
    George James WILLIAMS, et al., Plaintiffs-Appellants, v. NEW ORLEANS STEAMSHIP ASSOCIATION, et al., Defendants-Appellees.
    No. 80-3886.
    United States Court of Appeals, Fifth Circuit.
    April 9, 1982.
    
      George M. Strickler, Jr., New Orleans, La., Richard B. Sobol, Richard T. Seymour, Washington, D. C., for plaintiffs-appellants.
    Andrew P. Carter, David E. Walker, New Orleans, La., for N. O. Steamship Ass’n.
    Victor H. Hess, Jr., New Orleans, La., Seymour M. Waldman, New York City, Dennis M. Angelico, New Orleans, La., for Unions.
    Before THORNBERRY, TATE and WILLIAMS, Circuit Judges.
   JERRE S. WILLIAMS, Circuit Judge:

Plaintiffs George Williams, Duralph Hayes, and Ernest Turner, Jr. and intervenors Matthew Richard and John Aaron sued New Orleans Steamship Association (NOSA), sixteen of its member stevedoring companies, Locals 1418 and 1419 General Longshore Workers, International Longshoremen Association (ILA), and Locals 1802 and 1863 Sacksewers, Sweepers, Waterboys, and Coopers, ILA, alleging individual and class-wide employment discrimination in the Port of New Orleans in violation of Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e et seq., and 42 U.S.C. § 1981. After an eighteen day trial, the court ordered the merger of the previously segregated Locals 1418 and 1419 and Locals 1802 and 1863 but dismissed the remainder of plaintiffs’ claims and refused to certify a class pursuant to Fed.R.Civ.P. 23. In this appeal, plaintiffs contest the court’s dismissal of their claims of discrimination in the allocation of grain work and in the assignment of preferred positions in general cargo gangs as well as the court’s refusal to certify a plaintiff class. We hold that the court erred in denying plaintiffs’ claim concerning the allocation of grain work and in refusing to certify a class with respect to that claim. We affirm the dismissal of the discriminatory assignment claim and the court’s refusal to certify a class in that instance.

I. FACTS

The district court’s opinion amply describes the factual background of this eleven year old case. See Williams v. New Orleans Steamship Association, 466 F.Supp. 662 (E.D.La.1979). Because this appeal concerns the employment practices in particular areas of the stevedoring industry, it is necessary to describe briefly the operation of the industry in the Port of New Orleans.

Originally, employment on the waterfront was casual and unsystematic. After a 1974 Department of Labor study, a registration system was instituted. Today, waterfront workers are categorized by craft and registered accordingly. Each craft is under the jurisdiction of a different ILA local.

This appeal involves alleged discrimination against Craft I workers. Craft I is comprised of general longshoremen previously under the jurisdiction of Locals 1418 (white) and 1419 (black), now under the jurisdiction of the merged Local 3000. Within each craft, workers are classified according to their priority for employment opportunities based upon their length of service with a particular company. The highest ranking categories are considered “registered” (as opposed to “casual”) and comprise the majority of longshoremen. Throughout the relevant time period, approximately 75% of all registered longshoremen were black. Thus membership in Local 1419 was three times as great as that of Local 1418.

Longshoremen load and unload ships. The work is performed on a day-to-day basis, seven days a week. Stevedoring companies hire longshoremen daily through the Waterfront Employment Center owned and operated by NOS A. The workers are organized into “gangs” of varying size, depending on the type of cargo to be loaded or unloaded. Typically, grain gangs employ eight men and general cargo gangs sixteen. Pay rates for the various jobs are set out in the Deep Sea Agreement negotiated between NOSA and the Locals.

Hiring is done twice daily at “shape-ups.” Each stevedore chooses a foreman for each gang needed that day and the foreman then hires the necessary gang; members. Many companies have “regular” gangs comprised of registered longshoremen who frequently work for that company and are given preference on available work. If a company has more work than can be handled by its regular gangs, it employs “non-regulars” who are either regulars with other companies or “casuals” not associated with any particular company. This results in all longshoremen working for virtually all the stevedores at one time or another. Although many workers become associated with a particular company from time to time, none works exclusively for one company.

Despite the registration system, employment is still largely casual. The work performed by a longshoreman varies from day to day depending on a variety of factors including the work available as well as personal choice. Longshoremen are not required to work any particular days or hours. If they want to work, they simply come to a shape-up. The rates of pay vary for different jobs and different shifts. For example, in 1973, grain work paid a 20$ per hour premium. Work performed during mealtimes, weekends, and holidays also pays a premium. A longshoreman may choose to shape-up only when there is a certain type of work available or only during certain hours. Thus the longshoreman’s job and wages are determined in part by personal factors.

The employment relationship ultimately is controlled by the Deep Sea Agreement which specifies the terms and conditions of employment and the varying wages for each job. In this appeal, plaintiffs contest the employment practices concerning the allocation of grain work and the job assignments in general cargo gangs. Before 1974, the Agreement required that so far as practicable, grain work should be divided evenly between Locals 1418 and 1419, notwithstanding their disproportionate memberships. There was no corresponding provision respecting assignments in general cargo gangs; plaintiffs contest an alleged practice by white foremen of assigning white longshoremen to the more preferable jobs.

II. ALLOCATION OF GRAIN WORK

A. Separate Claim of Racial Discrimination in Grain Work.

Grain work comprises approximately 8% of all longshore work and involves the loading and unloading of ships carrying grain. It is physically less demanding than other types of work because the cargo is pumped rather than carried onto and off of vessels. Grain workers often become covered from head to toe in. grain and inhale particles, however, and because of this unpleasantness, a premium is paid for grain work.

