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Standard Deviation Calculator

Compute mean, variance, standard deviation, min, max, and count from a dataset.

Inputs

Results update as you edit.

Standard deviation

5.921711

Results update as the calculator inputs change.

Mean

19.333333

Variance

35.066667

Count

6

Min

12

Max

29

How to Calculate Standard Deviation

Dataset
Start with a list of numeric values.
Mean and Deviations
Each value is compared with the average to measure spread.
Sample vs Population
Sample standard deviation uses n - 1, while population uses n.

How to Interpret Standard Deviation

Standard deviation describes how spread out values are around the mean. A low value means observations cluster tightly; a high value means they vary more.

What Affects Standard Deviation?

Number of Values

Small datasets can produce unstable spread estimates.

Mean

Deviation is measured from the dataset average.

Outliers

Extreme values can increase standard deviation substantially.

Sample Setting

Sample mode adjusts for estimating from part of a larger population.

Units

Standard deviation uses the same unit as the original values.

Data Quality

Incorrect or mixed-unit inputs can make the result misleading.

Related Statistics

Mean

The average is the center used for deviation calculations.

Variance

Variance is the average squared deviation before taking the square root.

Range

Minimum and maximum show the full span but not the distribution shape.

Frequently Asked Questions

What does standard deviation mean?

It measures typical spread around the mean. Higher values indicate more variation.

Should I use sample or population standard deviation?

Use population when your data includes every value of interest. Use sample when estimating a larger group from a subset.

Why square deviations?

Squaring keeps positive and negative deviations from canceling and weights larger deviations more heavily.

Can outliers affect standard deviation?

Yes. Outliers can raise standard deviation significantly.

Is standard deviation the same as variance?

No. Variance is in squared units; standard deviation is the square root of variance and uses the original units.