A. 1161-62. In its original order denying certification, the district court observed that the assumptions regarding bidding “may be reasonable and the statistics based thereon may be relevant to prove discrimination at the plant,” but “the necessity of the assumptions diminishes their probative value.”10 J.A. 8987; see also Brown I, 576 F.3d at 156. As we previously concluded, an incremental reduction in probative value— which is a natural consequence of the use of proxy data^ — does not .itself render a statistical study unreliable in establishing a question of discrimination common to the class. Brown I, 576 F.3d at 156. Indeed, to conclude otherwise would undermine our prior precedent in cases like Lewis and Fairfax, rendering plaintiffs unable to bring a statistics-based employment discrimination claim after a company has intentionally or inadvertently destroyed actual applicant data.11 See Lewis, 773 F.2d at 568; Fairfax, 629 F.2d at 940.
3.
The dissent points to still more statistical assumptions — assumptions not discussed by either the district court or Nu-cor — to further question the reliability of the alternative benchmark. Specifically, the dissent suggests that the black workers may not have been qualified for higher paying jobs and that they may have been denied promotions because of disciplinary records that were not themselves the result of racial animus. See post at 940, 941-43. As to the qualifications of the workers, Nucor identifies nothing in the record — or in any factual findings by the district court — to suggest that black' workers regularly applied for jobs for which they were not qualified, such that the reliability of the study would be compromised. Indeed, the Nucor job postings explicitly listed the minimum qualifications required, and the workers’ experts reasonably assumed that individuals would normally apply only if they believe they met such qualifications. See J.A. 7763 (an example of a job posting); J.A. 1162. That is not to . say that patently unqualified workers did not apply in isolated cases. But there is no reason to believe that such incidents would have substantially reduced the reliability of the statistical conclusions. It also bears repeating that it was Nucor that failed to retain or produce records that would have allowed the experts to take other variables like qualifications more precisely into account. See J.A. 1165.
*907The dissent, however, goes a step farther in speculating that black workers may have been denied promotions because of their disciplinary records. See post at 940. Again, Nucor itself does riot make this argument. Instead, the argument the dissent constructs is based on the company’s self-serving responses to the workers’ interrogatories and requests for production — where Nucor asserts that some of the black workers were not chosen for promotions due to disciplinary issues. The record, however, does not include disciplinary records for the named plaintiffs or putative class members. More fundamental, the workers allege that any disproportionate disciplinary action levied against them was itself a product of racial discrimination, with the disciplinary records then used as a pretext in hiring decisions. As worker Ramon Roane has stated:
Discipline, attendancé, and safety allegations are similar factors that are not equally applied and that have been used as an excuse to deny promotions to me and other persons of my race. The attitudes I have experienced with white supervisors lead me to believe that my race and that of other black employees makes a difference in how we are treated and viewed for discipline]]] promotions]]] and training.
J.A. 1000; see also J.A. 1024 (Alvin Simmons’s statement that a white employee was promoted over him despite the fact that the white employee “had been disciplined less than a year earlier for ‘not paying attention’ when operating equipment”); J.A. 1111 (Earl Ravenell’s statement that black workers were disproportionately singled out for disciplinary action); J.A. 6783 (Michael Rhode’s description of discrimination in disciplinary action). See generally J.A. 10960-10972 (the district court’s factual findings regarding the existence of a racially hostile work environment); Desert Palace, Inc. v. Costa, 539 U.S. 90, 101-02, 123 S.Ct. 2148, 156 L.Ed.2d 84 (2003) (allowing the use of circumstantial evidence to show that race was a motivating factor in a “mixed-motive” case involving both legitimate and illegitimate reasons for an employment decision); Rowland v. Am. Gen. Fin., Inc., 340 F.3d 187, 193-94 (4th Cir.2003) (allowing the use of circumstantial evidence to show that gender was “a motivating factor” in a failure to promote an employee). Given that background, it is easy to see why the district court chose not to advance the arguments that the dissent makes today.
Finally, the dissent criticizes the assumption that the 27 positions identified were actually open for bidding.12 Post at 939-40. That assumption, however, derives directly from Nucor’s stated policy that every job vacancy is posted on plant bulletin boards and is open to bidding plant-wide — a policy cited by Nucor’s own expert and the district court. See J.A. 5887 (the Report of Finis Welch, observing that “[o]pen positions are posted on bulletin boards and through email,” and that “[a]ll employees in the plant are eligible to bid on a posted job”); see also Resp’ts’ Br. 9 (“Department managers set the process in motion by sending postings for available *908promotions to Personnel employees, who performed a purely clerical role and advertised postings plantwide.”); J.A. 8979 (the district court’s original order denying certification, finding that “[w]hen a position in a department becomes available, the job is posted on the plant’s e-mail system, which is accessible to all employees in the plant”). The dissent nonetheless argues that the statistical assumption was unreasonable.13 We disagree.
4.
With the alternative benchmark evidence included, the statistical disparity in promotions is statistically significant at 2.54 standard deviations from what would be expected if race were a neutral factor. See Hazelwood Sch. Dist. v. United States, 433 U.S. 299, 308 n. 14, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977) (indicating that anything greater than two or three standard deviations in racial discrimination cases is suspicious, at least for large sample sizes); Brown I, 576.F.3d at 156 n. 9 (applying the Hazelwood standard to the workers’ statistical evidence); Jones v. City of Boston, 752 F.3d 38, 46-47 (1st Cir.2014) (observing that two standard deviations has become the commonly accepted threshold for social scientists and federal courts “in analyzing statistical showings of disparate impact”). According to the experts’ analysis, black employees constitute 19.24% of those who applied for relevant promotions. Yet such employees were only 7.94% percent of those promoted.
Of course, statistical significance is not always synonymous with legal significance. EEOC v. Fed. Reserve Bank of Richmond, 698 F.2d 633, 648 (4th Cir.1983) rev’d on other grounds sub nom. Cooper v. Fed. Reserve Bank of Richmond, 467 U.S. 867, 104 S.Ct. 2794, 81 L.Ed.2d 718 (1984). Indeed, the usefulness of statistical evidence often “depends on all of the surrounding facts and circumstances.” Teamsters, 431 U.S. at 340, 97 S.Ct. 1843. Here, the surrounding circumstances and anecdotal evidence of discrimination, as described in greater detail below, are precisely what help animate the statistical findings.14 As we held in Brown I and reaffirm today, “because the appellants’ direct evidence alone was sufficient to demonstrate common claims of disparate treatment and disparate impact, their statistical data did not need to meet a two-standard-deviation threshold.” Brown I, 576 F.3d at 156-57. Thus it is plain that when the statistical disparity actually exceeded two standard deviations, the district court abused its discretion in decertifying the class.
B.
