opinion: Mr. Justice Blackmun
  delivered the opinion of the Court.
  The sole issue presented in this case is whether the State of Texas, in the person of petitioner, the Sheriff of Hidalgo County, successfully rebutted respondent prisoner’s prima facie showing of discrimination against Mexican-Americans in the state grand jury selection process. In his brief, petitioner, in claiming effective rebuttal, asserts:
  “This list [of the grand jurors that indicted respondent] indicates that 50 percent of the names appearing thereon were Spanish. The record indicates that 3 of the 5 jury commissioners, 5 of the grand jurors who returned the indictment, 7 of the petit jurors, the judge presiding at the trial, and the Sheriff who served notice on the grand jurors to appear had Spanish surnames.” Brief for Petitioner 6.
  I
  This Court on prior occasions has considered the workings of the Texas system of grand jury selection. See Hernandez v. Texas, 347 U.S. 475 (1954); Cassell v. Texas, 339 U. S. 282 (1950); Akins v. Texas, 325 U. S. 398 (1945); Hill v. Texas, 316 U. S. 400 (1942); Smith v. Texas, 311 U. S. 128 (1940). Texas employs the “key man” system, which relies on jury commissioners to select prospective grand jurors from the community at large. The procedure begins with the state district judge’s appointment of from three to five persons to serve as jury commissioners. Tex. Code Crim. Proc., Art. 19.01 (1966). The commissioners then “shall select not less than 15 nor more than 20 persons from the citizens of different portions of the county” to compose the list from which the actual grand jury will be drawn. Art. 19.06 (Supp. 1976-1977). When at least 12 of the persons on the list appear in court pursuant to summons, the district judge proceeds to “test their qualifications.” Art. 19.21. The qualifications themselves are set out in Art. 19.08: A grand juror must be a citizen of Texas and of the county, be a qualified voter in the county, be “of sound mind and good moral character,” be literate, have no prior felony conviction, and be under no pending indictment “or other legal accusation for theft or of any felony.” Interrogation under oath is the method specified for testing the prospective juror’s qualifications. Art. 19.22. The precise questions to be asked are set out in Art. 19.23, which, for the most part, tracks the language of Art. 19.08. After the court finds 12 jurors who meet the statutory qualifications, they are impaneled as the grand jury. Art. 19.26.
  Respondent, Rodrigo Partida, was indicted in March 1972 by the grand jury of the 92d District Court of Hidalgo County for the crime of burglary of a private residence at night with intent to rape. Hidalgo is one of the border counties of southern Texas. After a trial before a petit jury, respondent was convicted and sentenced to eight years in the custody of the Texas Department of Corrections. He first raised his claim of discrimination in the grand jury selection process on a motion for new trial in the State District Court. In support of his motion, respondent testified about the general existence of discrimination against Mexican-Americans in that area of Texas and introduced statistics from the 1970 census and the Hidalgo County grand jury records. The census figures show that in 1970, the population of Hidalgo County was 181,535. United States Bureau of the Census, 1970 Census of Population, Characteristics of the Population, vol. 1, pt. 45, § 1, Table 119, p. 914. Persons of Spanish language or Spanish surname totaled 143,611. Ibid., and id., Table 129, p. 1092. On the assumption that all the persons of Spanish language or Spanish surname were Mexican-Americans, these figures show that 79.1% of the county’s population was Mexican-American.
  Respondent’s data compiled from the Hidalgo County grand jury records from 1962 to 1972 showed that over that period, the average percentage of Spanish-surnamed grand jurors was 39%. In the 2½-year period during which the District Judge who impaneled the jury that indicted respondent was in charge, the average percentage was 45.5%. On the list from which the grand jury that indicted respondent was selected, 50% were Spanish surnamed. The last set of data that respondent introduced, again from the 1970 census, illustrated a number of ways in which Mexican-Americans tend to be underprivileged, including poverty-level incomes, less desirable jobs, substandard housing, and lower levels of education. The State offered no evidence at all either attacking respondent’s allegations of discrimination or demonstrating that his statistics were unreliable in any way.
