IQ Test Scale — Mean 100, Standard Deviation 15

A deviation IQ test scale is a re-labeled bell curve. Test designers take raw performance, compare it against a standardization sample, and report where it falls on a curve whose center is pinned at 100. That pin is arbitrary but universal — 100 is the mean by convention, so a score of 100 always means 'at the reference average', whatever the test. The pin is why a 100 means the same thing on every IQ test scale.

The second setting defines the unit. One standard deviation equals 15 points on most modern scales, which sets how fast scores spread out from the center: about 68 percent of the reference population lands within 85–115, and about 95 percent within 70–130. Some instruments use 16 or even 24 points per deviation — the classic Cattell scale — which is why a '130' on one scale is not identical rarity to a '130' on another. Whenever you compare scores across tests, first ask which IQ test scale each report used. Ask which IQ test scale a report used before comparing anything.

Together the two settings turn raw performance into a portable number. That is the entire genius of the deviation system: a score carries its meaning in its position, portable across tests that share the convention, without anyone computing a mental-age ratio — the method the scale replaced in the mid-twentieth century. Portability is the quiet benefit the IQ test scale was designed to deliver. Portability is what the deviation IQ test scale was built to deliver.

• 1Mean fixed at 100 — the reference average, by convention
• 2One standard deviation = 15 points on the common scale
• 385–115 holds ≈ 68% of the reference distribution
• 470–130 holds ≈ 95%
• 5Other scales exist (SD 16, SD 24) — check before comparing

Strip the IQ test scale to its mechanics and one formula remains: z = (score − 100) ÷ 15. The z-score measures distance from the mean in standard-deviation units — the natural unit of any normal curve. A z of +1 is one deviation above average; z of −2 is two below. Learn one formula and the whole IQ test scale becomes legible. Learn one formula and the whole IQ test scale becomes legible.

Worked through the milestones: for 85, z = (85 − 100) ÷ 15 = −1; for 100, z = 0; for 115, z = +1. The percentile then comes from the standard normal cumulative distribution at that z: z = 0 maps to the 50th percentile, z = +1 to the 84.13th, z = −1 to the 15.87th. The tool above performs the whole chain live as you move the score — arithmetic on the surface, distribution underneath.

This is also the honest answer to a question people ask quietly: how many points is 'one step' smarter? The IQ test scale has no such unit. It measures position, not increments of ability; the points are deviations of a score distribution, not rungs of a ladder. The ladder impression comes from banding, which is a convenience of presentation — the underlying quantity is continuous. That is the deepest thing the IQ test scale can teach: positions, not rungs. Positions, not rungs — the deepest lesson the IQ test scale teaches.

Conventions have edges, and three matter in practice. First, cross-scale comparison: a Cattell-scale 148 and a Wechsler-scale 130 both sit near two and a third deviations above their means — the raw numbers differ, the rarity matches. Always convert via z before comparing across systems. The z-bridge is the safe route across any IQ test scale difference. The z-bridge is the safe route across any IQ test scale difference.

Second, uncertainty: every real score carries a confidence interval, commonly around ±3 to ±5 points at 95 percent confidence. On a 15-point scale that is a third of a deviation — meaningful near band boundaries, invisible in the middle. Reports that omit the interval are omitting the error bars. Error bars are part of reading an IQ test scale like an adult.

Third, the tails: the normal model is an excellent description of the score distribution's bulk and an increasingly shaky description far into the tails, both because samples get thin and because human performance is not perfectly normal out there. That is why this site's tools cap at ±3σ and why extreme-range scores deserve professional interpretation rather than chart-reading. The scale is a sturdy convention — and like all conventions, it is strongest where it is most used. Respect the edges and the IQ test scale is a remarkably sturdy convention. Respect the edges and the IQ test scale is a sturdy convention.