z-score of a value: what it means and how to read it
In the report: zScore — The z-score of the value v: (v − mean) / std; 0 for a column without spread; empty without v.
How to read it
How many standard deviations v lies from the mean of the column: zScore.5 = 1.5 means that an answer of 5 is 1.5 standard deviations above the average.
In plain words
In a class the average mark was 70 and the marks usually differed from it by 10 points, the standard deviation. One student got 85 and another got 55, and the teacher could not tell which of them stood out more. She asked for zScore.85 and got 1.5: the mark 85 is one and a half standard deviations above the average. For zScore.55 she got minus 1.5. Now she can say that the two students are equally far from the usual mark, one above it and one below it. A mark of 100 would give 3, which is very rare.
How it is computed
(v − x̄) / sWhere you see it
STATS_DESCRIPTIVE— Column-wise descriptive statistics with flexible metric selection and optional column filtering.
Related values
- Weighted mean — The weighted mean with the weights in the column weightsCol, row by row; a zero, negative or missing weight leaves the row out, as SPSS WEIGHT. Empty when no row has a usable weight.
- Standard error — The standard error of the estimate: how much it would vary from sample to sample.
- Number of values — The number of values (rows) the result is computed on.
- Sum — The sum of the values; empty for a column without a single number (the sign . in a STATS_COMPUTE row where no item is answered), not 0.
- Mean — The arithmetic mean: the sum divided by n.
Get it in your sheet
One formula in a cell gives the whole report, z-score of a value included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)