Pursuant to the Deep Sea Agreement, grain work was allocated equally between the members of the black and white locals. Plaintiffs contend that this practice violated Title VII and § 1981.

The district court’s original order in this case, dated February 14, 1979, 466 F.Supp. 662, was five years after the trial. In that order, the court found that the 50-50 allocation of grain work was discriminatory, yet it did not find a violation of Title VII. Upon plaintiffs’ motion for reconsideration of the issue, the court clarified by saying its earlier holding meant that the contract clause requiring 50-50 allocation was not discriminatory but that it was evidence of the discriminatory potential inherent in a system that maintained segregated local unions.

The court then reconsidered plaintiffs’ allegation that the practice of 50-50 allocation was discriminatory in and of itself. Again, the court did not find a violation of Title VII. This time its conclusion was based upon its finding that, because longshoremen perform more than one type of work, evidence focusing on only one of these jobs, Le., grain work, would distort the analysis. “The important thing is how [the black longshoreman] fares overall.” The court then considered the overall welfare of black longshoremen and concluded that in the Port of New Orleans, they received their proportionate share of work and pay. Thus the court found no discrimination.

An appellate court must accept a trial court’s findings of subsidiary facts unless clearly erroneous; however, the court’s ultimate finding on the issue of discrimination is subject to review free of the clearly erroneous standard. Wright v. Western Electric Co., 664 F.2d 959, 963 (5th Cir. 1981). Furthermore, this Court is not bound to any degree by the district court’s conclusions as to the law, Parson v. Kaiser Aluminum & Chemical Corp., 575 F.2d 1374, 1382 (5th Cir. 1978), cert. denied, 441 U.S. 968, 99 S.Ct. 2417, 60 L.Ed.2d 1073 (1979), nor are we bound by findings of fact based upon erroneous applications of law, Johnson v. Uncle Ben's, Inc., 628 F.2d 419, 422 (5th Cir. 1980), vacated on other grounds, 451 U.S. 902, 101 S.Ct. 1967, 68 L.Ed.2d 290 (1981). We find that the district court’s opinion was based upon an erroneous legal conclusion as to the viability of plaintiffs’ grain claim. Thus our review of the court’s findings of fact is not bound by the clearly erroneous standard of Fed.R.Civ.P. 52(a).

In concluding that the plaintiffs failed to prove discrimination, the district court misconstrued plaintiffs’ allegation. By comparing the overall economic picture of blacks and whites, the court transformed plaintiffs’ claim of discrimination in the allocation of grain work into a claim of discrimination in the entire industry. The court erroneously concluded that plaintiffs’ segmented claim was not cognizable under Title VII and § 1981.

Claims alleging discrimination in only one segment of an employer’s workforce are cognizable under Title VII and § 1981. The Supreme Court recognized this principle in one of the landmark Title VII cases, International Brotherhood of Teamsters v. United States, 431 U.S. 324, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977). There, the United States brought suit on behalf of blacks and Spanish-surnamed persons against a large trucking company and the union which represented its employees claiming that the company engaged in a pattern or practice of discrimination in the hiring of line drivers. Minorities who were hired allegedly were relegated to the lower paying, less desirable positions and met wjth insurmountable difficulties in trying to gain promotions and transfers.

The government’s case consisted of powerful statistical evidence showing a gross disparity between the percentage of minorities in the company’s workforce as a whole and those in line driver positions. Those statistics, coupled with the testimony of individuals who recounted over forty specific instances of discrimination, established the government’s prima facie case. The company was unable to rebut this evidence, and the government prevailed on the issue.

Line drivers only comprised approximately one-fourth of the truck driver positions, yet the Court recognized the validity of the departmentalized claim. The Court did not look to the overall picture of minorities within the company’s employ to determine the validity of the claim. Minorities may have fared overall as well as their white counterparts, yet the Court did not consider this factor in evaluating the evidence. The government was permitted to charge discrimination in one job classification only and to prove its case by offering statistical evidence relevant only to that job.

In determining whether a particular claim of discrimination in only a segment of an employer’s work force is cognizable the operative factor must be the distinctiveness of the segment. In Teamsters, supra, the duties and compensation of line drivers differed from those of other driver positions and thus line drivers constituted a distinct job classification.

A similar distinction exists between grain work and other types of longshoring jobs in New Orleans. The tasks performed by grain workers differ from those performed by other longshoremen because of the nature of the cargo involved. Furthermore, the Locals and NOSA traditionally have treated grain work separately from other types of longshore work, as evidenced by the Deep Sea Agreement. The hourly wage paid for grain work is negotiated separately from other types of work. The mode of allocating jobs evenly between the black and white Locals was also unique to grain work. Thus, while longshoremen can and do perform a variety of jobs, the distinctiveness of grain work makes plaintiffs’ claim of discrimination in this one area of employment viable under Title VII and § 1981.

In fact, the court below recognized the validity of segmented claims within the industry in New Orleans. Although it refused to consider plaintiffs’ claims of discrimination in the allocation of grain work, it permitted similar segmented claims with respect to other sectors of the industry. A clear example is the court’s consideration of plaintiffs’ allegation of discrimination in job assignments in general cargo gangs. Although the court ultimately rejected plaintiffs’ claim on the merits, it recognized the segmented claim and considered statistics relevant only to general cargo gangs, not the entire industry.

Furthermore, both logic and the policies underlying Title VII dictate the conclusion that a segmented claim is cognizable. Title VII proscribes racial discrimination of any kind in virtually all aspects of employment. There is nothing in the Act to indicate that a- claim for discrimination in one distinct category of employment within a plant, industry or office, or even in one job, is not cognizable.