  The State District Court, nevertheless, denied the motion for a new trial.
  On appeal, the Texas Court of Criminal Appeals affirmed the conviction. Partida v. State, 506 S. W. 2d 209 (1974). Reaching the merits of the claim of grand jury discrimination, the court held that respondent had failed to make out a prima facie case. In the court’s view, he should have shown how many of the females who served on the grand juries were Mexican-Americans married to men with Anglo-American surnames, how many Mexican-Americans were excused for reasons of age or health, or other legal reasons, and how many of those listed by the census would not have met the statutory qualifications of citizenship, literacy, sound mind, moral character, and lack of criminal record or accusation. Id., at 210—211. Quite beyond the uncertainties in the statistics, the court found it impossible to believe that discrimination could have been directed against a Mexican-American, in light of the many elective positions held by Mexican-Americans in the county and the substantial representation of Mexican-Americans on recent grand juries. Id., at 211. In essence, the court refused to presume that Mexican-Americans would discriminate against their own kind.
  After exhausting his state remedies, respondent filed his petition for habeas corpus in the Federal District Court, alleging a denial of due process and equal protection, guaranteed by the Fourteenth Amendment, because of gross underrepresentation of Mexican-Americans on the Hidalgo County grand juries. At a hearing at which the state transcript was introduced, petitioner presented the testimony of the state judge who selected the jury commissioners who had compiled the list from which respondent's grand jury was taken. The judge first reviewed the State’s grand jury selection process. In selecting the jury commissioners, the judge stated that he tried to appoint a greater number of Mexican-Americans than members of other ethnic groups. He testified that he instructed the commissioners about the qualifications of a grand juror and the exemptions provided by law. The record is silent, however, with regard to instructions dealing with the potential problem of discrimination directed against any identifiable group. The judge admitted that the actual results of the selection process had not produced grand jury lists that were “representative of the ethnic balance in the community.” App. 84. The jury commissioners themselves, who were the only ones in a position to explain the apparent substantial underrepresentation of Mexican-Americans and to provide information on the actual operation of the selection process, were never called.
  On the basis of the evidence before it, the court concluded that respondent had made out a “bare prima facie case” of invidious discrimination with his proof of “a long continued disproportion in the composition of the grand juries in Hidalgo County.” 384 F. Supp. 79, 90 (SD Tex. 1974) (emphasis in original). Based on an examination of the reliability of the statistics offered by respondent, however, despite the lack of evidence in the record justifying such an inquiry, the court stated that the prima facie case was weak. The court believed that the census statistics did not reflect the true situation accurately, because of recent changes in the Hidalgo County area and the court’s own impression of the demographic characteristics of the Mexican-American community. On the other hand, the court recognized that the Texas key-man system of grand jury selection was highly subjective, and was “archaic and inefficient,” id., at 91, and that this was a factor arguing for less tolerance in the percentage differences. On balance, the court’s doubts about the reliability of the statistics, coupled with its opinion that Mexican-Americans constituted a “governing majority” in the county, caused it to conclude that the prima facie case was rebutted. The “governing majority” theory distinguished respondent’s case from all preceding cases involving similar disparities. On the basis of those findings, the court dismissed the petition.
  The United States Court of Appeals for the Fifth Circuit reversed. 524 F. 2d 481 (1975). It agreed with the District Court that respondent had succeeded in making out a prima facie case. It found, however, that the State had failed to rebut that showing. The “governing majority” theory contributed little to the State’s case in the absence of specific proof to explain the disparity. In light of the State’s abdication of its responsibility to introduce controverting evidence, the court held that respondent was entitled to prevail.
  We granted certiorari to consider whether the existence of a “governing majority” in itself can rebut a prima facie case of discrimination in grand jury selection, and, if not, whether the State otherwise met its burden of proof. 426 U. S. 934 (1976).
