Work out iq standard deviation score instantly with clear inputs, formula shown and shareable results.
IQ scales set the mean at 100 with a standard deviation of 15 on Wechsler tests and 16 on Stanford-Binet, so the same ability gives different numbers. An IQ of 130 is exactly two standard deviations up on the SD 15 scale - the 97.7th percentile, about one person in 44 - and would read 132 on an SD 16 scale.
Deviations from the mean
z = (IQ - 100) / scale standard deviation
Rarity
one in 100 / (100 - percentile) for above-average scores
Because of differing standard deviations and norming samples. A score is only meaningful with the scale and norm date stated.
Raw performance has risen about three IQ points a decade, so norms must be restandardised or scores drift upwards over time.