Were we to accept defendants’ contentions, we would be ruling in effect that an employer may discriminate with impunity as long as it confines such action to some units or departments within the workforce while maintaining an overall facade of equality. An employer guilty of plant or industry-wide discrimination may be a worse offender of Title VII than one who discriminates in only a single department. The remedies awarded to the former’s employees as well as the penalties assessed against it may be greater than those imposed upon the latter. As to liability, however, both are equally subject to the prohibitions of Title VII.

The cases relied upon by defendants in support of the judgment below are unpersuasive. None of these cases involved the question of whether a segmented claim may be brought against an employer. In Swint v. Pullman-Standard, 539 F.2d 77 (5th Cir. 1976), cert. granted (after an earlier remand), 451 U.S. 906, 101 S.Ct. 1972, 68 L.Ed.2d 293 (1981), plaintiffs alleged that the defendant engaged in a pattern or practice of racial discrimination in departmental assignments within its production plant. To prove their claim, plaintiffs offered statistical evidence of racial disparity in .nine of the twenty-eight departments. We discarded the proffered analysis because it focused on only nine of twenty-eight depártments. 539 F.2d at 94-95. Instead, we held the proper statistical focus should have encompassed the entire plant and thus plaintiffs’ evidence of racial imbalances in a segment of the plant was insufficient to establish a prima facie case of plant-wide discrimination.

In E.E.O.C. v. Datapoint Corp., 570 F.2d 1264 (5th Cir. 1978), plaintiffs raised a claim of racial discrimination in hiring and job assignments. They introduced statistical evidence showing gross imbalances in some job categories, but no evidence as to the employer’s workforce as a whole. The district court rejected this as proof of a prima facie case. We upheld its decision stating that while “plaintiffs’ statistical evidence alone might be sufficient to infer discrimination in these job categories ... [to prove] ■ a prima facie case of racial discrimination, such statistics must be relevant, material and meaningful. .. . ” 570 F.2d at 1269. Because plaintiffs’ claim was one of employer-wide discrimination, the segmented, isolated statistics offered were misleading and therefore meaningless.

Contrary to defendants’ contention, these two cases do not stand for the proposition that plaintiffs’ claim of discrimination in grain work is not cognizable. In both cases, plaintiffs charged the employer with plant-wide discrimination but offered statistical evidence which was limited to small segments of the plant. In denying plaintiffs’ claims, we held that the proffered limited statistics were insufficient to prove the broad claims asserted.

Here, plaintiffs alleged discrimination in one separate job category within the industry. Naturally, then, their statistics focused on the subject area. Unlike the Swint and Datapoint plaintiffs, they did not offer a segmented statistical analysis as a means of trying to prove industry-wide discrimination. Indeed, that was not their claim. The district court, nevertheless, treated their offer of proof as one for industry-wide discrimination. As such, plaintiffs’ statistics certainly would not prove a prima facie case, for the reasons cited in Swint and Datapoint. The court refused to consider plaintiffs’ proof in the context in which it was offered, and we find this to be reversible error.

Lee v. City of Richmond, 456 F.Supp. 756 (E.D.Va.1978) and Croker v. Boeing Co., 437 F.Supp. 1138 (E.D.Pa.1977), aff’d, 662 F.2d 975 (3d Cir. 1981), also relied upon by defendants, are equally unsupportive. . Both cases, as do our decisions set out above, stand only for the proposition that segmented statistical evidence of racial imbalances within a few departments cannot prove a prima facie case of employer-wide discrimination. Neither of these cases addresses the validity of a claim of segmented, departmentalized discrimination such as the one posed by plaintiffs herein. Therefore, they do not support defendants’ position in this' appeal.

We hold that the district court erred in refusing to recognize plaintiffs’ claim and in transforming it into one of industry-wide discrimination. Plaintiffs presented a cognizable claim under Title VII and § 1981. We now turn to the merits of that claim.

B. The Prima Facie Case

Having found plaintiffs’ claim for discrimination in the allocation of grain work to be cognizable under Title VII and § 1981, we turn now to plaintiffs’ evidence to determine whether a prima facie case was made. We note at the outset that the contract clause requiring the 50-50 allocation of grain work was eliminated in 1974. Because the clause formed a significant part of plaintiffs’ evidence, our discussion in this section pertains only to the time period in which the objectionable clause was in effect.

Plaintiffs’ claim is one of class-wide disparate treatment. Thus, the inquiry must be whether defendant treated members of the plaintiff class differently from their white counterparts, and if so, whether that difference was the result of discriminatory intent. In some cases, proof of the latter can be inferred from strong statistical evidence of the former. Teamsters, 431 U.S. at 335 n.15, 97 S.Ct. at 1854 n.15; Pouncy v. Prudential Insurance Company of America, 668 F.2d 795 at 802 (5th Cir. 1982); Wilkins v. University of Houston, 654 F.2d 388, 395 (5th Cir. 1981). Plaintiffs introduced statistical evidence which they contend proved a significant disparity between blacks and whites in the allocation of grain work.

Statistics have become an important and useful tool in civil rights litigation. In many cases, they are the only evidence available to plaintiffs. Pragmatically, too, statistics assist in the evaluation of employer practices because “absent explanation, it is ordinarily to be expected that nondiscriminatory . . . practices will in time result in a work force more or less representative of the racial and ethnic composition of the population ... from which employees are hired.” Teamsters, 431 U.S. at 339 n.20, 97 S.Ct. at 1856 n.20. Thus, “[wjhere gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof. . . . ” Hazelwood, 433 U.S. at 307-08, 97 S.Ct. at 2741. Wilkins, 654 F.2d at 395.