  III
  A. This Court has long recognized that “it is a denial of the equal protection of the laws to try a defendant of a particular race or color under an indictment issued by a grand jury . . . from which all persons of his race or color have, solely because of that race or color, been excluded by the State . . . .” Hernandez v. Texas, 347 U. S., at 477. See Alexander v. Louisiana, 405 U. S. 625, 628 (1972); Carter v. Jury Comm’n, 396 U. S. 320, 330 (1970). See also Peters v. Kiff, 407 U. S. 493, 497 (1972) (plurality opinion); id., at 507 (dissenting opinion). While the earlier cases involved absolute exclusion of an identifiable group, later cases established the principle that substantial underrepresentation of the group constitutes a constitutional violation as well, if it results from purposeful discrimination. See Turner v. Fouche, 396 U. S. 346 (1970); Carter v. Jury Comm’n, supra; Whitus v. Georgia, 385 U. S. 545, 552 (1967); Swain v. Alabama, 380 U. S. 202 (1965); Cassell v. Texas, 339 U. S. 282 (1950). Recent cases have established the fact that an official act is not unconstitutional solely because it has a racially disproportionate impact. Washington v. Davis, 426 U. S. 229, 239 (1976) ; see Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252, 264-265 (1977). Nevertheless, as the Court recognized in Arlington Heights, “[s]ometimes a clear pattern, unexplainable on grounds other than race, emerges from the effect of the state action even when the governing legislation appears neutral on its face.” Id., at 266. In Washington v. Davis, the application of these principles to the jury cases was considered:
  “It is also clear from the cases dealing with racial discrimination in the selection of juries that the systematic exclusion of Negroes is itself such an 'unequal application of the law . . . as to show intentional discrimination.’ . . . A prima facie case of discriminatory purpose may be proved as well by the absence of Negroes on a particular jury combined with the failure of the jury commissioners to be informed of eligible Negro jurors in a community, . . . or with racially non-neutral selection procedures . . . . With a prima facie case made out, ‘the burden of proof shifts to the State to rebut the presumption of unconstitutional action by showing that permissible racially neutral selection criteria and procedures have produced the monochromatic result.’ Alexander [v. Louisiana, 405 U. S.,] at 632.” 426 U. S., at 241.
  See Arlington Heights, supra, at 266 n. 13.
  Thus, in order to show that an equal protection violation has occurred in the context of grand jury selection, the defendant must show that the procedure employed resulted in substantial underrepresentation of his race or of the identifiable group to which he belongs. The first step is to establish that the group is one that is a recognizable, distinct class, singled out for different treatment under the laws, as written or as applied. Hernandez v. Texas, 347 U. S., at 478-479. Next, the degree of underrepresentation must be proved, by comparing the proportion of the group in the total population to the proportion called to serve as grand jurors, over a significant period of time. Id., at 480. See Norris v. Alabama, 294 U. S. 587 (1935). This method of proof, sometimes called the “rule of exclusion,” has been held to be available as a method of proving discrimination in jury selection against a delineated class. Hernandez v. Texas, 347 U. S., at 480. Finally, as noted above, a selection procedure that is susceptible of abuse or is not racially neutral supports the presumption of discrimination raised by the statistical showing. Washington v. Davis, 426 U. S., at 241; Alexander v. Louisiana, 405 U. S., at 630. Once the defendant has shown substantial underrepresentation of his group, he has made out a prima facie case of discriminatory purpose, and the burden then shifts to the State to rebut that case.
  B. In this case, it is no longer open to dispute that Mexican-Americans are a clearly identifiable class. See, e. g., Hernandez v. Texas, supra. Cf. White v. Regester, 412 U. S. 755, 767 (1973). The statistics introduced by respondent from the 1970 census illustrate disadvantages to which the group has been subject. Additionally, as in Alexander v. Louisiana, the selection procedure is not racially neutral with respect to Mexican-Americans; Spanish surnames are just as easily identifiable as race was from the questionnaires in Alexander or the notations and card colors in Whitus v. Georgia, supra, and in Avery v. Georgia, 345 U. S. 559 (1953).