The district court further concluded that the workers’ statistical and anecdo*909tal evidence was insufficient for class certification insofar as the evidence did not demonstrate a uniform class-wide injury that spanned the entire Nucor plant. As the court observed, Wal-Mart instructs that plaintiffs must present a common contention capable of being proven or disproven in “one stroke” to satisfy Rule 23(a)(2)’s commonality requirement. WalMart, 131 S.Ct. at 2551. Thus, a class-wide proceeding must be able to generate common answers that drive the litigation. Id.; see also Jimenez v. Allstate Ins. Co., 765 F.3d 1161, 1165 (9th Cir.2014) (observing that “a class meets Rule 23(a)(2)’s commonality requirement when the common questions it has raised are apt to drive the resolution of the litigation, no matter their number” (internal quotation marks omitted)). For a claim based on discrimination in employment decisions, “[wjithout some glue holding the alleged reasons for all those decisions together, it will be impossible to say that examination of all the class members’ claims for relief will produce a common answer to the crucial question why was I disfavored.” Wal-Mart, 131 S.Ct. at 2552 (emphasis omitted); see also Scott v. Family Dollar Stores, Inc., 733 F.3d 105,113 (4th Cir.2013).
The workers here most generally present two such common contentions capable of class-wide answers under Title VII. Under a disparate treatment theory, the common contention is that Nucor engaged in a pattern or practice of unlawful discrimination against black workers in promotions decisions. See Teamsters, 431 U.S. at 336, 97 S.Ct. 1843. Under the workers’ disparate impact theory, the common contention is that a facially neutral promotions policy resulted in a disparate racial impact. See Griggs, 401 U.S. at 429-31, 91 S.Ct. 849. As Wal-Mart observed, however, semantic dexterity in crafting a common contention is not enough. Commonality instead “requires the plaintiff to demonstrate that the class members ‘have suffered the same injury[.]’ ” Wal-Mart, 131 S.Ct. at 2551 (quoting Falcon, 457 U.S. at 157, 102 S.Ct. 2364). As such, a court must examine whether differences between class members impede the discovery of common answers. Id. at 2551.
In the absence of a common job evaluation procedure, Wal-Mart held that statistical proof of employment discrimination at the regional and national level, coupled with limited anecdotal evidence from some states, was insufficient to show that the company maintained a “general policy of discrimination” present in each store where class members worked. See WalMart, 131 S.Ct. at 2553. Similarly, the district court here found that the workers’ statistical and anecdotal evidence was insufficient to show a general policy in all Nucor departments that caused the class injury.
The district court, however, failed to adequately appreciate three significant differences ' from Wal-Mart that make the case largely inapposite to the facts at hand.
1.
First, Wal-Mart discounted the plaintiffs’ statistical evidence in large part because the statistics failed to show discrimination on a store-by-store basis. See WalMart, 131 S.Ct. at 2555. As such, the plaintiffs could not establish that a store greeter in Northern California, for instance, was subject to the same discrimination as a cashier in New Hampshire. These dissimilarities between class members were exacerbated by the sheer size of the Wal-Mart class — 1.5 million members working at 3,400 stores under “a kaleidoscope of supervisors (male and female), subject to a variety of regional policies *910that all differed.” Id. at 2557 (quoting Dukes v. Wal-Mart Stores, Inc., 603 F.3d 571, 652 (9th Cir.2010) (Kozinski, J., dissenting)). The scale and scope of the putative class, combined with the nature of the evidence offered, was thus essential to Wal-Mart’s holding. Had the class been limited to a single Wal-Mart store spanning multiple departments, or had the plaintiffs’ evidence captured discrimination at a store level, a very different Rule 23(a)(2) analysis would have been required.
In contrast to Wal-Mart, this litigation concerns approximately 100 class members in a single steel plant in Huger, South Carolina. The class members shared common spaces, were in regular physical contact with other departments, could apply for promotions in other departments, and were subject to hostile plant-wide policies and practices. See Brown I, 576 F.3d at 151. Such differences are not merely superficial. Instead, a more centralized, eir-. cumscribed environment generally increases the uniformity of shared injuries, the consistency with which managerial discretion is exercised, and the likelihood that one manager’s promotions decisions will impact employees in other departments. That is particularly the case where, as discussed further below, the entire Nucor plant was allegedly infected by express racial bias and stereotypes — a culture that management took few affirmative steps to meaningfully combat.
Nonetheless, the district court analogized to Wal-Mart in finding that the workers’ evidence of discrimination was insufficient because it disproportionately concerned a single department — the Beam Mill — and because there was an insufficient showing that all departments operated under a common policy of discrimination. J.A. 10949-54. As such, a class-wide proceeding would not generate “common answers” as Wal-Mart required, the district court found. See Wal-Mart, 131 S.Ct. at 2551.
The district court, however, inappropriately discounted, and often ignored, evidence that establishes discrimination in other Nucor departments. Although 11 of the 16 employees submitting declarations on behalf of the plaintiffs worked in the Beam Mill, the declarants describe frequent instances of alleged promotions discrimination in other departments. See J.A. 1021-24; 1032-35; 1049-51; 1055-56; 1061-63; 1085-86; 1091-92; 1103; 1110-11; 1118-19. Even the additional affidavits obtained by Nucor, discussed in further detail below, present numerous allegations of discrimination in non-Beam Mill departments. See J.A. 5992-95 (discrimination in the Hot Mill and Melt Shop); 6143-45 (discrimination in the Hot Mill); 6174 (general observations of promotions discrimination); 6369-70 (discrimination in the Melt Shop); 6505-07 (discrimination in the Hot Mill); 7036 (discrimination in the Melt Shop). The record additionally indicates numerous complaints of discrimination made to the plant’s general manager, who allegedly did little to nothing in response. Such alleged tolerance of discrimination from top management at the plant supports the workers’ contention of a class-wide injury that affected them all.15
*911The district court made a still more fundamental error by choosing to treat the Nucor departments as autonomous operations in the first place instead of part of a single facility, - contravening both this Court’s instructions in Brown I and the district court’s own prior findings. The district court’s original order to certify the class recognized that a department-by-department approach had been foreclosed, writing:
Since the Fourth Circuit rejected this Court’s characterization of the production departments as separate environments, the Court must proceed under the assumption that the production departments were permeable, if not unitary. This assumption is buttressed by the fact that Nucor’s bidding is plant-wide, and this Court already has held that “potential applicants are eligible to prove they would have applied for a promotion but for the discriminatory practice.”
J.A. 9705. Walr-Mart provided no grounds for the court to reconsider that finding because nothing in the Supreme Court’s opinion suggests that single, localized operations must be analytically dissected into component departments.16 Here, all of the workers’ evidence concerns a single connected facility.