Plaintiffs introduced statistical evidence showing the allocation of grain work in ten of the NOS A companies for the years 1971-73. In 1971, there were six grain gangs composed of 31 whites and 32 blacks; in 1972, there were 19 gangs composed of 72 whites and 76 blacks; and in 1973 there were 18 gangs composed of 67 whites and 71 blacks. Thus while blacks comprised 75% of the registered workforce, they held only 51.3% of the grain positions. A calculation of the binomial distribution, see Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977), reveals that the actual number of black grain workers deviated from the expected number by 10.24 standard deviations. This is well sufficient to prove a prima facie case of discrimination. Id. at 496 n.17, 97 S.Ct. at 1281 n.17.

In addition to this strong statistical data, plaintiffs introduced into evidence the contract between the Craft I unions and NOSA which specifically compelled the allocation of grain work according to race. It provided that “so far as is practical, work is to be divided between members of ILA Locals 1418 and 1419 in grain trimming machine gangs, and/or hand trimming gangs.” Williams v. NOSA, 466 F.Supp. at 673. In practice, this meant that grain gangs were half black and half white. Id.

The contract clause and the statistics are powerful evidence of purposeful discrimination. The statistics alone show that it is quite unlikely that random, impartial hiring practices would have produced such disparities. And, in light of the contract’s compelled discrimination, any doubts as to purposefulness must be resolved in plaintiffs’ favor. We hold that plaintiffs established a prima facie case of purposeful discrimination in the allocation of grain work.

C. Defendants’ Rebuttal

Once plaintiffs have proved a prima facie case of purposeful discrimination, defendants must rebut plaintiffs’ case by discrediting plaintiffs’ evidence or providing a “nondiscriminatory explanation for the apparently discriminatory result.” Teamsters, 431 U.S. at 360 n.46, 97 S.Ct. at 1876 n.46. If the defendants fail to rebut the prima facie case, plaintiffs prevail on the issue.

At no point in this eleven year proceeding have defendants disputed the validity of plaintiffs’ statistics relating to the allocation of grain work. In fact, the statistical data was derived from the defendant companies’ Answers to plaintiffs’ Interrogatories. Defendants challenged the designation of black grain workers as the sample and argued that the analysis should have focused upon a 11 black longshoremen. We responded to this contention in Part I, supra and need not reiterate our holding.

Instead, defendants offered explanations for the statistical disparity which they contend satisfied their rebuttal burden. First, they contend that because the offensive clause was included at the insistence of black Local 1419, in following its mandate they were only following the wishes of those who now claim to have been discriminated against. This appears to be factually correct; nevertheless, it does not excuse discrimination on the part of the union or the employer. “The rights assured by Title VII cannot be bargained away — either by a union, by an employer, or by both acting in concert.” United States v. St. Louis-San Francisco Railway Co., 464 F.2d 301, 309 (8th Cir. 1972) (en banc), cert. denied, 409 U.S. 1116, 93 S.Ct. 913, 34 L.Ed.2d 700 (1973). We have held “[t]he fact that a contract required this limitation [of employment opportunities] is not a justification if it is discriminating.” United States v. Hayes International Corp., 456 F.2d 112, 117 (5th Cir. 1972). Clearly, then, neither the existence of the contract nor its origin can exonerate defendants’ discriminatory practices.

Second, defendants claimed that because blacks in the longshore industry fared overall as well as or better than whites, any misallocation of grain work is irrelevant. As we stated above, this type of analysis transforms plaintiffs’ claim into one of industry-wide discrimination. Whether blacks as a whole suffered economically has no bearing on the issue of discrimination in the allocation of grain work. Swint, 539 F.2d at 92. Plaintiffs readily admit that industry-wide earnings of blacks may be relevant on the issue of backpay. This evidence has no place in the liability phase, however. Id. Defendants also argue that grain work was no more desirable than any other type of work. Although it paid a 20<t per hour premium, it was unpleasant. The desirability of grain work is irrelevant as well. Title VII provides for equal opportunities in all jobs whether better or worse than others. Teamsters, 431 U.S. at 338 n.18, 97 S.Ct. at 1855 n.18; Hayes International Corp., 456 F.2d at 118.

Finally, defendants argued that the casual nature of the longshore industry precludes a finding of discrimination. We have already described the shape-up process and the many variables that determine a longshoreman’s position and earnings. The unpredictability of available work coupled with the personal choices inherent in the system normally would complicate our inquiry. Because so many of the factors determining work patterns are not within the employer’s control, and in fact are determined by the employees, it is more difficult to attribute statistical imbalances to a discriminatory motive on the part of the employers. Here, however, we need not speculate as to the reasons for the imbalance because the contract shows that such an allocation was required. Whether the casual nature of the industry could or would have produced similar disparities is irrelevant in the face of the explicit language of the Deep Sea Agreement.

We hold that defendants failed to rebut plaintiffs’ prima facie case of purposeful discrimination in the allocation of grain work during the existence and application of the 50 -50 clause. The statistical data introduced by plaintiffs pertains only to the period during which the discriminatory contract was in force. Because our conclusions are based upon evidence relative to this period only, our finding of discrimination is limited accordingly. Plaintiffs contend that even after the deletion of the 50-50 clause, the practice of discriminatory allocation continued. We turn now to that claim.

D. Discrimination in the Allocation of Grain Work After the Deletion of the 50/50 Clause

Thus far we have held that there was purposeful discrimination in the allocation of grain work during the pendency of the grain clause. Plaintiffs contend that the discriminatory practice continued after the deletion of the clause and that the court below erred in refusing to consider the issue. Defendants argue that plaintiffs waived the issue of post-clause discrimination because they failed to request its consideration by the court.

