Standard Deviation

Standard deviation is a statistic describing the typical distance of data points from their mean. It is the square root of the variance, the average of squared deviations, which puts the result back in the original units, such as milliseconds or rupees.

Why it matters

Two datasets can have the same average but very different consistency. Standard deviation quantifies that. For roughly bell-shaped (normal) data, about 68 percent of values fall within one standard deviation of the mean and about 95 percent within two, a rule of thumb that does not hold for heavily skewed data. It is widely used in quality control, performance monitoring, anomaly detection and finance.

Example

Server A response ms: 98, 100, 102     mean 100, SD ~ 2
Server B response ms: 50, 100, 150     mean 100, SD ~ 50

Both average 100 ms, but Server B is far less predictable. For a sample, divide by n-1 rather than n when computing the variance.

Common mistakes

• Applying the 68-95 rule to skewed or heavy-tailed data.
• Mixing population and sample formulas.
• Ignoring that outliers inflate it strongly, since deviations are squared.

Related

• Mean vs median
• Outlier
• Histogram
• Outlier

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