  The disparity proved by the 1970 census statistics showed that the population of the county was 79.1% Mexican-American, but that, over an 11-year period, only 39% of the persons summoned for grand jury service were Mexican-American. This difference of 40% is greater than that found significant in Turner v. Fouche, 396 U. S. 346 (1970) (60% Negroes in the general population, 37% on the grand jury lists). Since the State presented no evidence showing why the 11-year period was not reliable, we take it as the relevant base for comparison. The mathematical disparities that have been accepted by this Court as adequate for a prima facie case have all been within the range presented here. For example, in Whitus v. Georgia, 385 U. S. 545 (1967), the number of Negroes listed on the tax digest amounted to 27.1% of the taxpayers, but only 9.1% of those on the grand jury venire. The disparity was held to be sufficient to make out a prima facie case of discrimination. See Sims v. Georgia, 389 U. S. 404 (1967) (24.4% of tax lists, 4.7% of grand jury lists); Jones v. Georgia, 389 U. S. 24 (1967) (19.7% of tax lists, 5% of jury list). We agree with the District Court and the Court of Appeals that the proof in this case was enough to establish a prima facie case of discrimination against the Mexican-Americans in the Hidalgo County grand jury selection.
  Supporting this conclusion is the fact that the Texas system of selecting grand jurors is highly subjective. The facial constitutionality of the key-man system, of course, has been accepted by this Court. See, e. g., Carter v. Jury Comm’n, 396 U. S. 320 (1970); Akins v. Texas, 325 U. S. 398 (1945) ; Smith v. Texas, 311 U. S. 128 (1940). Nevertheless, the Court has noted that the system is susceptible of abuse as applied. See Hernandez v. Texas, 347 U. S., at 479. Additionally, as noted, persons with Spanish surnames are readily identifiable.
  The showing made by respondent therefore shifted the burden of proof to the State to dispel the inference of intentional discrimination. Inexplicably, the State introduced practically no evidence. The testimony of the State District Judge dealt principally with the selection of the jury commissioners and the instructions given to them. The commissioners themselves were not called to testify. A case such as Swain v. Alabama, 380 U. S., at 207 n. 4, 209, illustrates the potential usefulness of such testimony, when it sets out in detail the procedures followed by the commissioners. The opinion of the Texas Court of Criminal Appeals is particularly revealing as to the lack of rebuttal evidence in the record:
  “How many of those listed in the census figures with Mexican-American names were not citizens of the state, but were so-called ‘wet-backs’ from the south side of the Rio Grande; how many were migrant workers and not residents of Hidalgo County; how many were illiterate and could not read and write; how many were not of sound mind and good moral character; how many had been convicted of a felony or were under indictment or legal accusation for theft or a felony; none of these facts appear in the record.” 506 S. W. 2d, at 211 (emphasis added).
  In fact, the census figures showed that only a small part of the population reported for Hidalgo County was not native born. See n. 6, supra. Without some testimony from the grand jury commissioners about the method by which they determined the other qualifications for grand jurors prior to the statutory time for testing qualifications, it is impossible to draw any inference about literacy, sound mind and moral character, and criminal record from the statistics about the population as a whole. See n. 8, supra. These are questions of disputed fact that present problems not amenable to resolution by an appellate court. We emphasize, however, that we are not saying that the statistical disparities proved here could never be explained in another case; we are simply saying that the State did not do so in this case. See Turner v. Fouche, 396 U. S., at 361.
  C. In light of our holding that respondent proved a prima facie case of discrimination that was not rebutted by any of the evidence presently in the record, we have only to consider whether the District Court’s “governing majority” theory filled the evidentiary gap. In our view, it did not dispel the presumption of purposeful discrimination in the circumstances of this case. Because of the many facets of human motivation, it would be unwise to presume as a matter of law that human beings of one definable group will not discriminate against other members of their group. Indeed, even the dissent of Mr. Justice Powell does not suggest that such a presumption would be appropriate. See post, at 514-516, n. 6, 516 n. 7. The problem is a complex one, about which widely differing views can be held, and, as such, it would be somewhat precipitate to take judicial notice of one view over another on the basis of a record as barren as this.
