Sample vs population?

Use sample when data is a subset; population when it's every value.

Why n−1 for sample?

Bessel's correction: it produces an unbiased estimate of population variance.

The typical distance of a value from the mean.

Variance is σ squared — same information, different units.

Paste a list of numbers to compute standard deviation, variance, and mean — sample or population.

Reviewed & updated: January 1970

Numbers (comma or space separated)

Distribution

μ−3σ (-1.41)μ+3σ (11.41)

Count8

Results are estimates for general information only and are not professional financial, medical, tax, or legal advice. Read the full disclaimer.

σ = √(Σ(x−μ)²/N). Sample uses (n−1) in the denominator.

Example

Values 2, 4, 4, 4, 5, 5, 7, 9 → mean 5, σ (population) = 2.

Sample vs population?: Use sample when data is a subset; population when it's every value.
Why n−1 for sample?: Bessel's correction: it produces an unbiased estimate of population variance.
What does σ tell me?: The typical distance of a value from the mean.
Is variance the same?: Variance is σ squared — same information, different units.

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