Even if not required by our prior ruling, treating the plant as a single entity remains sound. In addition to the direct and circumstantial evidence of discrimination in promotions decisions in multiple departments, racial bias in one Nucor plant department itself diminished the promotional opportunities for black workers in all the departments — including those who wanted promotions into the infected department and those who sought promotions to other departments and needed their supervisors’ recommendations. To that end, the workers cogently observe that requirements for dual approvals for promotions — by originating and ■ destination department heads — “carried] the effects of racial discrimination from one department and supervisor to another, either by systemic tolerance, acquiescence or design.” Appellants’ Reply Br. 24 (citing Smith v. Bray, 681 F.3d 888, 897 & n. 3 (7th Cir.2012)).
Such a conclusion is further strengthened by the workers’ hostile work environment claim. As the district court itself found, “the plaintiffs have submitted significant proof that the landscape of the total work environment at the Berkeley plant was hostile towards African-Americans and that the defendants failed to take ‘remedial action reasonably calculated to end the harassment.’ ” J.A. 10966; see also Brown I, 576 F.3d at 157-58. That environment, the workers argue, supports their showing of an atmosphere of systemic tolerance of racial hostility by managers and supervisors, forming part of the overall pattern or practice that “infected black *912employees’ promotion opportunities.” We agree.
2.
Second, the Wal-Mart plaintiffs’ theory of commonality relied, in part, on showing that the company maintained a corporate culture that facilitated the uniform transmission of implicit, or subconscious, bias into the hiring process. See Wal-Mart, 131 S.Ct. at 2548. To that end, the plaintiffs’ expert testified the company was “vulnerable” to “gender bias.” Id. at 2553. The Court, however, concluded that the expert could not with specificity determine how the culture concretely influenced individual employment decisions. Id. at 2553-54. The testimony was therefore insufficient to show a common policy that produced a common injury.
Here, however, the workers have provided substantial evidence of unadulterated, consciously articulated, odious racism throughout the Nucor plant, including affirmative actions by supervisors and a widespread attitude of permissiveness of racial hostility. The examples in the record are ubiquitous: bigoted epithets and monkey noises broadcast across the plant radio system, emails with highly offensive images sent to black workers, a hangman’s noose prominently displayed, a white supervisor stating that “niggers aren’t smart enough” to break production records, and abundant racist graffiti in locker rooms and shared spaces. Moreover, no more than one black supervisor worked in the Nucor production departments until after the EEOC charge that preceded this litigation. It strains the intellect to posit an equitable promotions system set against that cultural backdrop, particularly in light of the other evidence presented.
The dissent rejects the idea that evidence of a racially hostile work environment may help establish a claim for disparate treatment in promotions decisions.17 Post at 945-46. Indeed, the dissent goes so far as to observe that “locker rooms and radios bear no relationship to promotions decisions.” Id. at 946. Such a perspective, however, is perplexingly divorced from reality and the history of workplace discrimination. It is difficult to fathom how widespread racial animus of the type alleged here, an animus that consistently emphasized the inferiority of black workers, bears no relationship to decisions whether or not to promote an employee of that race. Although the dissent asserts that “nothing in the record supports” making a connection between the work environment and promotions practices, we are not limited to the record in making such elementary judgments. Justice is not blind to history, and we need not avert our eyes from the broader circumstances surrounding employment decisions, and the inferences that naturally follow.
3.
Third, and related, the anecdotal evidence of discrimination in this case is substantially more probative than that in Wal-Mart. The Wal-Mart plaintiffs presented affidavits from about 120 female employees, representing approximately one affidavit for every 12,500 class members. Wal-Mart, 131 S.Ct. at 2556. The affidavits captured only 235 of Wal-Mart’s 3,400 stores, and there were no affidavits *913from workers in 14 states. Id. The evidence thus fell far short of the benchmark for a showing of company-wide discrimination established by Teamsters, 431 U.S. 324, 97 S.Ct. 1843. In Teamsters, the plaintiffs produced statistical evidence of racial bias combined with approximately 40 accounts of discrimination from particular individuals. Id. at 338, 97 S.Ct. 1843. Given the class size of approximately 334 persons, there was roughly one anecdote for every eight members of the class. See id. .at 331, 338, 97 S.Ct. 1843; Wal-Mart, 131 S.Ct. at 2556. “[T]he anecdotes came from individuals spread throughout the company who for the most part worked at the company’s operational centers that employed the largest numbers of the class members.” See Wal-Mart, 131 S.Ct. at 2556 (internal quotation marks omitted). Similarly, this litigation includes anecdotal evidence from more than 16 individuals18 in a class that numbered approximately one-hundred “past and present black employees at the plant” at the time litigation commenced — an approximate ratio of one anecdote for every 6.25 class members.19 See Brown I, 576 F.3d at 151 (describing the class size).
Balanced against such evidence, the district court gave “limited weight” to approximately 80 affidavits from Nucor employees largely disclaiming discrimination at the plant — affidavits taken by company lawyers after the EEOC charges had been filed. See J.A. 10950-51. Common sense and prudence, however, instruct that the affidavits do little to rebut the evidence of discrimination insofar as they were given under potentially coercive circumstances, where the company reserved its ability to
*914use them against other employees in any future lawsuit (a fact that was omitted from the Statement of Participation given to affiants). See J.A. 6003 (the Statement of Participation), 9379 (Nucor’s statement that it intended “to use the affidavits for every purpose permitted under the Federal Rules of Evidence,” including the opposition to class certification and the impeachment of witnesses); see also Kleiner v. First Nat’l Bank of Atlanta, 751 F.2d 1193, 1202 (11th Cir.1985) (observing that after a class action has been filed, “[a] unilateral communications scheme ... is rife with potential for coercion”); Quezada v. Schneider Logistics Transloading & Distrib., No. CV 12-2188 CAS, 2013 WL 1296761, at *5 (C.D.Cal. Mar. 25, 2013) (finding in a class action context that “[flailing to inform the employees of the evidence-gathering purpose of the interviews rendered the communications fundamentally misleading and deceptive because the employees were unaware that the interview was taking place in an adversarial context, and that the employees’ statements could be used to limit their right to relief’); Longcrier v. HL-A Co., 595 F.Supp.2d 1218, 1228 (S.D.Ala.2008); Mevorah v. Wells Fargo Home Mort., Inc., No. C 05-1175 MHP, 2005 WL 4813532, at *4 (N.D.Cal. Nov. 17, 2005). Of course, companies may investigate allegations of discrimination and take statements from employees. But when it comes to assessing the probative value of those statements- — when weighed against the numerous declarations of employees who took the often grave risk of accusing an employer of a workplace violation — courts should proceed with eyes open to the imbalance of power and competing interests.20 Moreover,. as previously observed, the company-obtained affidavits still contain numerous allegations of discrimination in promotions decisions — allegations that carry significant weight given the circumstances in which they were made. See J.A. 5992-95, 6143-46, 6174, 6370, 6506, 7036.
