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What is standard deviation?

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Quick answer

Standard deviation is a number that tells you how spread out data is around its average. A small standard deviation means values cluster close to the mean; a large one means they're scattered widely. It measures how far data points typically sit from the average.

Key things to understand

  1. It measures how far data points typically sit from the average.
  2. Low value = tightly clustered data; high value = widely spread.
  3. It's the square root of the variance.
  4. It's used everywhere from test scores to finance and quality control.

People also ask

What does standard deviation tell you?
How spread out a set of numbers is around their average value.
Is a high or low standard deviation better?
Neither is inherently better — it depends on context. Low means consistency; high means variety or risk.
How is standard deviation related to variance?
Standard deviation is the square root of the variance, putting the spread back into the data's original units.