Using common, widely accepted IQ charts, what % of whites have IQ of 80 or less?

In common, widely accepted IQ scales (such as Wechsler or Stanford-Binet tests), scores are normalized to a normal (bell curve) distribution with a mean of 100 and a standard deviation (SD) of 15 for the general population, and this is the standard reference applied to white (non-Hispanic white) Americans in most psychometric literature and discussions.

An IQ of 80 is exactly 1.333 SD below the mean (calculation: (100 - 80) / 15 = 20 / 15 ≈ 1.333).

For a standard normal distribution:

The cumulative probability (percentage below a given z-score) can be found using z-tables or calculators.

z = -1.333 corresponds to approximately 9.1% of the population scoring 80 or below.

This is a precise value from the standard normal cumulative distribution function (CDF). Sources often round it slightly:

One common reference table lists ~9% below IQ 80.

Some discussions approximate it as "less than 10%" or around 9-10%.

Multiple sources analyzing US data (including bell curve descriptions for whites centered at mean 100, SD 15) explicitly state that less than 10% of whites have an IQ below 80 (often phrased as "<10%" or "~9%").

For context, this contrasts with estimates for other groups in the literature (e.g., ~35% for blacks when their mean is ~85 with similar SD), but for whites specifically, the figure aligns with the ~9% calculation under the standard assumptions.

To arrive at this yourself without a calculator:

1 SD below mean (IQ 85) covers ~16% below it (since ~68% are within ±1 SD, so half of the remaining 32% is ~16% below 85).

2 SD below (IQ 70) covers ~2.3% below it.

IQ 80 falls between these (closer to 1.33 SD), so interpolate roughly between 16% and 2.3% → lands around 9%.

Thus, approximately 9% (or roughly 9-10%, commonly rounded as less than 10%) of whites have an IQ of 80 or less under these standard parameters.

ok, using those same IQ charts, what % of blacks have IQ at or below 80?

Using the same widely accepted IQ charts and assumptions as before (normal distribution with SD = 15, white mean = 100), the standard reference point in the psychometric literature for African Americans (blacks in the US) is a mean IQ of 85 (1 SD below whites, or about 15 points lower on average, as reported in sources like The Bell Curve, Rushton & Jensen reviews, Brookings analyses, Roth et al. meta-analysis, and many others).

An IQ of 80 is then (80 - 85) / 15 = -0.333 SD below the black mean.

For a standard normal distribution:

The cumulative probability below z = -0.333 is approximately 36.9% (precise CDF value from statistical tables/calculators: norm.cdf(-1/3) ≈ 0.3694, or roughly 37%).

This aligns closely with common statements in the literature:

Around 35% of blacks score below 80 (often cited as a round figure in summaries comparing to whites' ~9-10% below 80).

For example, one detailed analysis notes "~35% of blacks have an IQ below 80, compared to less than 10% of whites" under these parameters.

Another source contrasts it with military enlistment cutoffs (AFQT/IQ ~80-83 often disqualifying ~30-35% of blacks vs. ~10% of whites).

To calculate this yourself (without software):

0 SD (IQ 85) → 50% below.

-1 SD (IQ 70) → ~16% below.

IQ 80 is one-third of the way from 85 to 70, so roughly interpolate: from 50% down toward 16% by about one-third of that 34% drop → lands around 50% - 11-12% ≈ 38-39%, close to the precise 37%.

Thus, approximately 35-37% (commonly rounded as ~35% or about one-third) of blacks have an IQ of 80 or below under these standard assumptions. Note that some recent data suggest slight narrowing of the mean gap (e.g., to ~10-12 points in certain samples), which would reduce this percentage a bit, but the classic / most-referenced figure uses the 85 mean.

ok, so these charts typically don't include hispanics, but are there numbers for the % of hispanics with 80 IQ and below?

Yes, using the same widely accepted IQ charts and normalization (mean of 100 and SD of 15 for non-Hispanic whites, normal distribution), the psychometric literature often places the average IQ for US Hispanics (primarily Mexican-American and other Latin American descent groups) around 89 (a gap of about 0.73 SD below whites, or roughly 11 points lower). This figure appears consistently in sources referencing The Bell Curve, Rushton & Jensen reviews, Roth et al. meta-analyses, and similar discussions (e.g., averages cited as 89 for Hispanics vs. 85 for blacks and 100/103 for whites).

