How To Calculate Stanine Scores

Stanine scores are used in education to compare student performance over a normal distribution. Stanine scores convert raw test scores to a one-digit whole number to simplify test interpretation. Typically, stanine scores between 4 and 6 are considered average, scores of 3 or less are below average while scores of 7 or greater are above average.

Find the mean test score and subtract this from each score. Square each of these differences and then add the results. Divide this sum by the number of scores, and take the square root of the quotient to find the standard deviation. For example, for scores of 40, 94 and 35, the standard deviation would be about 27. To find the z-score, divide the difference between each test score and the average by the standard deviation. The z-score describes how many standard deviations each test score is from the mean. A z-score of zero is average. For example, the z-score for the score of 40 would be about -0.6.

Compare the z-score to the ranges of stanine scores. Stanine 1 consists of z-scores below -1.75; stanine 2 is -1.75 to -1.25; stanine 3 is -1.25 to -0.75; stanine 4 is -0.75 to -0.25; stanine 5 is -0.25 to 0.25; stanine 6 is 0.25 to 0.75; stanine 7 is 0.75 to 1.25; stanine 8 is 1.25 to 1.5; and stanine 9 is above 1.75. For example, the test score of 40 would fall in stanine 4.