Glossary
Standard deviation
Definition
Standard deviation is a measure of how spread out a set of scores is around its average. A small standard deviation means scores cluster near the mean; a large one means they spread widely. On most modern IQ tests one standard deviation equals 15 points.
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Why it matters for IQ scores
Modern IQ tests standardize scores to a mean of 100 and a standard deviation of 15 (Wikipedia: Intelligence quotient). That one choice sets the spacing of the whole scale. About 68% of people score within one standard deviation of the mean (85 to 115), about 95% within two (70 to 130) and about 99.7% within three (55 to 145) (the 68-95-99.7 rule).
An example
An IQ of 130 is two standard deviations above the mean, higher than about 97.7% of people. On a test that uses a standard deviation of 24, the same rank prints as about 148, and on one that uses 16, about 132 (Wikipedia: IQ classification). Same person, same rank, three different numbers.
Common confusions
A standard deviation is not a grade boundary or a margin of error. It describes the spread of a whole group, while the standard error of measurement describes the uncertainty in one person's score. To turn any score into standard deviation units, see z-score. The IQ bell curve guide shows the full picture, and the percentile to IQ converter works on all three scales.
Try one · Abstract Reasoning
Which tile completes the grid?
Tap the option you think is right, or show the answer.
Show the answer
The missing tile has a large hatched triangle (option 8).
How to solve it
- Start with the first row and name what changes from tile to tile.
- Every row and every column contains each shape (pentagon, triangle and star) exactly once.
- Every row and every column contains each fill (hatched, solid and outline) exactly once.
- The size (large) stays the same in every tile.
- Check the rules on the second row, then apply them to the third.
- So the missing tile has a large hatched triangle.
That was 1 puzzle. The full test has 25.
Sources
- Intelligence quotient. Wikipedia. en.wikipedia.org/wiki/Intelligence_quotient
- IQ classification. Wikipedia. en.wikipedia.org/wiki/IQ_classification
- 68-95-99.7 rule. Wikipedia. en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule