Opinion of the Court

433 U.S. standard, the appellate court found 16 cases of individual discrimination,10 which "buttressed" the statistical proof. Because Hazelwood had not rebutted the Government's prima facie case of a pattern or practice of racial discrimination, the Court of Appeals directed judgment for the Government and prescribed the remedial order to be entered."

11

We granted certiorari, 429 U. S. 1037, to consider a substantial question affecting the enforcement of a pervasive federal law.

The petitioners primarily attack the judgment of the Court of Appeals for its reliance on "undifferentiated work force statistics to find an unrebutted prima facie case of employment discrimination." 12 The question they raise, in short, is

10 The Court of Appeals held that none of the 16 prima facie cases of individual discrimination had been rebutted by the petitioners. See 534 F.2d, at 814.

11 The District Court was directed to order that the petitioners cease from discriminating on the basis of race or color in the hiring of teachers, promulgate accurate job descriptions and hiring criteria, recruit Negro and white applicants on an equal basis, give preference in filling vacancies to the 16 discriminatorily rejected applicants, make appropriate backpay awards, and submit periodic reports to the Government on its progress in hiring qualified Negro teachers. Id., at 819-820.

12 In their petition for certiorari and brief on the merits, the petitioners have phrased the question as follows:

"Whether a court may disregard evidence that an employer has treated actual job applicants in a nondiscriminatory manner and rely on undifferentiated workforce statistics to find an unrebutted prima facie case of employment discrimination in violation of Title VII of the Civil Rights Act of 1964."

Their petition for certiorari and brief on the merits did raise a second question: "Whether Congress has authority under Section 5 of the Fourteenth Amendment to prohibit by Title VII of the Civil Rights Act of 1964 employment practices of an agency of a state government in the absence of proof that the agency purposefully discriminated against applicants on the basis of race." That issue, however, is not presented by the facts in this case. The Government's opening statement in the trial court explained that its evidence was designed to show that the scarcity

whether a basic component in the Court of Appeals' finding of a pattern or practice of discrimination-the comparatively small percentage of Negro employees on Hazelwood's teaching staff was lacking in probative force.

This Court's recent consideration in Teamsters v. United States, 431 U. S. 324, of the role of statistics in pattern-orpractice suits under Title VII provides substantial guidance in evaluating the arguments advanced by the petitioners. In that case we stated that it is the Government's burden to "establish by a preponderance of the evidence that racial discrimination was the [employer's] standard operating procedure the regular rather than the unusual practice." Id., at 336. We also noted that statistics can be an important source of proof in employment discrimination cases, since

"absent explanation, it is ordinarily to be expected that nondiscriminatory hiring practices will in time result in a work force more or less representative of the racial and ethnic composition of the population in the community from which employees are hired. Evidence of longlasting and gross disparity between the composition of a work force and that of the general population thus may be significant even though § 703 (j) makes clear that Title VII imposes no requirement that a work force mirror the general population." Id., at 340 n. 20.

See also Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252, 266; Washington v. Davis, 426 U. S. 229, 241-242. Where gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof

of Negro teachers at Hazelwood "is the result of purpose" and is attributable to "deliberately continued employment policies." Thus here, as in Teamsters v. United States, 431 U. S. 324, "[t]he Government's theory of discrimination was simply that the [employer], in violation of § 703 (a) of Title VII, regularly and purposefully treated Negroes. . . less favorably than white persons." Id., at 335 (footnote omitted).

of a pattern or practice of discrimination. Teamsters, supra, at 339.

There can be no doubt, in light of the Teamsters case, that the District Court's comparison of Hazelwood's teacher work force to its student population fundamentally misconceived the role of statistics in employment discrimination cases. The Court of Appeals was correct in the view that a proper comparison was between the racial composition of Hazelwood's teaching staff and the racial composition of the qualified public school teacher population in the relevant labor market." See Teamsters, supra, at 337-338, and n. 17. The percentage of Negroes on Hazelwood's teaching staff in 1972-1973 was 1.4%, and in 1973-1974 it was 1.8%. By contrast, the percentage of qualified Negro teachers in the area was, according to the 1970 census, at least 5.7%. Although these differ

14

13

13 In Teamsters, the comparison between the percentage of Negroes on the employer's work force and the percentage in the general areawide population was highly probative, because the job skill there involvedthe ability to drive a truck-is one that many persons possess or can fairly readily acquire. When special qualifications are required to fill particular jobs, comparisons to the general population (rather than to the smaller group of individuals who possess the necessary qualifications) may have little probative value. The comparative statistics introduced by the Government in the District Court, however, were properly limited to public school teachers, and therefore this is not a case like Mayor v. Educational Equality League, 415 U. S. 605, in which the racialcomposition comparisons failed to take into account special qualifications for the position in question. Id., at 620-621.