It is plaintiffs’ assertion that the clause was eliminated after the close of the record; defendants contend the opposite. We find plaintiffs’ assertion ironic. If the clause were eliminated after trial, the record would have closed, and thus the only evidence plaintiffs could have produced would have concerned the practices existing during the application of the clause. Because a court’s consideration need not extend to claims for which plaintiffs produce no evidence, Rivera v. City of Wichita Falls, 665 F.2d 531, 536 n.6 (5th Cir. 1982), the district court would have been justified in refusing to consider the claim of post-clause discrimination. Thus, if plaintiffs are correct in their assertion as to when the clause was eliminated, the only way they could be entitled to a finding on post-clause discrimination would be by petitioning the court to reopen the case, which they have not done.

On the other hand, if the clause were eliminated during the trial, plaintiffs’ failure to request a ruling would not constitute a waiver of the claim. Plaintiffs claimed that defendants were guilty of allocating grain work in a discriminatory manner. The contract clause was offered as evidence of that practice. While plaintiffs certainly objected to the clause, the subject of their claim was the practice of discriminatory allocation, whatever its source, and the court’s inquiry should have focused on the practice. By bringing such a claim, plaintiffs requested consideration of the issue of post-clause discrimination. An additional request would not have been necessary.

We believe both parties are partially correct in their statements as to when the clause was deleted. The trial took place from July 22 to September 20, 1974, during the time that the Deep Sea Agreement was being renegotiated. The Agreement was to expire on September 30,1974. By mid-September, it must have become painfully apparent that the grain clause was doomed, and as “a tactic of this litigation,” Williams v. NOSA, 466 F.Supp. at 673, NOSA and Locals 1418 and 1419 decided to eliminate the clause from the new contract. But the new contract was not actually effective until October 1, 1974. So although it was agreed during the trial that the clause would be deleted, the action was not officially taken until after the trial ended.

Because the trial court was aware of the imminent elimination of the clause, we find that the issue was before it and should have been considered. At the close of the trial, however, plaintiffs had produced no evidence on the issue. In subsequent affidavits submitted on a summary judgment motion, plaintiffs offered evidence showing that the discriminatory practice continued notwithstanding the elimination. of the clause. Defendants responded with counter-affidavits. When plaintiffs moved for reconsideration of the grain issue in 1979, their supporting memorandum noted the conflicting affidavits and insisted that the issue could not be resolved without an evidentiary hearing.

The trial court granted plaintiffs’ motion for reconsideration of the grain issue. But, without another hearing and relying only upon the evidence adduced at trial five years earlier, the court reiterated its former holding that the proper comparison was between blacks and whites in the entire industry. This conclusion foreclosed a decision on post-clause discrimination in grain work. The grain work issue was not mentioned despite the fact that plaintiffs brought to the court’s attention the conflicting affidavits. The court, however, would consider only the industry-wide claim.

Plaintiffs are entitled to a hearing on the issue of post-clause discrimination. We remand this issue to the district court so that all parties may present evidence as to whether or not discrimination continued after the 50-50 clause was deleted.

III. DECK AND WHARF JOBS

A. The Prima Facie Case

Next, plaintiffs claim that the court below erred in refusing to find discrimination in the assignment to deck and wharf positions in integrated general cargo gangs. General cargo gangs are comprised of sixteen members, eight of whom work in the hold of the ship while the other eight work on the deck or wharf. Deck and wharf jobs are regarded by all as more desirable than hold positions because the work is less physically demanding and permits the longshoreman to be out in the fresh air rather than confined to the bowels of the ship.

Job assignments are made by gang foremen. During the relevant time period, gangs were either all black or integrated. Black gangs had either black or white foremen, while integrated gangs always had white foremen. Plaintiffs alleged discrimination by white foremen in the assignment of the preferred positions in integrated gangs. They offered statistical proof of this and argue that they met their prima facie burden of proof and that defendants’ rebuttal evidence was insufficient.

Again, we are faced with a dispute over the proper statistical analysis. Plaintiffs contend that the only relevant statistics are those reflecting assignments within integrated gangs, all of which were overseen by white foremen. Defendants argue that such an analysis ignores 40-45% of all general cargo workers and in doing so penalizes those companies which have promoted blacks to foreman positions or have given all their general cargo work to black longshoremen. The district court agreed with defendants and examined the situation of all general cargo workers in making its findings.

We find plaintiffs’ focus to be the proper one. Although it excluded over 40% of the general cargo workers, many of whom were black, it did so because those statistics were irrelevant to the issue. Plaintiffs alleged racially discriminatory assignments. Unless a gang was integrated, racial discrimination within the gang was impossible. Therefore, the proper analysis includes only integrated gangs. And, because integrated gangs always had white foremen, the analysis must exclude gangs with black foremen.

Plaintiffs produced statistics showing that in 1972 and 1973, whites in integrated gangs were twice as likely as blacks to be assigned to deck and wharf jobs. In 1972, blacks made up 82% of the integrated general cargo gang population but held only 68% of the deck and wharf jobs producing a variance of 8.3 standard deviations. In 1973, blacks comprised 80% of the population but held only 63% of the preferred jobs, producing a variance of 8.9 standard deviations.

Plaintiffs’ statistics revealed gross disparities giving rise to an inference of purposeful discrimination. Hazelwood, 433 U.S. at 307-08, 97 S.Ct. at 2741. The burden then fell to defendants to rebut this evidence.

B. The Defendants’ Rebuttal

Defendants contend that assignments to deck and wharf jobs were made on the basis of gang longevity and individual skill without regard to race. The district court accepted this contention and based its finding of nondiscrimination on those factors. Plaintiffs argue that the court erred in making this finding and that its conclusion was actually based upon its belief that there was a “trend of a steady movement of black longshoremen into ‘preferred’ work. ... ” Williams v. NOSA, 466 P.Supp. at 675-76.

