Guide

How to read a standard deviation

A standard deviation is large or small only next to the mean, the units, and the question you asked. The number is not a grade.

Same mean, different mix

Compare two classes with the same mean exam score. The one with the larger SD has a wider mix of results. That is the cleanest classroom use of the statistic.

Coefficient of variation

Coefficient of variation (σ / μ × 100%) is useful when you compare spread across different scales — heights in cm vs weights in kg. Do not use it when the mean is at or near zero; the ratio blows up.

Zero spread

If every value equals the mean, SD is 0. There is no spread to plot.

Outliers

SD is sensitive to outliers. One extreme value inflates the squared deviations. Always glance at min, max, and the graph before trusting a single headline figure. Tukey fences (1.5×IQR) are one simple check; they are not the only definition of an outlier.

Z-scores

A z-score says how many standard deviations a single x sits from the mean: (x − mean) / SD. A value equal to the mean has z = 0.

How Standard Deviation Calculator helps

After you calculate, you get mean, SD, CV, range, IQR, and a note about Tukey outliers. Tap a bar or point to see that value’s z-score.

Read spread on a graph

Dataset bars showing each value against the mean for reading spread