Of course, a plaintiff need not “offer evidence that each person for whom it will ultimately seek relief was a victim of the employer’s discriminatory policy.” Teamsters, 431 U.S. at' 360, 97 S.Ct. 1843; see also EEOC v. Korn Indus., Inc., 662 F.2d 256, 260 (4th Cir.1981). Instead, a bifurcated class action proceeding allows for a “liability” stage to first determine whether an employer engaged in a pattern or practice of discriminatory conduct. Teamsters, 431 U.S. at 360, 97 S.Ct. 1843; Korn, 662 F.2d at 260. Upon a finding of liability, a second damages stage allows for the consideration of which individuals were specifically harmed by the policy. Teamsters, 431 U.S. at 361, 97 S.Ct. 1843; Korn, 662 F.2d at 260.
4.
Here, for a liability determination in a disparate treatment claim, the workers’ statistical and anecdotal evidence, especially when combined, thus provide precisely the ‘glue’ of commonality that Wal-Mart demands. See Brown I, 576 F.3d at 156. Such a claim requires proof of a “system-wide pattern or practice” of discrimination such that the discrimination is “the regular rather than the unusual practice.” Teamsters, 431 U.S. at 336, 97 S.Ct. 1843; Cooper, 467 U.S. at 875-76, 104 S.Ct. 2794; see also Wal-Mart, 131 S.Ct. at 2552 n. 7. The required discriminatory intent may be inferred upon such a showing. See Teamsters, 431 U.S. at 339-40, 97 S.Ct. 1843; *915Hazelwood, 433 U.S. at 308-09, 97 S.Ct. 2736 (observing that “[w]here gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof of a pattern or practice of discrimination”).
Whereas there may have been many answers in Wal-Mart to the question of why any individual employee was disfavored, the workers here have sufficiently alleged that there is only one answer to the question of why Nucor’s black workers were consistently disfavored.21 Unlike a disparate impact claim, a showing of disparate treatment does not require the identification of a specific employment policy responsible for the discrimination. See Teamsters, 431 U.S. at 336 n. 16, 97 S.Ct. 1843 (discussing the legislative history of Title VII and concluding that the words “pattern or practice” should be interpreted according to their plain meaning). A pattern of discrimination, revealed through statistics and anecdotal evidence, can alone support a disparate treatment claim, even where the pattern is the result of discretionary decision-making.
To hold otherwise would dramatically undermine Title VII’s prophylactic powers. As the Supreme Court observed in Griggs, a central purpose of Title VII is “to achieve equality of employment opportunities and remove barriers that have operated in the past to favor an identifiable group of white employees over other employees.” 401 U.S. at 429-30, 91 S.Ct. 849; see also Albemarle Paper Co. v. Moody, 422 U.S. 405, 417-18, 95 S.Ct. 2362, 45 L.Ed.2d 280 (1975) (stressing Title VII’s prophylactic goals in addition to its purpose “to make person’s whole for injuries suffered on account of unlawful employment discrimination”). Here, where substantial evidence suggests a pattern of engrained discriminatory decision-making that consistently disadvantaged black workers at Nucor, to deny class certification would significantly weaken Title VII as a bulwark against discrimination.
C.
Statistics and anecdotes suggesting a pattern of discrimination, however, are not enough alone to sustain a disparate impact claim. See Wal-Mart, 131 S.Ct. at 2555; Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 994, 108 S.Ct. 2777, 101 L.Ed.2d 827 (1988). Disparate impact liability requires the identification of a specific employment practice that caused racially disparate results. See 42 U.S.C. § 2000e-2(k); Watson, 487 U.S. at 986-87, 108 S.Ct. 2777; Griggs, 401 U.S. at 431, 91 S.Ct. 849. Unlike disparate treatment, the disparate impact theory does not require proof of improper intent to sustain a Title VII violation. Teamsters, 431 U.S. at 349, 97 S.Ct. 1843; Griggs, 401 U.S. at 429-31, 91 S.Ct. 849 (finding the use of standardized tests resulted in a disparate impact). Instead, liability is premised on facially neutral policies. Griggs, 401 U.S. at 431, 91 S.Ct. 849.
Under Wal-Mart, a mere showing that a “policy of discretion has produced an overall ... disparity does not suffice.” Wal-Mart, 131 S.Ct. at 2556. Instead, plaintiffs who allege such a policy of discretion must demonstrate that a “common mode of exercising discretion” actually existed throughout a company. Id. at 2554; see also Tabor v. Hilti, Inc., 703 F.3d 1206, 1229 (10th Cir.2013) (observing that “after Wal-Mart, federal courts ... have generally denied certification when allegedly dis*916criminatory policies are highly discretionary and the plaintiffs do not point to a common mode of exercising discretion that pervades the entire company” (internal quotation marks omitted)). Given that standard, the district court here found that the workers “failed to identify any factor that unites the manner in which the various decision makers throughout the Berkeley plant exercised their discretion.” J.A. 10955.
Wal-Mart recognizes that in certain cases, “giving discretion to lower-level supervisors can be the basis of Title VII liability under a disparate-impact theory,” 131 S.Ct. at 2554, because “an employer’s undisciplined system of subjective decisionmaking [can have] precisely the same effects as a system pervaded by impermissible intentional discrimination.” Id. (alteration in original) (quoting Watson, 487 U.S. at 990,108 S.Ct. 2777). For a nationwide class, Wal-Mart found that proving a consistent exercise of discretion will be difficult, if not impossible in some circumstances. Id.; see also Davis v. Cintas Corp., 717 F.3d 476, 488 (6th Cir.2013) (noting the difficulties Wal-Mart presents for parties seeking to certify a nationwide class).
But for a localized, circumscribed class of workers at a single facility, a policy of subjective, discretionary decision-making can more easily form the basis of Title VII liability, particularly when paired with a clear showing of pervasive racial hostility. In such cases, the underlying animus may help establish a consistently discriminatory exercise of discretion.
This Court’s recent opinion in Scott v. Family Dollar Stores, Inc. specifically provides several ways that such a disparate impact claim may satisfy Rule 23 after Wal-Mart, including: (1) when the exercise of discretion is “tied to a specific employment practice” that “affected the class in a uniform manner”; (2) when there is “also an allegation of a company-wide policy of discrimination” that affected employment decisions; and (3) “when high-level personnel exercise” the discretion at issue. Scott, 733 F.3d at 113-14.
The first and second of Scott’s alternatives are most relevant to this case. A specific employment practice or policy can comprise affirmative acts or inaction. Cf. Ellison v. Brady, 924 F.2d 872, 881 (9th Cir.1991) (explaining an employer’s responsibility to act to rectify a hostile or offensive work environment under Title VII). Regarding affirmative acts, the district court has established that Nucor’s promotions practice provides that “Employees in each of the production departments may bid on positions available in other departments,” and that in order to promote one of the bidders, “the supervisor, the department manager, and the general manager must approve a written change of status and then submit the change of status form to the personnel office.” J.A. 477-78.
For purposes of class certification, the workers have provided sufficient evidence that such a policy, paired with the exercise of discretion by supervisors acting within it, created or exacerbated racially disparate results. The promotions system, requiring approvals from different levels of management, created an environment in which the discriminatory exercise of discretion by one department head harmed the promotions opportunities for all black workers at the plant by foreclosing on opportunities in that department and generally impeding upward mobility. Moreover, the disproportionate promotions of white workers had to be ratified by the general manager, Ladd Hall, who was thus on notice, or should have been on notice, that there were pronounced racial disparities in department-level promotion prac*917tices, as indicated by the statistical and anecdotal evidence presented.
The workers have also presented sufficient evidence of a practice of inaction by the general manager who ignored the evidence of, and complaints regarding, discrimination in promotions at the plant. See, e.g., J.A. 996-97, 1016, 1056, 1087, 1104. Such managerial inaction occurred despite Nucor’s status as an “Equal Opportunity Employer” and its claim to have a “plantwide policy barring racial discrimination.” Resp’ts’ Br. 6. One black worker, Ray Roane, has testified that he complained directly to Hall about discrimination in promotions. J.A. 996-97. Hall threatened his job. J.A. 997. Consistent with that evidence, the workers observe in the context of their hostile work environment claim that despite a policy of investigating complaints of racial harassment, “[n]ot even one of the five department managers has been shown to have lifted a finger to redress the racially hostile work environment found to exist both plant-wide and in each department.” Appellants’ Br. 25. The workers have sufficiently alleged that such a uniform policy of managerial inaction also contributed to racial disparities in promotions decisions.
Consistent with Scott, the workers have further demonstrated that the exercise of discretion at Nucor was joined by “a company-wide policy of discrimination” that was encouraged, or at least tolerated, by supervisors and managers. See Scott, 733 F.3d at 114. In addition to the evidence of a hostile work environment previously described in detail, one white supervisor has expressly stated in a deposition that he heard the head of the Beam Mill declare, “I don’t think we’ll ever have a black supervisor while I’m here.” J.A. 1885-86. Such facts provide a critical nexus between the racial animus at the plant and promotions decisions that impacted all black workers by foreclosing opportunities for them. Or, using Wal-Mart’s language, the evidence of pervasive racial hostility in the working environment provides a “common mode of exercising discretion that pervadefd] the entire company.” WalMart, 131 S.Ct. at 2554-55.
In the end, Wal-Mart simply “found it unlikely” that thousands of managers across different regions “would exercise their discretion in a common way without some common direction.” Tabor, 703 F.3d at 1222. Here, however, the workers have provided ample evidence supporting their allegation of a common, racially-biased exercise of discretion throughout the plant— demonstrated through alleged incidents of specific discrimination in promotions decisions, statistical disparities, and facts suggesting pervasive plant-wide racism. The district court abused its discretion in finding that such evidence was insufficient to meet the burden that Wal-Mart imposes.
IV.
Nucor further argues that the workers have failed to contest the district court’s independent finding that the putative class failed to satisfy Rule 23(b)(3). As the company observes, the district court specifically held that the class failed to meet the rule’s requirements for a class action seeking individualized money damages, namely, that common questions predominate over individualized inquiries and that the class action is “superior to other available methods for fairly and efficiently adjudicating the controversy.” Fed.R.Civ.P. 23(b)(3). The court remarked that “even if the Fourth Circuit subsequently concludes that the plaintiffs have identified a common issue that satisfies Rule 23(a)(2), this Court nonetheless finds that ‘common issues,’ as that term is defined by WalMart, do not predominate over individual *918issues with regárd to the plaintiffs’ promotions claims.”22 J.A. 10956.
Nucor contends that nowhere in the workers’ opening brief is the Rule 23(b)(3) ruling addressed, and that any challenge to derives from the Federal Rules of Appellate Procedure, which require that the argument section of an appellant’s opening brief contain the “appellant’s contentions and the reasons for them, with citations to the authorities and parts of the record on which the appellant relies.” Fed. R.App. P. 28(a)(8)(A); see also Mayfield v. Nat’l Ass’n for Stock Car Auto Racing, Inc., 674 F.3d 369, 376-77 (4th Cir.2012). “Failure of a party in its opening brief to challenge an alternate ground for a district court’s ruling ... waives that challenge.” United States ex rel. Ubl v. IIF Data Solutions, 650 F.3d 445, 456 (4th Cir.2011) (quoting Rodriguez v. Hayes, 591 F.3d 1105, 1118 n. 6 (9th Cir.2010)).
The workers contend first, and we agree, that no waiver occurred because their arguments in the opening brief extended to the district court’s discussion of both predominance and commonality. The single issue identified by the workers on appeal did not differentiate between the court’s findings on either question. The issue, as presented, was this:
Was it error or an abuse of discretion for the district court not to follow this Circuit’s mandate holding that sufficient statistical and non-statistical evidence has been presented to certify a pattern- or-practiee and disparate impact class covering all six production departments of the defendants’ manufacturing plant in Huger, South Carolina?
Consistent with that framing, the workers’ opening brief describes the district court’s decision in equally broad terms without distinguishing between commonality and predominance. See Appellants’ Br. 28-29 (“The district court erred as a matter of law by declining to follow this Court’s mandate that held there is sufficient statistical and non-statistical evidence to certify a class covering all six production departments.”); Appellants’ Br. 3 (citing to the portion of the district court opinion where predominance is discussed).
Although more explicit separation of the predominance and commonality inquiries would no doubt have been wise, the workers’ arguments throughout their brief directly respond to the issues the district court raised in both contexts (issues that, as discussed below, were intertwined by the court). The workers, for instance, specifically cite cases discussing predominance when arguing about the extent to which a court may look to merits in deciding certification. See Appellants’ Br. 34-35. Elsewhere, in discussing the sufficiency of the anecdotal evidence presented, the workers argued in favor of our holding in Brown I that “[t]his evidence alone establishes common claims of discrimination worthy of class certification.” Appellants’ Br. 42 (citing Brown I, 576 F.3d at 153). Certification of the workers’ class required a finding that Rule 23(b) was satisfied, in addition to a finding of commonality under Rule 23(a)(2). More generally, without limiting its analysis to the question of commonality, the workers’ opening brief ob*919serves that “[t]he district court’s finding that there is no pattern-or-practice evidence in the non-Beam Mill departments is directly contrary to the evidence and [the Fourth Circuit’s] mandate.” Appellants’ Br. 42-43.