More recent or NAEP-based estimates sometimes show a slightly higher mean for Hispanics (e.g., around 90-94 in adjusted or later data, reflecting some narrowing of gaps over generations, especially for second+ generation individuals), but the classic / most-referenced value in these bell curve-style comparisons is ~89.

An IQ of 80 is then (80 - 89) / 15 = -0.6 SD below the Hispanic mean.

For a standard normal distribution:

The cumulative probability below z = -0.6 is approximately 27.4% (from z-tables/CDF: norm.cdf(-0.6) ≈ 0.2743, or roughly 27-28%).

This is a direct calculation under the assumptions:

At the mean (IQ 89) → 50% below.

At -1 SD (IQ 74) → ~16% below.

IQ 80 is 0.6 SD below the mean, so interpolate roughly: the drop from 50% to 16% over 1 SD is 34%, so over 0.6 SD it's about 0.6 × 34% ≈ 20.4% drop → 50% - 20.4% ≈ 29.6%, close to the precise 27.4% (slight variance due to non-linear CDF).

In the literature, direct statements on the percentage below 80 for Hispanics are less common than for blacks/whites, but the figure aligns with intermediate positioning: higher than the ~35-37% for blacks (mean 85) but substantially higher than the ~9% for whites (mean 100). Some sources note Hispanics fall "midway" or between blacks and whites in distribution terms, which supports around 25-30% below 80 depending on the exact mean used.

Note that gaps can vary by generation (first-generation immigrants often score lower due to language/cultural factors, with narrowing in second+ generations to ~0.57 SD below whites in some meta-analyses), and recent trends show modest closing of the white-Hispanic gap (e.g., NAEP data suggesting effective means closer to 93-94 in some cohorts). Using the standard 89 mean, however, yields approximately 27-28% (or commonly rounded as about one-quarter to one-third) of US Hispanics having an IQ of 80 or below under these parameters.

can you do the same percentages for 75 IQ and below?

Using the same widely accepted IQ charts and normalization as before (normal distribution, SD = 15 for all groups, white/non-Hispanic white mean = 100, black/African American mean = 85, Hispanic/Latino mean = 89), here are the percentages scoring 75 or below (IQ ≤ 75). An IQ of 75 is 2 SD below the white mean, often a threshold discussed in contexts like mild intellectual disability or low cognitive functioning.

Whites (mean 100):

z = (75 - 100) / 15 = -1.667 SD

Cumulative probability below this z-score ≈ 4.8% (from standard normal CDF/z-tables; commonly rounded as ~5% in sources like The Bell Curve population distribution tables, which show about 5% of the general US population below 75, but closer to 4-5% for whites specifically given their higher mean).

Blacks (mean 85):

z = (75 - 85) / 15 = -0.667 SD

Cumulative probability ≈ 25.3% (precisely 25.25% from calculation; literature often cites ~16% below 70 for blacks vs. ~2-3% for whites, and the figure for ≤75 falls in the mid-20% range under the 85 mean assumption, consistent with distributions where ~25% are more than ~0.67 SD below their group mean).

Hispanics (mean 89):

z = (75 - 89) / 15 = -0.933 SD

Cumulative probability ≈ 17.5% (precisely 17.53% from calculation; this positions Hispanics intermediately, higher than blacks but well above whites, aligning with their mean between the two groups in classic references).

To arrive at these yourself using a standard normal distribution (without software):

For any mean μ and SD 15, z = (75 - μ) / 15.

Look up the CDF for that negative z (area to the left).

Common z-table anchors:  

z = -1.67 ≈ 4.75-4.8% (whites).  

z = -0.67 ≈ 25.1-25.3% (blacks, close to -2/3 SD).  

z = -0.93 ≈ 17.6% (Hispanics, roughly midway in drop from 50%).

These are the standard bell-curve calculations under the referenced parameters (e.g., as in The Bell Curve, Rushton-Jensen reviews, APA task force summaries, and related psychometric sources). Note that IQ 75 or below is often linked to borderline/mild intellectual disability criteria (with prevalence around 2-3% in the general population, but higher in lower-mean groups). Recent trends (e.g., some NAEP-based analyses) suggest modest gap narrowing, particularly for Hispanics and to a lesser extent blacks, which could slightly lower these percentages in newer cohorts, but the classic/most-cited figures use the means above.