We must disagree with plaintiffs on both assertions. First, we interpret the courts’ language concerning the “trend” to mean that despite pre-Title VII discrimination, defendants’ assignment system permitted blacks to make great strides in general cargo gangs. The court ruled against plaintiffs because defendants’ assignment system was a legitimate and reasonable explanation for the disparities as well as the catalyst for the upward movement apparent in the statistics, and not because the strides negated any existing discrimination.

Plaintiffs contest the district court’s reliance on the seniority-based assignment system not because such a system violates Title VII or § 1981, but because defendants allegedly failed to prove its existence. Again, we disagree.

At trial, both sides presented evidence concerning the assignment system. Several witnesses, including class representative Richard, testified that there was a custom or practice of filling openings in the preferred deck and wharf jobs with the most senior member in the hold, provided he had the requisite skills. There was testimony by defense witnesses recounting various incidents where this custom was enforced, and contradictory testimony by some plaintiffs’ witnesses concerning promotions without regard to gang tenure.

The district court was justified in concluding that there was a custom or practice of making assignments on the basis of seniority. In fact, plaintiffs’ witness so testified. The fact that the system occasionally was disregarded does not render it invalid. Because plaintiffs alleged a pattern or practice of discriminatory assignments, they had to “prove more than the mere occurrence of isolated or ‘accidental’ or sporadic discriminatory acts.” Teamsters, 431 U.S. at 336, 97 S.Ct. at 1855.

Defendants rebutted plaintiffs’ prima facie case with more than mere “affirmations of good faith,” Alexander v. Louisiana, 405 U.S. 625, 632, 92 S.Ct. 1221, 1226, 31 L.Ed.2d 536 (1972). They produced evidence, including evidence from one of plaintiffs’ own witnesses, proving that assignments were made according to gang longevity and individual skill.

The record amply supports the district court’s conclusion that job assignments within general cargo gangs were made on the basis of seniority and skill. Prior to Title VII’s enactment, virtually no blacks were in the preferred positions. Since then, however, the figures indicate that blacks have been moving rapidly into deck and wharf jobs. Plaintiffs’ exhibits showing that as of 1973, 63% of all deck and wharf jobs were performed by blacks illustrate the effectiveness of the system. If this trend continues, by the time this appeal is resolved, blacks may have overcome completely the final vestiges of pre-Title VII discrimination even though seniority is applicable.

Although we disagree with some of the court’s statistical analysis, we affirm its finding on the ultimate issue of discriminatory assignments.

IV. CLASS CERTIFICATION

Plaintiffs brought this suit as a class action pursuant to Fed.R.Civ.P. 23. The district court denied a pre-trial motion by defendants to dismiss the class claims and allowed the case to proceed as a class action. Ultimately, class certification was denied on the ground that the proposed class lacked the requisite numerosity, and in the alternative, that plaintiffs failed to prove discrimination against any group of employees similarly situated.

We find that the court erred in refusing to certify a class with respect to the grain claim but properly refused certification for the deck and wharf claim.

A. The Grain Claim

In pressing this claim, plaintiffs sought to represent all blacks who were denied opportunities to work in grain gangs because of defendants’ discriminatory practices. This would include all those who actually sought grain work but were refused the opportunity, those who had been deterred from trying to get grain work because of knowledge of the discriminatory policy, and those who would become subject to this practice in the future. Phillips v. Joint Legislative Committee on Performance & Expenditure Review, 637 F.2d 1014, 1022 (5th Cir. 1981). During the relevant time period, there were hundreds of blacks working in the Port of New Orleans any or all of whom might have been affected by the discrimination.

In determining whether a proposed class is sufficiently numerous, the court’s inquiry must focus upon the practicability of joining all aggrieved parties. Here, an accurate count of all those aggrieved is virtually impossible, much less an identification of the actual persons. In these circumstances, joinder is certainly impossible, id. at 1022; Jack v. American Linen Supply Co., 498 F.2d 122, 124 (5th Cir. 1974), and because of this impossibility, the numerosity requirement is met.

The court relied upon Bailey v. Ryan Stevedoring Co., 528 F.2d 551 (5th Cir. 1976), cert. denied, 429 U.S. 1052, 97 S.Ct. 767, 50 L.Ed.2d 769 (1977), in concluding that most of the black longshoremen plaintiffs sought to represent did not want to be included in the class. This case is distinguishable from Bailey, however. There we denied certification because a majority of the members of the proposed class petitioned the court to be excluded from the class. In this case, there was no such action by black longshoremen. The court referred to its awareness of the black Local’s resistence to and resentment of the merger of the segregated locals. Whether members of the black Local were in favor of or opposed to union merger is irrelevant because our concern in this appeal is with the issues of discrimination in grain work allocation. Furthermore, the resistence relied upon by the court is a far cry from the unequivocal message contained in the Bailey class members’ petition.

The court held, in the alternative, that certification was inappropriate because discrimination had not been proved. Because we have found discrimination in the allocation of grain work, this basis for the court’s denial of certification is no longer valid.

B. Deck and Wharf Claims

For the reasons just stated, we find that plaintiffs met the numerosity requirement. We affirm the court’s denial of certification, however, on the alternative ground that no discrimination was proved, as set out above.

