Standard Deviation: The Number That Says How Spread Out Your Data Is

Mean tells you the centre. Standard deviation tells you how far points typically stray from it.

Calculators do the heavy lifting, but knowing what is going on underneath is what saves you money — or stress — later. Mean tells you the centre. Standard deviation tells you how far points typically stray from it.

The intuition

Low SD = data clusters near mean. High SD = data spreads wide.

The empirical rule

Normal distribution: ~68% within 1 SD, ~95% within 2 SD, ~99.7% within 3 SD.

Why we square the differences

Squaring prevents positives and negatives cancelling, and weights big deviations more.

Pro tips

  • Always report SD alongside mean for any continuous data.
  • Standard error ≠ standard deviation — SE shrinks with sample size.

Frequently asked questions

What's variance? SD squared. Same info, different units. SD is usually more interpretable.

Population vs sample SD? Divide by n for population, by (n−1) for sample (Bessel's correction).

The math is the easy part. Acting on what it tells you is where the real win lives.

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