How rare is an IQ of 159?

About under 1 in 10,000 people score 159 or higher. That is 3.9 standard deviations above the mean of 100.

What does an IQ of 159 mean?

IQ tests are scored so that the population mean is 100 and one standard deviation is 15. About 68% of people score between 85 and 115, and 95% between 70 and 130. 159 sits in the "very superior" band. The number says where you rank on a test, not how your life goes.

Is an IQ of 159 good?

An IQ of 159 is higher than over 99% of people, on a scale where 100 is the mean and 15 is one standard deviation. That is under 1 in 10,000, and 3.93 standard deviations above the mean.

Percentile

>99%

of people score below 159

IQ 159

Very superiorWAIS-IV descriptive band for 159. Newer manuals use softer words for the same ranges.

IQ 159 by group

Percentile

Normal curve, mean 100, SD 15
Group	Mean	Score below you	1 in X
Everyone, Wechsler scale	100	>99%	under 1 in 10,000

Where the bands fall

Share of people in each WAIS-IV band, from the normal curve
Band	Scores	Share of people
Very superior	130+	2%
Superior	120 to 129	7%
High average	110 to 119	17%
Average	90 to 109	49%
Low average	80 to 89	16%
Borderline	70 to 79	6%
Extremely low	up to 69	2%

Percentile is the share of people who score below this IQ. “1 in X” counts the rarer side: people at or beyond this value above the median, at or under it below. IQ scores are normed to a normal curve by construction, so the percentile follows from the score alone.

What this means

In a school of 1,000 pupils, most likely nobody would score 159 or higher. You would need over 10,000 people.
Mensa admits the top 2%, which is about 131 on this scale. 159 clears it.
Online IQ tests are not normed on a population sample. A score from one of those is a guess in a confident font.

Questions

Is an IQ of 159 good?: An IQ of 159 is higher than over 99% of people. That is the top 2%, the Mensa cut-off. The WAIS-IV calls 130 to above "very superior".
How rare is an IQ of 159?: About under 1 in 10,000 people score 159 or higher. That is 3.9 standard deviations above the mean of 100.
What does an IQ of 159 mean?: IQ tests are scored so that the population mean is 100 and one standard deviation is 15. About 68% of people score between 85 and 115, and 95% between 70 and 130. 159 sits in the "very superior" band. The number says where you rank on a test, not how your life goes.

Source: Wechsler scale definition: mean 100, SD 15 (WAIS-IV, Pearson 2008). Percentiles on this page are our estimate from a normal distribution with the stated mean and SD.

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