It is true that the workers arguments often focus expressly on the question of commonality, as Wal-Mart focused its analysis. In that regard, however, the workers have merely followed the district court’s lead insofar as the court itself raised the same arguments under Rule 23(b)(3) as it did regarding commonality under Rule 23(a)(2).23 See J.A. 10958-59; see also United States v. Goforth, 465 F.3d 730, 737 (6th Cir.2006) (observing that “where an argument advanced in an appellant’s opening brief applies to and essentially subsumes an alternative basis for affirmance not separately argued therein, the appellant does not waive that alternative basis for affirmance”). The district court based its conclusion that common issues did not predominate on the observation that because the workers’ evidence disproportionately concerns the Beam Mill, “there is no ‘glue’ connecting the promotions decisions in the Beam Mill to the decisions in the other departments.” J.A. 10959. That is exactly the same argument raised, and responded to by the workers, in the context of Rule 23(a)(2) commonality. See J.A. 10950-54; Appellants’ Br. 42-47. Elsewhere in its Rule 23(b)(3) discussion, the court observes that “[although there are, to varying degrees, a few allegations of discrimination in promotions in departments other than the Beam Mill, there is nothing to link these allegations to the pattern of behavior alleged in the Beam Mill.” J.A. 10959. Again, this argument is also made in the Rule 23(a)(2) context and responded to in detail by the workers there. Indeed, the district court itself acknowledged that it “employ[ed] the language of Wal-Mart” regarding Rule 23(a)(2) in discussing the requirements of Rule 23(b)(3). J.A. 10958-59. In responding directly to the reasons given by the district court for its predominance determination, the workers have thus done far more than take a mere “passing shot at the issue.” See Belk, Inc. v. Meyer Corp., 679 F.3d 146, 152 n. 4 (4th Cir.2012) (finding that an issue was waived after a party mentioned the issue in a heading but failed to further develop the argument); see also Williams v. Woodford, 384 F.3d 567, 587 n. 5 (9th Cir.2004) (concluding that an appellant preserved a claim for review even though the argument consisted of “eight sentences in a footnote,” where the argument identified the basis of disagreement with the district court, the requested relief, and relevant citations to case law and the record).
Nonetheless, the dissent argues that “many different reasons underlay [the district court’s] predominance finding, including several individual questions that could ‘overwhelm’ common ones.” Post at 924. But a plain reading of the district court’s opinion belies the idea that it made any predominance arguments that were not responded to by the workers. The only specific argument cited by the dissent as unaddressed contends that because of the workers’ reliance on anecdotal evidence, a jury “would have to delve into the merits of each individual promotion decision.” J.A. 10959; post at 924. Yet, as observed above, the workers specifically argued that the anecdotal evidence establishes “common claims of discrimination” that merit certification, not merely a finding of corn*920monality. Appellants’ Br. 42 (quoting Brown I, 576 F.3d at 153). Indeed, such an argument is consistent with the workers’ fundamental contention throughout their brief that plant-wide discrimination existed.
As this Court has observed, the purpose of the waiver doctrine is to avoid unfairness to an appellee and minimize the “risk of an improvident or ill-advised opinion being issued on an unbriefed issue.” United States v. Leeson, 453 F.3d 631, 638 n. 4 (4th Cir.2006) (citing McBride v. Merrell Dow & Pharm., Inc., 800 F.2d 1208, 1211 (D.C.Cir.1986)). Given the briefing presented, the fully developed record below, and the lack of any showing of unfairness or prejudice, there is simply no reason why we should exercise our discretion to discard years of litigation on appeal because of an inartful opening brief. See A Helping Hand, LLC v. Baltimore Cnty., Md., 515 F.3d 356, 369 (4th Cir.2008) (observing that even when an argument has been waived, this Court may nonetheless consider it if a “miscarriage of justice would otherwise result” (internal quotation marks omitted)); cf. In re Am. W. Airlines, Inc., 217 F.3d 1161, 1165 (9th Cir. 2000) (observing that a court may refuse to find waiver and consider an argument raised for the first time on appeal when the issue “is one of law and either does not depend on the factual record, or the record has been fully developed”).
Independent of the adequacy of the workers’ opening brief, the district court had no grounds to revisit the question of predominance in the first place given this Court’s remand instructions and mandate in Brown I. Unlike the requirement of commonality under Rule 23(a)(2) discussed above, Wal-Mart did not change, nor purport to change, the Rule 23(b)(3) analysis. Indeed, any impact of the Supreme Court’s ruling on the question of whether common questions predominate is only incidental insofar as WalMart recalibrated what constitutes a common question in the first place. The majority in Walr-Mart only invoked Rule 23(b)(3) to argue that the rule’s well-established procedural protections should apply to the plaintiffs’ claims for backpay. See Wal-Mart, 131 S.Ct. at 2559.
Following our instructions in Brown I for the district court to “certify the appellants’ class' action,” the court found that “the putative class satisfied both the predominance and superiority requirements of Rule 23(b)(3).” J.A. 10930. The court then certified the class for those employed in all six Nucor operations departments. The district court cites no new facts or legal precedent after Brown I to justify revisiting that determination once the underlying question of commonality has been resolved.
Nonetheless, the dissent insists that our decision in Brown I “did not prevent the district court in any way from considering predominance because our prior decision did not say anything about predominance.” Post at 926 (emphasis added). Such a conclusion misconstrues both the plain language of our original mandate and ignores the district court’s equally plain understanding of it. The pivotal question in determining the scope of the mandate is whether the district court was free on remand to find that the workers had not satisfied the predominance requirement. If so, then our mandate did not reach the issue and the district court was free to reconsider it. But if the court did not have such liberty, then we must ask whether “controlling legal authority has changed dramatically” regarding Rule 23(b)(3) such that the court could reconsider the question. See Bell, 5 F.3d at 67. If no such change has occurred, then the district court could not revisit it.
*921As for the first question, the district court had no discretion to find that the workers’ class failed to satisfy Rule 23(b)(3), after we expressly told it “to certify the appellants’ class action and to engage in further proceedings consistent with this opinion.” Brown 1, 576 F.3d at 160; see also Bell, 5 F.3d at 66 (requiring that a district court “implement both the letter and spirit of the ... mandate, taking into account [our] opinion and the circumstances it embraces” (internal quotation marks and citation omitted)); United States v. Pileggi, 703 F.3d 675, 679 (4th Cir.2013) (observing that the mandate rule “forecloses relitigation of issues expressly or impliedly decided by the appellate court” (quoting Bell, 5 F.3d at 66)); S. Atl. Ltd., 356 F.3d at 583 (observing that a mandate must be “scrupulously and fully carried out” (internal quotation marks and citation omittéd)).
