Standard deviation: what it means and how to read it
In the report: std — The square root of the variance: sample formula (n − 1); with pop = TRUE in Settings, population (n).
Also shown as: sd
How to read it
How far the values typically lie from the mean, in the units of the data: with a mean of 3 and std 1.3 on a 1–5 scale most answers are between about 2 and 4.
In a report next to the mean: M = 3.04, SD = 1.29.
In plain words
A teacher asked 50 students to rate a lesson from 1 to 5. The average was 3, but she could not tell whether everybody said 3 or half said 1 and half said 5. First comes an awkward number, the variance; from it comes a handy one, std, the standard deviation: 1.3. Now she knows that most answers lie between about 2 and 4. A 2 or a 4 is a usual answer, and a 5 is far from the usual. If std had come out 2, the answers would have been split between the two ends.
How it is computed
√(Σ (x − x̄)² / (n − 1))Example
The cell with std is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_ONE_SAMPLE(Data!A1:T51, "score", 5, 0.95,"two-sided") - —
=STATS_DESCRIPTIVE(Data!A1:T51, "mean,std,median","x1,x2") - — all columns starting with q
=STATS_CI(Data!A1:T51, "/^q/", 0.95, "two-sided")
Where you see it
STATS_ONE_SAMPLE— One-sample t-test against mu0.STATS_DESCRIPTIVE— Column-wise descriptive statistics with flexible metric selection and optional column filtering.STATS_CI— Calculates the confidence interval of the mean for filtered columns (Student's t).STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Coefficient of variation — std / mean; empty when the mean is 0.
- Relative dispersion — std / median; empty when the median is 0.
- Skewness — The asymmetry of the distribution, with the sample correction as in Excel and SPSS; empty for fewer than 3 values or a column of equal values.
- Kurtosis — Excess kurtosis: how heavy the tails are compared with the normal distribution (0), with the sample correction as in Excel and SPSS; empty for fewer than 4 values or a column of equal values.
- First quartile — The first quartile: 25% of the values are below it; computed as in SPSS, so it can differ from the Sheets QUARTILE and PERCENTILE functions.
Get it in your sheet
One formula in a cell gives the whole report, Standard deviation included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)