Variance and Standard Deviation

Same center, different consistency

Two datasets can share a mean but behave very differently. Variance measures average squared distance from the mean. Squaring prevents positive and negative differences from canceling and emphasizes large deviations. Standard deviation is the square root of variance, returning spread to the original unit, which makes it easier to interpret.

service A: 98, 99, 100, 101, 102 ms
service B: 20, 60, 100, 140, 180 ms
both means: 100 ms; B has much larger standard deviation

In ML, spread helps determine whether a feature changed and supports standardization, which expresses values in units of training standard deviations from the training mean. Standard deviation is most informative for roughly symmetric data; extreme outliers can inflate it dramatically.

Scenario: Two APIs both advertise 100 ms average latency. One is nearly always near 100 ms; the other alternates between instant and painfully slow. Users experience the second as unreliable even though the mean is identical.

Tip: Keep raw counts and a distribution view beside summary statistics. A single center-and-spread pair can still hide multiple clusters or long tails.