Dataset (separate values with commas, spaces, or new lines) Enter numbers separated by commas or spaces

Formula: Sample (n−1) Population (n)

Std Deviation

Mean (Average)

Variance

Median

Mode

Range

Count (n)

Min

Max

About the Standard Deviation Calculator

What standard deviation measures

Standard deviation quantifies how spread out a set of numbers is around their mean. A low value means numbers cluster close to the average; a high value means they are spread widely.

Population vs sample

Use population standard deviation (σ) when your data represents the entire group. Use sample standard deviation (s) when your data is a subset — it applies Bessel's correction (dividing by n−1) to reduce bias.

Mean — sum of all values divided by count
Variance — the average of squared differences from the mean
Standard deviation — the square root of variance; in the same units as your data
Median — the middle value when sorted; less sensitive to outliers than the mean

When to use standard deviation vs variance

Standard deviation and variance measure the same thing — spread of data around the mean — but in different units. Variance is the average squared deviation. Standard deviation is the square root of variance, expressed in the same units as the original data, making it more interpretable. Use standard deviation for communication; variance is used internally in statistical formulas.

Population vs sample — population SD divides by N; sample SD divides by N-1 (Bessel's correction) to be unbiased
Coefficient of variation — SD divided by mean; allows comparing variability between datasets with different scales
68-95-99.7 rule — for normal distributions: 68% of data within 1 SD, 95% within 2 SD, 99.7% within 3 SD
Z-score — (value - mean) / SD; measures how many standard deviations from the mean a value falls

Frequently Asked Questions

What is the difference between sample and population standard deviation?

Population std dev (σ) divides by n and is used when you have data for the entire population. Sample std dev (s) divides by n−1 and is used when your data is a sample from a larger population. The n−1 correction (Bessel's correction) makes the sample estimate less biased.

What is a standard deviation?

Standard deviation measures how spread out values are from the mean. A low std dev means values are clustered close to the average; a high std dev means values are spread over a wider range.

What counts as an outlier?

This calculator highlights values more than 2 standard deviations from the mean as potential outliers. In a normal distribution, about 95% of values fall within 2σ of the mean.

What does a high standard deviation mean?

A high standard deviation means the data points are spread widely from the mean — there is high variability in your dataset. A low standard deviation means data points cluster closely around the mean. For example, consistent exam scores produce a low SD; wildly varying scores produce a high SD.

What is the difference between population and sample standard deviation?

Population SD (σ) is used when your data represents every member of a group. Sample SD (s) is used when your data is a subset drawn from a larger population — it divides by n−1 instead of n to correct for the underestimation bias that occurs with smaller samples. Use sample SD for most real-world data.