Nine bands, half a sigma each
Stanine is short for standard nine: a scale that compresses any normally distributed score into a single digit from 1 to 9. The bands are slices of the normal curve, each half a standard deviation wide except the open-ended extremes. Stanine 5 is the centre slice, z from −0.25 to +0.25, holding about 20% of a group; the slices step outward through fixed z boundaries at ±0.25, ±0.75, ±1.25 and ±1.75, with stanines 1 and 9 collecting everything beyond ±1.75. The shares under a perfect normal are memorisable: 4, 7, 12, 17, 20, 17, 12, 7, 4 percent.
A score of 118 on a test with mean 100 and SD 15 has z = 18/15 = 1.20. The band boundaries say stanine 7 covers z from 0.75 to 1.25, so the score is a stanine 7, in raw terms any score from 111.25 up to 118.75 on this test. The percentile (89.69) is more precise; the stanine is more legible. Schools report stanines to parents because "7 out of 9, above average" carries the message without a statistics lesson attached.
What stanines cost and buy
Compression is the point and the risk. Two students half a mark apart can land in adjacent stanines if they straddle a boundary, while two students 14 marks apart can share stanine 5. Any banded reporting has this edge effect; stanines at least keep the bands narrow near the centre where most students sit, and equal in z terms everywhere. Treat a stanine as a summary band, never as a measurement: decisions about individuals deserve the raw score and its percentile as well.
Averaging stanines as if they were marks. The bands are percentile slices, not equal steps of achievement in the tails, and a mean of stanines has no clean interpretation. Average the raw scores, then convert.
Frequently asked questions
What stanine is average?
5 is the central band, and 4 to 6 together form the usual 'average range' in school reporting, holding about 54% of a normal group.
How are stanines calculated from a z-score?
By the band boundaries: z below -1.75 is stanine 1, then each 0.5 of z adds a band, up to stanine 9 above +1.75.
What percentage of students score stanine 9?
About 4% under a normal distribution: everyone with z above +1.75. Stanine 1 also holds about 4%.