Z-Scores and Stanines

Z-scores

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:

1. The student’s result
2. The mean result 
3. The standard deviation.

Once you have these figures, calculate the z-score using this formula: 

z-score = (student result – mean)/ standard deviation.

Stanines 

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 and Stanine Calculator

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.