What percentile is IQ 120/130? (Normal approximation example)
Using a normal distribution example (mean 100, SD 15) to interpret IQ 120/130 as rough percentiles.
1) Fix the assumption first (mean and SD)
For a worked example, assume mean 100 and SD 15 (a common explanatory convention).
Real tests may use different norms or SD conventions—treat this as an illustration.
2) Convert to z-scores
A z-score is (score - mean) / SD. For IQ 120: z ≈ (120-100)/15 ≈ 1.33.
For IQ 130: z = (130-100)/15 = 2.00.
3) Map z-scores to approximate percentiles
Using the normal CDF, z≈1.33 corresponds to roughly the top ~9% (about 91st percentile).
z=2.0 corresponds to roughly the top ~2.5% (about 97.5th percentile).
4) Site ranking vs. the normal example
A site’s ranking/percentile may be based on internal samples and an estimation pipeline.
The normal example is a statistical illustration—do not assume they are identical.
5) Next step: compare under the same version and conditions
Scores can change with item count, time limits, and difficulty mix.
For meaningful comparisons, use the same tier/version and similar conditions.
FAQ
Is IQ 120 always top 9%?
It is an example under mean 100, SD 15 normal approximation; real norms can differ.
What about IQ 130?
Under the same example, z=2.0 corresponds to roughly the top ~2.5%.
Why do we need a distribution assumption?
Percentiles require a reference distribution to map raw scores to ranks.
Why does the site percentile differ?
Internal ranking may use different samples and estimation rules than the normal example.
Can I compute IQ 115/125 too?
Yes—use z-scores and a normal CDF (or a table) under the same assumption.
What matters beyond the number?
Look at interpretation and variability (state/strategy) alongside the score.