IQ Standard Deviation: What the Numbers Mean

The same positions on three scales

A position on the curve keeps its percentile; the number that names it depends on the scale’s standard deviation.

Position	SD 15	SD 16	SD 24
−2 SDPercentile 2.3	70	68	52
−1 SDPercentile 15.9	85	84	76
MeanPercentile 50.0	100	100	100
+1 SDPercentile 84.1	115	116	124
+2 SDPercentile 97.7	130	132	148
+3 SDPercentile 99.87	145	148	172
98th percentilePercentile 98.0	130.8	132.9	149.3

What does one standard deviation mean?

A standard deviation is the size of one step away from the mean. On an IQ scale with a mean of 100 and a standard deviation of 15, one step is 15 points.

This step describes a statistical position in a score distribution. It does not say how much more intelligent one person is than another. The same number of steps has the same statistical rank across scales, even though the score numbers differ.

Why do IQ scales use different steps?

IQ scales can use different step sizes. Wechsler IQ scores are standardized to a mean of 100 and a standard deviation of 15, while older Stanford-Binet editions report scores with a standard deviation of 16.

Mensa’s own page says standard deviations of 16 or 24 points are used. It gives the Cattell-scale qualifying score as 148, which fits a standard deviation of 24. For background on score scales, see the IQ scale page.

What scores mark the same statistical rank?

Scores at the same number of standard deviation steps above the mean have the same percentile rank, even when their score numbers differ. The table uses the normal distribution, with scores grouped in a bell-shaped pattern around the mean.

One step above the mean is percentile 84.1: the scores are 115 on SD 15, 116 on SD 16, and 124 on SD 24. Two steps is percentile 97.7: 130, 132, and 148, respectively. Three steps is percentile 99.87: 145, 148, and 172, respectively.

For example, 130 on SD 15 and 132 on SD 16 are both two steps above the mean. Use the IQ percentile calculator to interpret a score when you know its scale.

How do you convert between IQ scales?

To convert a score, keep its distance from 100 in standard deviation steps. Subtract 100 from the score and divide by the original scale’s standard deviation. Multiply that result by the new scale’s standard deviation, then add 100.

For example, two steps above the mean is 130 on SD 15 and 148 on SD 24. This conversion compares statistical position, not test content or quality. If you are reading a Wechsler IQ test result, check which scoring scale it uses.

Why can a cutoff differ from the table?

A cutoff can sit between whole-number scores because a percentile boundary may not be a whole number. The top 2 percent starts at 130.8 on SD 15, 132.9 on SD 16, and 149.3 on SD 24.

A qualification rule may state a whole-number score that differs from the calculated boundary. Check the scale and the rule being applied. The free test is a timed reasoning exercise and does not print an IQ score.

Questions

Is an IQ standard deviation always 15?

No. Wechsler scores use a standard deviation of 15, older Stanford-Binet editions use 16, and Cattell uses 24. Check which scale a test uses before interpreting its score.

Is 130 the same as 130 on every IQ test?

No. The score’s position depends on the scale. For example, 130 is two standard deviations above the mean on SD 15, while the same position is 132 on SD 16.

How do I compare scores from two IQ scales?

Convert each score into standard deviation steps from 100, then compare the steps. This compares statistical position. It does not show that the tests measure the same skills or use the same testing conditions.

What does two standard deviations above average mean?

It means a score is two scale-specific steps above the mean of 100. On the scales described here, that position is percentile 97.7, with a different score number on each scale.