  Furthermore, the relevance of a governing majority of elected officials to the grand jury selection process is questionable. The fact that certain elected officials are Mexican-American demonstrates nothing about the motivations and methods of the grand jury commissioners who select persons for grand jury lists. The only arguably relevant fact in this record on the issue is that three of the five jury commissioners in respondent’s case were Mexican-American. Knowing only this, we would be forced to rely on the reasoning that we have rejected—that human beings would not discriminate against their own kind—in order to find that the presumption of purposeful discrimination was rebutted. Without the benefit of this simple behavioral presumption, discriminatory intent can be rebutted only with evidence in the record about the way in which the commissioners operated and their reasons for doing so. It was the State’s burden to supply such evidence, once respondent established his prima facie case. The State’s failure in this regard leaves unchallenged respondent’s proof of purposeful discrimination.
  Finally, even if a “governing majority” theory has general applicability in cases of this kind, the inadequacy of the record in this case does not permit such an approach. Among the evidentiary deficiencies are the lack of any indication of how long the Mexican-Americans have enjoyed “governing majority” status, the absence of information about the relative power inherent in the elective offices held by Mexican-Americans, and the uncertain relevance of the general political power to the specific issue in this case. Even for the most recent time period, when presumably the political power of Mexican-Americans was at its greatest, the discrepancy between the number of Mexican-Americans in the total population and the number on the grand jury lists was substantial. Thus, under the facts presented in this case, the “governing majority” theory is not developed fully enough to satisfy the State’s burden of rebuttal.
  IV
  Rather than relying on an approach to the jury discrimination question that is as faintly defined as the “governing majority” theory is on this record, we prefer to look at all the facts that bear on the issue, such as the statistical disparities, the method of selection, and any other relevant testimony as to the manner in which the selection process was implemented. Under this standard, the proof offered by respondent was sufficient to demonstrate a prima facie case of discrimination in grand jury selection. Since the State failed to rebut the presumption of purposeful discrimination by competent testimony, despite two opportunities to do so, we affirm the Court of Appeals’ holding of a denial of equal protection of the law in the grand jury selection process in respondent’s case.
  It is so ordered.
  The other principal state mode of juror selection is a random method similar to that used in the federal system. See 28 U. S. C. § 1864. See generally Sperlich & Jaspovice, Grand Juries, Grand Jurors and the Constitution, 1 Hastings Const. L. Q. 63, 68 (1974).
  During the time period covered by this case, the statute was amended to omit the requirement that the commissioners be freeholders in the county. 1971 Tex. Gen. Laws, c. 131, § 1. That change has no bearing on the issues before us.
  Prior to 1965, the law directed the commissioners to select “sixteen men.” The legislature amended the statute that year to substitute the words “twenty persons” for “sixteen men.” 1965 Tex. Gen. Laws, c. 722, p. 317. In 1967, the law was amended again to provide the present range of from 15 to 20 persons. 1967 Tex. Gen. Laws, c. 515, § 1. These changes in the number of persons required to be on the list account for the jump from 16 to 20 in the grand jury list statistics set forth in n. 7, infra.
  In the state courts and in the federal courts on habeas, the State argued that respondent’s challenge was not timely raised as a matter of state procedure, and therefore that he waived any complaint of this kind that he might have. Since the Texas courts considered the claim on its merits, however, we are free to do so here. See Coleman v. Alabama, 377 U. S. 129 (1964); cf. Francis v. Henderson, 425 U. S. 536, 542 n. 5 (1976). Furthermore, petitioner abandoned the waiver point in his petition for certiorari.
  For our purposes, the terms “Spanish-surnamed” and “Mexican-American” are used as synonyms for the census designation “Persons of Spanish Language or Spanish Surname.” Persons of Spanish language include both those whose mother tongue is Spanish and all other persons in families in which the head of the household or spouse reported Spanish as the mother tongue. Persons of Spanish surname, as the census uses that term, are determined by reference to a list of 8,000 Spanish surnames compiled by the Immigration and Naturalization Service. For Texas, social and economic characteristics are presented for persons of Spanish language combined with all other persons of Spanish surname in the census reports. United States Bureau of the Census, 1970 Census of Population, Characteristics of the Population, vol. 1, pt. 45, § 2, App. B.
  At oral argument, counsel for petitioner appears to have suggested that the presence of illegal aliens who have Spanish surnames might inflate the percentage of Mexican-Americans in the county’s population. Tr. of Oral Arg. 10-12. We cannot agree that the presence of noncitizens makes any practical difference. Table 119 of the census breaks down the 181,535 people who composed the total county population into three groups: native of native parentage, native of foreign parentage, and foreign born. The only persons as to whom the assumption of noncitizenship would be logically sustainable are the foreign born. Even for them, it is probable that some were naturalized citizens. Furthermore, only 22,845 persons were in the “foreign born” category. If those persons are excluded from the population of the county, the total becomes 158,690. Assuming that every foreign-born person was counted as a Spanish-surnamed person (an assumption that favors the State), the total number of Mexican-Americans is reduced from 143,611 to 120,766. Using these adjusted figures, Mexican-Americans constitute 76.1% of the county’s population, a figure only 3%, and thus negligibly, smaller than the one used throughout this litigation. For consistency, we shall continue to refer to the population figures for the entire county, particularly since the State has not shown why those figures are unreliable.
  The statistics for grand jury composition can be organized as follows:
  Year No. persons on grand jury list Av. No. Spanish surnamed per list Percentage Spanish surnamed
  1962 16 6 37.5%
  1963 16 5.75 35.9%
  1964 16 4.75 29.7%
  1965 16.2 5 30.9%
  1966 20 7.5 37.5%
  1967 20.25 7.25 35.8%
  1968 20 6.6 33%
  1969 20 10 50%
  1970 20 8 40%
  1971 20 9.4 47%
  1972 20 10.5 52.5%
  Of the 870 persons who were summoned to serve as grand jurors over the 11-year period, 339, or 39%, were Spanish surnamed. See table showing Hidalgo County grand jury panels from 1962 to 1972, App. 17-18.
  At oral argument, counsel for petitioner suggested that the date regarding educational background explained the discrepancy between the percentage of Mexican-Americans in the total population and the percentage on the grand jury lists. Tr. of Oral Arg. 8. For a variety of reasons, we cannot accept that suggestion. First, under the Texas method of selecting grand jurors, qualifications are not tested until the persons on the list appear in the District Court. Prior to that time, assuming an unbiased selection procedure, persons of all educational characteristics should appear on the list. If the jury commissioners actually exercised some means of winnowing those who lacked the ability to read and write, it was incumbent on the State to call the commissioners and to have them explain how this was done. In the absence of any evidence in the record to this effect, we shall not assume that the only people excluded from grand jury service were the illiterate.
  Second, it is difficult to draw valid inferences from the raw census data, since the data are incomplete in some places and the definition of “literacy” would undoubtedly be the subject of some dispute in any event. The State’s failure to discuss the literacy problem at any point prior to oral argument compounds the difficulties. One gap in the data occurs with respect to the younger persons in the jury pool. The census reports for educational background cover only those who are 25 years of age and above. Yet the only age limitation on eligibility for grand jury service is qualification to vote. Tex. Code Crim. Proc., Art. 19.08 (Supp. 1976-1977). During the period to which the census figures apply, a person became qualified to vote at age 21. Tex. Elec. Code, Art. 5.01 (1967). (In 1975, Art. 5.01 was amended to give the franchise to all persons 18 and over. 1975 Tex. Gen. Laws, c. 682, § 3.) It is not improbable that the educational characteristics of persons in the younger age group would prove to be favorable to Mexican-Americans.
  Finally, even assuming that the statistics for persons age 25 and over are sufficiently representative to be useful, a significant discrepancy still exists between the number of Spanish-surnamed people and the level of representation on grand jury lists. Table 83 of the 1970 census shows that of a total of 80,049 persons in that age group, 13,205 have no schooling. (Data for McAllen-Pharr-Edinburg Standard Metropolitan Statistical Area. This SMSA is identical to Hidalgo County.) Table 97 shows that of the 55,949 Spanish-surnamed persons in the group, 12,817 have no schooling. This means that of the 24,100 persons of all other races and ethnic groups, 388 have no schooling. Translated into percentages, 22.9% of the Spanish-surnamed persons have no schooling, and 1.6% of the others have no schooling. This means that 43,132 of the Spanish-surnamed persons have some schooling and 23,712 of the others have some schooling. The Spanish-surnamed persons thus represent 65% of the 66,844 with some schooling, and the others 35%. The 65% figure still creates a significant disparity when compared to the 39% representation on grand juries shown over the 11-year period involved here.