V. CONCLUSION

Plaintiffs proved that defendants engaged in purposeful discrimination against black longshoremen in the allocation of grain work through July of 1974. We certify the plaintiff class to consist of all registered black longshoremen who were eligible for grain work during the relevant time period. This includes all those who sought grain work but were refused as well as those who were deterred from seeking grain work because of the discriminatory allocation. This class is certified for purposes of this claim, and we remand the cause to the district court to determine the appropriate relief for discrimination through July of 1974 as well as the defendants’ liability, if any, for post-July, 1974 discrimination. We affirm the district court’s finding that there was no racial discrimination in assignments within general cargo gangs, and its denial of class certification with respect to this class.

AFFIRMED in part, REVERSED in part and REMANDED. 
      
      . NOSA is composed of 62 stevedoring and shipping companies. Originally, thirty-two companies were named as defendants, but plaintiffs voluntarily dismissed charges against sixteen companies prior to trial.
     
      
      . Although there are differences between Title VII and § 1981 actions, i.e. statute of limitations and remedies available, those differences are not present in the issues considered in this appeal. Therefore, when we refer to either statute, our reasoning encompasses the other as well, unless we specify otherwise.
     
      
      . At the time of trial, Local 1418 was more than 99% white and Local 1419 was all black. The district court found the maintenance of segregated locals violated Title VII because of the potential for discrimination created by dual unions. The court ordered their merger. 466 F.Supp. 662, 680 (E.D.La.1979). Merger was accomplished in 1980.
     
      
      . The relevant time period for the Title VII claim began in September, 1967, 180 days before the first charge was filed by plaintiffs with the E.E.O.C. See McWilliams v. Escambia County School Board, 658 F.2d 326 (5th Cir. 1981). It began on March 30, 1970 for the § 1981 claim. Pegues v. Morehouse Parish School Board, 632 F.2d 1279, 1281 (5th Cir. 1980), cert. denied, 451 U.S. 987, 101 S.Ct. 2322, 68 L.Ed.2d 844 (1981) (§ 1981 claim of employment discrimination is subject to Louisiana’s one year statute of limitations. La.Civ.Code Art. 3653).
     
      
      . At the time of trial, Local 1418 had 750 members, 744 of whom were white. Local 1419 had 3608 members all of whom were black.
     
      
      . This clause was eliminated by agreement of NOSA and the Locals in 1974.
     
      
      . We also note that the district court’s statistical analysis concluding that blacks overall fared as well as whites is flawed. The chart showing these figures is derived from defendant NOSA’s exhibits and contains a comparison between earnings of the 702 highest paid blacks and whites which reveals higher earnings for blacks. See 466 F.Supp. at 667. Actually, the court states that the comparison is based upon the 600, rather than 702, highest earners of each race. As both parties point out, the data in fact encompasses the 702 top earners of each race. During the period reflected in the chart, there were 702 white and over 2100 black longshoremen. Thus, this chart ignores the earnings of approximately 1500 blacks. All the chart shows is that man for man from the top down, 702 of 2100 blacks fared at least as well as all whites. A better comparison would have been between the average earnings of all black and all white longshoremen.
     
      
      . The fact that the wage is the same as that paid for some other job situations does not change our conclusion that the grain wage is a separately bargained-for part of the Agreement. Grain work has traditionally carried a premium of at least 20$ per hour over the basic longshoring rate.
     
      
      . The district court’s opinion could be interpreted as recognizing plaintiffs’ departmentalized claim but rejecting the proffered statistics as non-probative because of the statistical “population” chosen by plaintiffs. We reject such an interpretation, however. Statistical analyses are easily manipulated by choosing as a comparative population a pre-selected group which will reflect the desired outcome. Therefore, a fundamental principal in the use of statistics in Title VII cases is that the population chosen for comparison must be meaningful, relevant, and probative to the claims asserted. A population appropriate in one case might be inappropriate in another. In Teamsters, supra, plaintiffs compared the percentage of black line drivers to the percentage of blacks in the general population of various cities. 431 U.S. at 337 n.17, 97 S.Ct. at 1855 n.17. The same population was rejected by the Court in Hazelwood School District v. United States, 433 U.S. 299, 308, 97 S.Ct. 2736, 2741, 53 L.Ed.2d 768 (1977). There, plaintiffs alleged racial discrimination in teacher hiring in a public school district. Their statistical evidence included a comparison of the percentage of black teachers hired by the district with the percentage of blacks in the geographical area. The Court held that the proper population encompassed only those blacks qualified as teachers and that plaintiffs’ suggested population had little probative value in the context of the claim asserted.
      The court below did not reject plaintiffs’ selection of the meaningful population; rather, it rejected the sample. Both the parties and the district court agreed that the relevant population was the registered longshore workforce in New Orleans. Neither the court nor the defendants were willing to accept plaintiffs’ choice of black grain workers as the appropriate sample, however. Their designation of this sample as irrelevant is the equivalent of finding the claim uncognizable under Title VII. Plaintiffs did not allege industry-wide discrimination; therefore, an analysis showing their overall welfare was not probative. Nevertheless, the court insisted on using blacks in the whole industry as the sample, thereby ignoring plaintiffs’ claim and creating one of its own. We believe this action constitutes a rejection of plaintiffs’ claim, not their statistical analysis.
     
      
      . Such an inference differs from the proof required by the plaintiff in a case alleging individual discrimination. There, a plaintiff must prove (1) that he belongs to a racial minority; (2) that he applied and was qualified for a job for which the employer was seeking applicants; (3) that, despite his qualifications, he was rejected; and (4) that the position remained open and the employer continued to seek applicants. McDonnell Douglas Corp. v. Green, 411 U.S. 792, 802 , 93 S.Ct. 1817, 1824, 36 L.Ed.2d 668 (1973); Wright, 664 F.2d at 962.
     
      
      . In this case, all parties agree that the appropriate population is the registered workforce in the Port of New Orleans.
     
