A z-score is a common way of standardising data on a scale, allowing for easy comparison. The z-score is a common measure for all types of data. Each z-score corresponds to a point in a normal distribution.
Z-scores are used in student analytics as a way of portraying how far above or below the mean a student sits. A z-score of 0, for example, is right on the mean, while a positive z-score, such as +1, tells you it is 1 standard deviation above the mean. Similarly, a negative z-score will tell you how many standard deviations it is below the mean.
To find the z-score of a student’s result in a select group, you will need:
Once you have these figures, calculate the z-score using this formula:
z-score = (student result – mean)/ standard deviation.
A stanine, also known as a ‘standard nine’ score, is a way to convert raw test scores to a whole number on a nine-point scale, simplifying test interpretation. Like z-scores, stanines are a way to assign a relative numerical value to a member of a group.
Stanine scores are used in education to compare student performance over a normal distribution.
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.
To calculate stanine scores, rank the group’s results from lowest to highest, then assign the score based on the percentile they fall in:
| Z-Score | Stanine Score | Percentage of Scores |
| <-1.75 | 1 | Bottom 4% |
| -1.75 to -1.25 | 2 | Next bottom 7% |
| -1.25 to -0.75 | 3 | Next bottom 12% |
| -0.75 to -0.25 | 4 | Next Bottom 17% |
| -0.25 to 0.25 | 5 | Middle 20% |
| 0.25 to 0.75 | 6 | Next top 17% |
| 0.75 to 1.25 | 7 | Next top 12% |
| 1.25 to 1.75 | 8 | Next top 7% |
| >1.75 | 9 | Top 4% |
Need a faster solution? This Excel spreadsheet will calculate z-scores and stanines from any data set for you. Download the sheet to get started.