Deviation IQ: how the number is built
Modern IQ figures are not ratios of mental age to actual age. They are standard scores: a statement of how far above or below your group mean you fell, measured in standard deviations.
Step one, the weighted raw score
Each item carries a difficulty weight, so a hard item is worth more than an easy one. The weighted total is a better estimate of ability than a plain count of correct answers, because it uses the information in which items you solved.
Step two, the standard score
Subtract the expected mean for your norm group from your weighted score and divide by the group standard deviation. The result, z, is your distance from average in deviation units: 0 is exactly average, +1 is one deviation above.
Step three, the familiar scale
Multiply z by 15 and add 100. A z of +1 becomes 115, a z of −1 becomes 85. The percentile then comes from the normal distribution for the same z, which is why 115 lands on the 84th percentile.
Scored against age, education and area norms. Free certificate with a QR code anyone can verify.
Questions people ask
Why 15 and not 16?
It is a convention. Wechsler scales use 15, some older instruments use 16, so the same ability produces slightly different numbers on each.
Can I see the working for my score?
Yes. The score report lists the group mean, the standard deviation, your weighted score, your z and the conversion.