The following table shows the average estimate among all respondents. Because total estimates exceed 100%*, the third column adjusts for this and displays results as if each racial category is mutually exclusive and capture the population in its entirety. The fourth column shows the actual percentages of each group as recorded by the 2000 US Census. Finally, the fifth column shows to what extent a group's size is over(under)estimated:
It probably comes as little surprise to find that the white share of the population is underestimated, while the shares of the four non-white groups was overestimated. The same general tendency applies to the popular media depictions of American demography, after all.
Steve Sailer has noted on multiple occasions that in the media's conception of race-related issues, there are three categories: White, black, and other. By the turn of the century, though, Hispanics had already displaced blacks as the largest non-white group in the US.
At first blush, the (non-Hispanic) public's conception seemed to mirror the that of the media. It appears a bit more nuanced than that, however. Asians and Native Americans are both extremely overstated (by factors of 5 and 20, respectively) in the public mind, suggesting that the general notion is of minority groups making up somewhere between one-tenth and one-fifth of the population a piece without much differentiation between their sizes, except in the case of blacks, who comprise the nation's head minority group.
This is not merely a function of non-whites overestimating the size of their respective groups, either. At best, that marginally skews the numbers towards the white share being understated and the non-white shares being overstated. The next table shows the same, but only non-Hispanic white respondents are included:
Not much variance. Despite often being portrayed as clueless dolts, the American public is actually quite progressive in its assumptions! These dreams shall come!
Parenthetically, the question is, interestingly, also asked with regards to size of the US' Jewish population. The average estimate, at 17.7%, is nearly an order of magnitude larger than is actually the case, although that estimate would probably come in too low as a relative measure of Jewish influence on American popular media!
GSS variables used: RACECEN1, USBLK, USWHT, USHISP, USASN, USAMIND, USJEWS
* Likely for a variety of reasons: Responses were given all at once, but as individual answers to individual questions, so it would not have been natural for people to ensure the totals added up to exactly 100%; there were surely some people (especially Hispanics) who considered many Hispanics to also be white, and some to also be black; similarly, there were respondents who took multiracial people into account and presumably double-counted them; presuming a group is more diminutive than is actually the case is vaguely considered to be insulting, so better to error on the high end than on the low side.