What does a high standard deviation mean?

A high standard deviation indicates that data points are spread out widely across a broader range of values, whereas a low standard deviation indicates that data clusters tightly around the mean.

Mathematics Tools• Math

Standard Deviation & Statistics Calculator

Enter a comma- or space-separated list of numbers to compute comprehensive statistical metrics: Mean, Median, Mode, Sample Standard Deviation (s), Population Standard Deviation (σ), Variance, and Sum of Squares.

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Standard Deviation Calculator

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Data Set Input

Enter numbers separated by commas or spaces.

Statistical Summary

Sample Std Dev (s)

6.251

Population Std Dev (σ)

5.847

Mean (Average)

21.25

Sample Variance (s²)

39.071

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How to Use Standard Deviation & Variance Calculator

Enter Numbers

Paste or type your data points separated by commas, spaces, or line breaks.

Choose Sample or Population

Select Sample (Bessel's correction n-1) or Population (N).

View Step-by-Step Table

Inspect the deviation table showing (x - x̄) and (x - x̄)² for every data point.

About Standard Deviation & Variance Calculator

Standard deviation measures the dispersion of a dataset relative to its mean. Sample standard deviation divides the sum of squared differences by (n - 1) rather than n (Bessel's correction) to eliminate downward bias when estimating population parameters from limited samples.

Key Features

Calculates both Sample Standard Deviation (s) and Population Standard Deviation (σ)
Displays Variance (s² and σ²), Mean (average), Median, Mode, Min, Max, Range, and Count (N)
Detailed step-by-step calculation table demonstrating each squared deviation
Identifies statistical outliers using 1.5 × IQR and Z-scores
Instant copy and CSV export of statistical summary

Frequently Asked Questions

Use Population (N) when your dataset includes every single member of the group you are studying. Use Sample (n-1) when your data is a sample taken from a larger overall population.

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