      
      . Not all of the defendant companies use grain gangs and some do so only in certain years. Thus, from 1971-73, only ten companies used grain gangs.
     
      
      . The calculation is as follows:
      Number of S/D = O-NP
      _/NP (1-P) '
      
        where
      S/D = Standard deviations
      O = Actual number of black grain workers during 1971-73
      N = Total number of grain workers during 1971-73
      P = Probability of black person working in grain gang
      S/D = 179 - (349 X .75) = -10.24
      
        _J (349 X .75 (.25)
      The standard deviation is the measure of the predicted fluctuations from the expected value. In this case, it is the predictable variance between the number of blacks expected to be grain workers in a random selection system and the number of blacks actually receiving grain work. That number is the square root of 65.4375 (349 X .75 X .25) or 8.09. This means that you would normally expect the random fluctuation departing from the ratio of 75% blacks and 25% whites to be no more than 8 employees. That is the standard deviation. Actually in this case, the variance was over ten times the standard deviation, 82 employees (349 X .75 = 261.75-179 = 82.75). A deviation greater than three times the standard deviation is prima facie proof that the selection system is not random. Castaneda, 430 U.S. at 496 n.17, 97 S.Ct. at 1281 n.17.
     
      
      . This is more onerous than the rebuttal burden required of defendants in individual Title VII claims under Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 254-256, 101 S.Ct. 1089, 1094-95, 67 L.Ed.2d 207 (1981). Cf. Castaneda v. Pickard, 648 F.2d 989, 994 (5th Cir. 1981).
     
      
      . Statistics for 12 NOSA Companies, 1972-73
      1972: WHITE BLACK TOTAL
      Number in integrated general cargo gangs ,_194_884_1078
      % in integrated general cargo gangs_18%' 82% 100%
      Number in deck and wharf jobs_162_340_502
      % in deck and wharf jobs 32% 68% 100%
      Number of S/D = 340 - (502) (.82) - _g.33
      _/ (502) (.82) (.18)
      1973 WHITE BLACK TOTAL
      Number in integrated general cargo gangs_220_885_1105
      1973 WHITE BLACK TOTAL
      % in integrated general cargo gangs_20%_80%_100%
      Number in deck and wharf jobs_196_341_537
      % in deck and wharf jobs_36%_64%_100%
      Number of S/D = 347 - (537) (.80) - _8.9
      _/ (537) (.80) (.20)
     
      
      . Even if we accept defendants’ contention that all general cargo gangs must be included in the analysis, the figures still favor plaintiffs. For example, in 1973, blacks comprised 87.6% of the general cargo gang population but held only 673 of the 869 deck and wharf jobs, producing a variance of 8.3 standard deviations.
     
      
      . At trial, it was established that prior to the enactment of Title VII, blacks automatically were relegated to hold positions and whites to the deck and wharf.
     
      
      . 42 U.S.C. § 2000e-2(h) provides as follows:
      Notwithstanding any other provisions of this subchapter, it shall not be an unlawful employment practice for an employer to apply different standards of compensation, or different terms, conditions, or privileges of ■ employment pursuant to a bona fide seniority ... system, ... provided that such differences are not the result of an intention to discriminate because of race....
      Prior to the enactment of Title VII, there was discrimination in work assignments. Although Title VII prohibits the continuation of such a practice, this provision has been interpreted to permit assignments based upon an otherwise fair seniority system even if that system perpetuates the effects of pre-Title VII discrimination. Teamsters, 431 U.S. at 345-356, 97 S.Ct. at 1859-1865. A bona fide seniority system is also a defense to § 1981 claim. Terrell v. United States Pipe & Foundry Co., 644 F.2d 1112, 1118 (5th Cir. 1981); Pettway v. American Cast Iron Pipe Co., 576 F.2d 1157 (5th Cir. 1978), cert. denied, 439 U.S. 1115, 99 S.Ct. 1020, 59 L.Ed.2d 74 (1979).
     
      
      . In most cases, the terms of a seniority system are contained in the contract negotiated between the employer and the union, e.g., Teamsters, supra; however, there is nothing in Title VII, its legislative history, nor the Teamsters case to indicate that a system unilaterally adopted by the employer can not be bona fide. E.E.O.C. v. E.I. du Pont de Nemours & Co., 445 F.Supp. 223, 248 (D.Del.1978). The same is true of a system which is not embodied in a written document. That the terms of the system are not in writing may go to the force of the proof necessary to establish its existence, but that fact does not render the system automatically invalid. In the instant case, defendants succeeded in proving the existence and bona fides of the system through the testimony of witnesses, including one of the plaintiffs, despite the fact that there was no written evidence of the system.
     
      
      
        . Defendants also argue that the named plaintiffs may not represent the class because none testified that he sought work in a grain gang or was denied a deck or wharf position. The Pre-Trial Order, however, refutes this contention. At least one of the named plaintiffs claimed to be a victim of each type of discrimination alleged in this appeal. That they did not prevail on their individual claims does not render them inappropriate representatives. Johnson v. Georgia Highway Express, Inc., 417 F.2d 1122 (5th Cir. 1969).
     
      
      . Defendants interpret the court’s alternative ground as meaning that certification was denied because there was no similarly situated group of employees who could have been discriminated against. They argue that the casual employment relationship between the stevedores and their employees coupled with the manifold personal factors involved in the determination of positions renders the proposed class too differentiated. We disagree with this interpretation. Our understanding of the court’s opinion is that certification was denied because plaintiffs lost on the merits, not because a finding of discrimination was impossible by virtue of the nature of the industry. Furthermore, even if we accepted defendants’ interpretation, we would reject its rationale. As we have already held, the nature of the industry does not shield it from charges of discrimination.
     