  The suggestion is made in the dissenting opinion of The Chief Justice, post, at 504-506, that reliance on eligible population figures and allowance for literacy would defeat respondent’s prima facie showing of discrimination. But the 65% to 39% disparity between Mexican-Americans over the age of 25 who have some schooling and Mexican-Americans represented on the grand jury venires takes both of The Chief Justice’s concerns into account. Statistical analysis, which is described in more detail in n. 17, infra, indicates that the discrepancy is significant. If one assumes that Mexican-Americans constitute only 65% of the jury pool, then a detailed calculation reveals that the likelihood that so substantial a discrepancy would occur by chance is less than 1 in 1050.
  We prefer not to rely on the 65% to 39% disparity, however, since there are so many implicit assumptions in this analysis, and we consider it inappropriate for us, as an appellate tribunal, to undertake this kind of inquiry without a record below in which those assumptions were tested. We rest, instead, on the fact that the record does not show any way by which the educational characteristics are taken into account in the compilation of the grand jury lists, since the procedure established by the State provides that literacy is tested only after the group of 20 are summoned.
  The court noted that the foreman of the grand jury that indicted respondent was Mexican-American, and that 10 of the 20 summoned to serve had Spanish surnames. Seven of the 12 members of the petit jury that convicted him were Mexican-American. In addition, the state judge who presided over the trial was Mexican-American, as were a number of other elected officials in the county.
  The Federal District Judge observed, during the state judge’s testimony, that the selection process for grand jurors in Hidalgo County typically resulted in a progressive reduction of the number of Mexican-Americans involved at each stage. See Alexander v. Louisiana, 405 U. S. 625 (1972). For example, said the court, if 60% of the jury commissioners were Mexican-American, the jury panel might be only 55%, and the actual grand jury only 43%. The court speculated that the reason for this might be cultural. App. 84-85.
  The court suggested that the actual discrimination operating might be economic. The jury commissioners were from the higher socio-economic classes, and they tended to select prospective jurors from among their peers. Consequently, the number of Mexican-Americans was disproportionately low, since they were concentrated at the lower end of the economic scale. We find it unnecessary to decide whether a showing of simple economic discrimination would be enough to make out a prima facie case in the absence of other evidence, since that case is not before us. Cf. Thiel v. Southern Pacific Co., 328 U. S. 217 (1946).
  Cases in this Court holding unconstitutional discriminatory selection procedures in the grand jury context include Alexander v. Louisiana, supra; Arnold v. North Carolina, 376 U. S. 773 (1964); Eubanks v. Louisiana, 356 U. S. 584 (1958); Reece v. Georgia, 350 U. S. 85 (1955); Cassell v. Texas, 339 U. S. 282 (1950); Hill v. Texas, 316 U. S. 400 (1942); Smith v. Texas, 311 U. S. 128 (1940); Pierre v. Louisiana, 306 U. S. 354 (1939) ; Rogers v. Alabama, 192 U. S. 226 (1904); Carter v. Texas, 177 U. S. 442 (1900); and Bush v. Kentucky, 107 U. S. 110 (1883).
  The idea behind the rule of exclusion is not at all complex. If a disparity is sufficiently large, then it is unlikely that it is due solely to chance or accident, and, in the absence of evidence to the contrary, one must conclude that racial or other class-related factors entered into the selection process. See Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252, 266 n. 13 (1977); Washington v. Davis, 426 U. S. 229, 241 (1976); Eubanks v. Louisiana, 356 U. S., at 587; Smith v. Texas, 311 U. S., at 131. Cf. n. 17, infra.