Indeed, the district court itself recognized that we had “dictate[d] the general outcome to be reached (class certification) while leaving [the district court] to fill in the details.” J.A. 9886 (Order Den. Mot. for Recons. 8 n.2). Of course, the court could have, and did, evaluate whether certification was best under Rule 23(b)(2) or (b)(3). But it had no discretion to then find that the prerequisites of either rule were not met. As the court observed, Nucor’s argument on remand that the workers had failed to satisfy Rule 23(b) “overlook[ed] the Fourth Circuit’s prior holding in this ease.” J.A. 9704 (Certification Order).24 Thus, the dissent misstates the record when it maintains that our original decision did not “in any way” prevent the district court from considering predominance. Post at 926-27. Indeed, following our instructions and findings in Brown I, the court proceeded to make the only finding it could under Rule 23(b)(3), namely, that “common issues predominate and that a class action is superior to any other method for adjudication of the claims in this case.” The dissent is thus also misinformed when it states we are now certifying. “a Rule 23(b)(3) class action without any court ever finding that the Rule 23(b)(3) requirements are satisfied.” Post at'927.
Given the fact that our prior ruling foreclosed the denial of certification on the basis of Rule 23(b)(3), the district court needed some compelling reason to reconsider the question. Bell, 5 F.3d at 67 (describing the “extraordinary” exception to the mandate rule when there is “a showing] that controlling legal authority has changed dramatically”). But the court cited no such reason and, unlike the question of commonality, Wal-Mart provided none. Indeed, as the district court itself acknowledged, Wal-Mart only incidentally narrowed an inquiry into whether common questions predominate by clarifying what constitutes a common question in the first place under Rule 23(a)(2). J.A. 10971-72.
V.
More than seven years have now elapsed since the workers first filed their class certification motion, and the district court twice has refused to certify the class. The nature of the allegations, the evidentiary support buttressing them, and the inherent cohesiveness of the class all demonstrate that the court’s failure to certify was an error. Rule 23 provides wide discretion to district courts, in part, to promote the *922systemic class action virtues of efficiency and flexibility. The realization of such benefits, however, requires that a district court exercise its judgment in a reasoned and expeditious manner.
The dissent rightly observes that the majority presses forward “[o]n the road to its desired result.” Post at 956. And that result is simple justice. At bottom, the workers seek nothing more than the chance to speak with one voice about the promotions discrimination they allegedly suffered as one class on account of one uniting feature: the color of their skin. The dissent would deny them that chance while leading this Court down a different road — a road that would further weaken the class action as a tool to realize Title VII’s core promise of equality.
We vacate the district court’s decertification of the workers’ promotions class and remand the ease to the district court with instructions to certify the class.
VACATED IN PART, AND REMANDED WITH INSTRUCTIONS.
. .The district court refused to decertify the workers' ’ hostile work environment claim. We have previously denied as untimely Nu-cor's petition for interlocutory review of that decision. Nucor Corp. v. Brown, 760 F.3d 341, 342 (4th Cir.2014).
. By comparison, more than 38% of the available local labor market is black, according to Census data provided by the workers’ experts.
. Furthermore, this Court’s original mandate did not entirely divest the district court of its ongoing authority under Rule 23(c)(1)(C) to monitor the class and make changes when appropriate. See Prado-Steiman v. Bush, 221 F.3d 1266, 1273 (11th Cir.2000) ("Class certification orders ... are not final judgments impervious to lower court review and revision.”); Gene & Gene, L.L.C. v. BioPay, L.L.C., 624 F.3d 698, 702-03 (5th Cir.2010).
. The dissent is skeptical that an appellate court can articulate a deferential standard of review while then finding reversible error in many of the factual and legal determinations made by a district court. See post at 930. Deference, however, clearly does not excuse us from conducting a detailed review of the record. Nor does it blind us from factual findings that were not supported and legal determinations that represent a fundamental misunderstanding of Wal-Mart’'s scope. Indeed, we recently applied similar scrutiny when overturning a district court's class certification order. See EQT Production, 764 F.3d at 357-58.
. The Wal-Mart majority confronted a split among courts regarding the depth of review necessary to sustain class certification under Rule 23. See Dukes v. Wal-Mart Stores, Inc., 603 F.3d 571, 582-84 (9th Cir.2010),' rev’d, - U.S. -, 131 S.Ct. 2541, 180 L.Ed.2d 374 (2011) (describing the split between circuits); Wal-Mart, 131 S.Ct. at 2551-52. On one end of the spectrum, a number of courts liberally construed the Supreme Court’s language in Eisen v. Carlisle & Jacquelin, 417 U.S. 156, 94 S.Ct. 2140, 40 L.Ed.2d 732 (1974), stating that "nothing in either the language or history of Rule 23 ... gives a court any authority to conduct a preliminary inquiry into the merits of a suit in order to determine whether it may be maintained as a class action.” 417 U.S. at 177, 94 S.Ct. 2140. On the other end, many courts, including this Circuit, heeded the Supreme Court's later call for a "rigorous analysis,” as announced in Falcon. See 457 U.S. at 160, 102 S.Ct. 2364. As Falcon held, "sometimes it may be necessary for the court to probe behind the pleadings before coming to rest on the certification question.” Id.
. In Lewis, the company had “improperly disposed" of the relevant employment applications, unlike the present case where there is no direct evidence of any impropriety. 773 F.2d at 768. That fact, however, does not affect our analysis of the workers' alternative benchmark.
. The dissent cites Allen v. Prince George's County, 737 F.2d 1299, 1306 (4th Cir.1984), to support its argument that a court has wide discretion to reject alternative benchmarks. Post at 940. In Allen, however, the defendants produced actual "applicant flow data” that contradicted the conclusions of the plaintiffs’ statistics that were based on more general workforce/labor market comparisons. Allen, 737 F.2d at 1306. Here, like in Lewis, such actual applicant data is unavailable. See Lewis, 773 F.2d at 568 (noting that "applicant flow data” was not available). Furthermore, Nucor has not presented any alternative statistical study, or shown that data exists that may be more reliable than the alternative benchmark used by the workers.
. Nucor instead argued that the change of status forms failed to capture whether black employees bid on the positions, and whether the positions were open for bidding in the first place. Given the lack of controversy surrounding whether the 27 forms described promotions, the forms themselves were not introduced into the record until 2012, after the district embraced the fact-finding conducted by the dissent in Brown I and observed that "the Court has never seen the 27 change-of-status forms....” J.A. 10943. The workers then appended all the forms to their motion to "alter and amend” the decertification order— a motion that was denied. J.A. 11005, 11083. Notably, it also appears that in 2006 the workers’ expert provided Nucor with a list of the 27 employees used in the benchmark analysis. See J.A. 1409, 1438.
. Given that history, we would be remiss not to acknowledge the irony inherent in the dissent's insistence that we are now impermissibly making factual determinations without due deference to the district court.
. After we pointed to this language in Brown I, the district court did an about-face and changed its conclusion to state that the statistics were "fundamentally unreliable.” J.A. 10941.
. The workers’ experts acknowledged that the incomplete data "undermined” their "ability to use posting and bidding records to analyze [those] promotions.” J.A. 1161. In context, however, the experts were lamenting the failure of Nucor to “produce all such records.” J.A. 1161. As the experts concluded, they were able to "calculate reliable statistics” for the limited universe of positions they analyzed, even though greater discovery • would have allowed them to make a more "powerful” study of plantwide disparities. J.A. 1253-54; see also J.A. 1340-41.
