IQ Score Chart Explained: Mean, Standard Deviation, Percentiles, and Ranges

Many, but not all, IQ scales are reported with mean 100 and standard deviation 15. Roughly speaking, 85 and 115 are one standard deviation below and above the mean on such a scale.

This convention describes transformed norm scores. It is not a universal raw-score ruler and does not authorize conversion from an unrelated test.

A standard score describes distance from the norm mean on the chosen scale. A percentile rank describes the proportion of the norm distribution at or below a score under that test's rules.

Percentile intervals are uneven: equal standard-score differences do not produce equal percentile-point differences near the center and tails.

Labels such as average, high average or superior are publisher-specific interpretive conventions. Cut points and wording differ, and some terms carry historical baggage.

Use the manual for the administered test. A generic web chart can illustrate a distribution, but it should not overwrite the test's official score definitions.

No observed score is perfectly precise. A confidence interval communicates a plausible range for the underlying score under a stated model and confidence level.

Small differences between two numbers may not support a meaningful rank order, especially across different domains or instruments.

Suppose a manual reports a standard score of 112 on a scale with mean 100 and standard deviation 15, together with a confidence interval of 106–118. The observed value is 12 scale points above the norm mean, but the interval shows that plausible values cover a wider band. The correct interpretation comes from that manual's norms and precision study—not from treating 112 as 112 questions, 112 percent or a universal ranking.

If another website reports 16 of 20 correct, that result is 80 percent correct on its form. It does not become IQ 112 by matching the numbers to a generic chart. A norm conversion must be estimated for that exact form and eligible population, and it should carry its own uncertainty.

Very high and very low scores are supported by fewer observations in most norm samples. Short forms may also have too few appropriately targeted items to distinguish people near the ends of a distribution. Ceiling and floor effects can compress different performances into the same reported result.

Percentiles amplify this issue because small standard-score changes in the tails can look like large differences in rarity. Claims about giftedness, impairment or membership thresholds should use the required approved instrument and administration, not a rounded online chart.

Before interpreting a chart, identify the exact test, edition, age or comparison group, standard deviation, norm date, confidence level and intended use.