  The dissenters argue that the subjectivity of the system cuts in favor of the State where those who control the selection process are members of the same class as the person claiming discrimination. The fact remains, however, that the class to which respondent belongs was substantially underrepresented on the grand jury lists of Hidalgo County. The dissenters’ argument here is another aspect of the “governing majority” theory, see Part III-C, infra; under the circumstances presented in this case, that theory does not dispel the presumption of purposeful discrimination created by the combined force of the statistical showing and the highly subjective method of selection.
  Since the 1960 census did not compile separate statistics for Spanish-surnamed persons, it is impossible to ascertain whether the percentage of Mexican-Americans in the county changed appreciably over the period of time at issue. We therefore are forced to rely on the assumption that the 79.1% figure remained constant.
  Statistical analysis of the grand jury lists during the 2½-year tenure of the State District Judge who selected the commissioners in respondent’s case reveals that a significant disparity existed over this time period as well. See n. 17, infra. Thus, the District Court’s assumption that reference to a shorter time period would show that the prima facie case of discrimination could not be proved was unwarranted.
  If the jurors were drawn randomly from the general population, then the number of Mexican-Americans in the sample could be modeled by a binomial distribution. See Finkelstein, The Application of Statistical Decision Theory to the Jury Discrimination Cases, 80 Harv. L. Rev. 338, 353—356 (1966). See generally P. Hoel, Introduction to Mathematical Statistics 58-61, 79-86 (4th ed. 1971); F. Mosteller, R. Rourke, & G. Thomas, Probability with Statistical Applications 130-146, 270-291 (2d ed. 1970). Given that 79.1% of the population is Mexican-American, the expected number of Mexican-Americans among the 870 persons summoned to serve as grand jurors over the 11-year period is approximately 688. The observed number is 339. Of course, in any given drawing some fluctuation from the expected number is predicted. The important point, however, is that the statistical model shows that the results of a random drawing are likely to fall in the vicinity of the expected value. See F. Mosteller, R. Rourke, & G. Thomas, supra, at 270-290. The measure of the predicted fluctuations from the expected value is the standard deviation, defined for the binomial distribution as the square root of the product of the total number in the sample (here 870) times the probability of selecting a Mexican-American (0.791) times the probability of selecting a non-Mexican-American (0.209). Id., at 213. Thus, in this case the standard deviation is approximately 12. As 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 the jury drawing was random would be suspect to a social scientist. The 11-year data here reflect a difference between the expected and observed number of Mexican-Americans of approximately 29 standard deviations. A detailed calculation reveals that the likelihood that such a substantial depature from the expected value would occur by chance is less than 1 in 10140.
  The data for the 2½-year period during which the State District Judge supervised the selection process similarly support the inference that the exclusion of Mexican-Americans did not occur by chance. Of 220 persons called to serve as grand jurors, only 100 were Mexican-Americans. The expected Mexican-American representation is approximately 174 and the standard deviation, as calculated from the binomial model, is approximately six. The discrepancy between the expected and observed values is more than 12 standard deviations. Again, a detailed calculation shows that the likelihood of drawing not more than 100 Mexican-Americans by chance is negligible, being less than 1 in 1025.
  It has been said that random selection methods similar to the federal system would probably avoid most of the potential for abuse found in the key-man system. See Sperlich & Jaspovice, supra, n. 1.
  This is not to say, of course, that a simple protestation from a commissioner that racial considerations played no part in the selection would be enough. This kind of testimony has been found insufficient on several occasions. E. g., Alexander v. Louisiana, 405 U. S., at 632; Hernandez v. Texas, 347 U. S. 475, 481 (1954); Norris v. Alabama, 294 U. S. 587, 598 (1935). Neither is the State entitled to rely on a presumption that the officials discharged their sworn duties to rebut the case of discrimination. Jones v. Georgia, 389 U. S. 24 (1967).
  This is not a case where a majority is practicing benevolent discrimination in favor of a traditionally disfavored minority, although that situation illustrates that motivations not immediately obvious might enter into discrimination against “one’s own kind.”
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