. At times, the dissent seems to suggest that statistical assumptions themselves are to be viéwed with great suspicion. What matters, however, is not whether an analysis makes assumptions based on imperfect data, but whether those assumptions are reasonable. Indeed, statistics are not certainties but are merely “a body of methods for making wise decisions in the face of uncertainty.” W. Allen Wallis & Harry V. Roberts, The Nature of Statistics 11 (4th ed.2014); see also M.J. Moroney, Facts from Figures 3 (1951) ("A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a surgery of suppositions.").
. The record does indicate that "supervisory positions" are not typically posted for bidding under the Nucor hiring policy. J.A. 257. Neither Nucor nor the district court, however, has provided any reason to believe that any of the 27 records at issue describe open supervisory jobs, as Nucor defined the term, and were thus not posted. Furthermore, the dissent suggests that there may have been isolated instances when Nucor did not follow its posting policy for non-supervisory jobs. The fact that a company does not follow its policy to a tee, however, does not fatally undermine a statistical assumption based upon such a policy.
. Indeed, the workers’ statistical analysis may actually underestimate the impact of race on promotions at Nucor. As worker Eric Conyers stated in his declaration: “If I believed that a truly level playing field existed at the company I would have bid on numerous other positions such as Roll Guide Builder in the Beam Mill.” J.A. 1079. But the expert analysis at issue could not capture the impact of discrimination on depressed bidding rates.
. As the district court found in the context of the workers’ hostile work environment claim:
These affidavits support the Court’s conclusion that although allegations of a hostile work environment were most prevalent and severe in the Beam Mill, employees from all of the production departments were subjected to abusive behavior. Specifically, employees from every department reported seeing the Confederate flag, employees from every department reported seeing racist graffiti; and employees from every department reported receiving racially offensive e-mails. Furthermore, in several *911instances, employees who worked in one department indicated they were harassed by employees from other departments, and many employees reported observing what they considered to be racist symbols and racist graffiti in common areas of the plant:
J.A. 10968.
. ' The dissent insists that Brown I's determination that the Nucor plant should be treated as a single facility only extended to the hostile work environment claim. Post at 945. Yet the discussion of the issue in Brown I was specifically premised on the district court’s findings regarding both the "pattern or practice” and the work environment claims. Brown I, 576 F.3d at 157. A district court may not typically relitigate "issues expressly or impliedly decided by the appellate court.” Bell, 5 F.3d at 66. Here, even the district court has recognized that Brown I prevented a finding that the plant was not a unitary environment in the context of the promotions claim. J.A. 9705 (Certification Order).
. We do not suggest, of course, that evidence of a hostile work environment is sufficient by itself to support a disparate treatment or disparate impact claim. Rather, we merely observe that the substantial showing of endemic prejudice at the plant — a prejudice that was allegedly tolerated and/or encouraged by management — heightens the probativeness of the workers' other evidence.
. This number includes both the 16 declarations introduced by the workers and other accounts of discrimination included in affidavits obtained by Nucor after the EEOC charge was filed. See, e.g., J.A. 5992-95, 6143-45, 6174, 6369-70, 6505-07, 7036. Of the 16 worker-filed • declarations, Byron Turner's statement fails to mention specific instances of promotions discrimination, but instead affirms that that he was "affected by the same practices that Ramon Roane and the other named plaintiffs” have raised. J.A. 1124. The dissent argues that the declaration of Walter Cook also fails to mention promotions. Post at 949. Cook’s declaration, however, states that he heard white employees talking about a black worker’s application for an Operator position. According to Cook, the employees stated they would "do everything that they could to make sure that nigger didn’t get the job.” J.A. 1075. Further, the dissent argues that the declaration from Kenneth Hubbard includes a complaint that Nu-cor in fact promoted him. Post at 949. Hubbard’s declaration, however, accuses Nucor of placing him "in the position to get [him] out of the mill and the line of progression that lead to supervisory positions.” J.A. 1097. Hubbard also observes that his trajectory at the company was dramatically different from that of a white co-worker who started at the plant at the same time and later became a supervisor. Id. Indeed, the dissent's approach to the affidavits, consistent with its approach to the anecdotal evidence throughout, appears to be to cherry pick facts from an 11,000 page record, strip those facts of context, and then argue that they undermine the substantial, credible evidence of discrimination that the workers have produced.
. There is some uncertainty about the precise size of the class. At the time the litigation began, seventy-one workers at the Nucor plant were black. Brown I, 576 F.3d at 151. As the district court found, there was a total . of "ninety-four black employees who worked at the plant from 2001 through 2004.” Id. at 152. The workers’ experts estimated that there may have been about 150 black workers in total who "were potentially affected by the selection decisions regarding promotion at Nucor-Berkeley.” J.A. 1154. Even assuming a class size of 150, there would be more than one anecdotal account of racial discrimination for every 9.38 class members, a ratio that remains in line with the evidence in Teamsters. Furthermore, that number does not take into account the descriptions of discrimination in promotions decisions in the affidavits that Nucor itself obtained, as previously described.
. The dissent is thus mistaken when it asserts that we are articulating a new rule that courts categorically may not consider the affidavits obtained by companies as part of an investigation into allegations of discrimination. See post at 951-52. Instead, our analysis concerns the weight that should be given to such affidavits in these circumstances.
. Contrary to the dissent’s assertion, we do not find "in the first instance” that the worker's allegation is correct. Instead, we conclude that the district court clearly erred in finding that the allegation was not sufficiently supported by the record.
. This Court has previously observed that "[i]n a class action brought under Rule 23(b)(3), the ‘commonality’ requirement of Rule 23(a)(2) is ‘subsumed under, or superseded by, the more stringent Rule 23(b)(3) requirement that questions common to the class predominate over’ other questions.” Lienhart v. Dryvit Sys., Inc., 255 F.3d 138, 146 n. 4 (4th Cir.2001) (quoting Amchem, 521 U.S. at 609, 117 S.Ct. 2231). But as WalMart made clear, the Rule 23(a) commonality requirement and the Rule 23(b)(3) predominance requirement remain separate inquiries. Wal-Mart, 131 S.Ct. at 2556.
. Even superficially, the district court includes its predominance analysis under the heading of “Subjectivity as a Policy,” dovetailing a discussion of commonality, instead of as a separate section of analysis. See J.A. 10954, 10956.
. The dissent also maintains that our mandate did not reach the question of predominance because we amended our original opinion in Brown I to delete a specific reference to Rule 23(b)(3). Post at 927. Such a deletion, however, did not change either our mandate to certify — a mandate that required the court to find the workers had met Rule 23(b) — or the district court's express understanding of that mandate!