Although the petitioners concede as a general matter the probative force of the comparative work-force statistics, they object to the Court of Appeals' heavy reliance on these data on the ground that applicant-flow data, showing the actual percentage of white and Negro applicants for teaching positions at Hazelwood, would be firmer proof. As we have noted, see n. 5, supra, there was no clear evidence of such statistics. We leave it to the District Court on remand to determine whether competent proof of those data can be adduced. If so, it would, of course, be very relevant. Cf. Dothard v. Rawlinson, post, at 330.

14 As is discussed below, the Government contends that a comparative

ences were on their face substantial, the Court of Appeals erred in substituting its judgment for that of the District Court and holding that the Government had conclusively proved its "pattern or practice" lawsuit.

The Court of Appeals totally disregarded the possibility that this prima facie statistical proof in the record might at the trial court level be rebutted by statistics dealing with Hazelwood's hiring after it became subject to Title VII. Racial discrimination by public employers was not made illegal under Title VII until March 24, 1972. A public employer who from that date forward made all its employment decisions in a wholly nondiscriminatory way would not violate Title VII even if it had formerly maintained an all-white work force by purposefully excluding Negroes.15 For this rea

figure of 15.4%, rather than 5.7%, is the appropriate one. See infra, at 310-312. But even assuming, arguendo, that the 5.7% figure urged by the petitioners is correct, the disparity between that figure and the percentage of Negroes on Hazelwood's teaching staff would be more than fourfold for the 1972-1973 school year, and threefold for the 1973-1974 school year. A precise method of measuring the significance of such statistical disparities was explained in Castaneda v. Partida, 430 U. S. 482, 496-497, n. 17. It involves calculation of the "standard deviation" as a measure of predicted fluctuations from the expected value of a sample. Using the 5.7% figure as the basis for calculating the expected value, the expected number of Negroes on the Hazelwood teaching staff would be roughly 63 in 19721973 and 70 in 1973-1974. The observed number in those years was 16 and 22, respectively. The difference between the observed and expected values was more than six standard deviations in 1972-1973 and more than five standard deviations in 1973-1974. The Court in Castaneda noted that "[a]s a general rule for such large samples, if the difference between the expected value and the observed number is greater than two or three standard deviations," then the hypothesis that teachers were hired without regard to race would be suspect. 430 U. S., at 497 n. 17.

15 This is not to say that evidence of pre-Act discrimination can never have any probative force. Proof that an employer engaged in racial discrimination prior to the effective date of Title VII might in some circumstances support the inference that such discrimination continued, particularly where relevant aspects of the decisionmaking process had

son, the Court cautioned in the Teamsters opinion that once a prima facie case has been established by statistical workforce disparities, the employer must be given an opportunity to show that "the claimed discriminatory pattern is a product of pre-Act hiring rather than unlawful post-Act discrimination." 431 U. S., at 360.

The record in this case showed that for the 1972-1973 school year, Hazelwood hired 282 new teachers, 10 of whom (3:5%) were Negroes; for the following school year it hired 123 new teachers, 5 of whom (4.1%) were Negroes. Over the two-year period, Negroes constituted a total of 15 of the 405 new teachers hired (3.7%). Although the Court of Appeals briefly mentioned these data in reciting the facts, it wholly ignored them in discussing whether the Government had shown a pattern or practice of discrimination. And it gave no consideration at all to the possibility that post-Act data as to the number of Negroes hired compared to the total number of Negro applicants might tell a totally different story.16

What the hiring figures prove obviously depends upon the figures to which they are compared. The Court of Appeals accepted the Government's argument that the relevant comparison was to the labor market area of St. Louis County and the city of St. Louis, in which, according to the 1970 census, 15.4% of all teachers were Negro. The propriety of that comparison was vigorously disputed by the petitioners, who urged that because the city of St. Louis has made special attempts to maintain a 50% Negro teaching staff, inclusion of undergone little change. Cf. Fed. Rule Evid. 406; Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252, 267; 1 J. Wigmore, Evidence § 92 (3d ed. 1940); 2 id., §§ 302-305, 371, 375. And, of course, a public employer even before the extension of Title VII in 1972 was subject to the command of the Fourteenth Amendment not to engage in purposeful racial discrimination.

16 See n. 13, supra, and n. 21, infra. But cf. Teamsters, 431 U. S., at 364-367.