Statistics

Standard Deviation

Calculate Sample and Population Standard Deviation, Variance, and dispersion metrics.

Reviewed & Maintained by

Aadil Malik — Software Engineer

1 min read · 27 words

What is a Standard Deviation Calculator?

A standard deviation calculator computes sample standard deviation ($s$), population standard deviation ($\sigma$), and variance ($s^2$) with complete step-by-step deviations.

Frequently Asked Questions

Standard deviation measures the dispersion or spread of data points around their arithmetic mean.

Population (σ) divides by N (entire population). Sample (s) divides by n-1 (Bessel's correction to remove sample bias).

Variance is the average squared deviation from the mean: Variance = (Standard Deviation)².

For a normal distribution: 68.2% of data falls within ±1σ, 95.4% within ±2σ, and 99.7% within ±3σ.

A high standard deviation means data values are spread widely over a broad range from the mean (high volatility/variability).

CV = (Standard Deviation / Mean) * 100, which normalizes dispersion across different units.

No. Standard deviation is always zero or positive because distances from the mean are squared.

SEM = s / sqrt(n), measuring the precision of a sample mean estimate.