Standard Deviation Calculator

Calculate standard deviation, variance, mean, and other statistics for your data set instantly.

Enter Your Data

Enter numbers separated by commas or spaces

Count: 8 numbers

Results

Mean (Average)

18.0000

Population SD (σ)

4.8990

Sample SD (s)

5.2372

Population Variance

24.0000

Sample Variance

27.4286

Count (n)

8

Sum

144.00

Median

18.50

Range

13.00

Min

10.00

Max

23.00

Data Distribution

Min: 10Mean: 18.0Max: 23

How Standard Deviation is Calculated

  1. Calculate the mean (average) of all values
  2. Subtract the mean from each value to get deviations
  3. Square each deviation
  4. Calculate the mean of squared deviations (= variance)
  5. Take the square root of variance (= standard deviation)

Standard Deviation Calculator FAQ

What is standard deviation?▼

Standard deviation measures how spread out data values are from the mean. A low standard deviation means values are close to the mean; a high standard deviation means values are spread over a wider range.

What is the difference between population and sample standard deviation?▼

Population SD divides by N (total count), while sample SD divides by N-1 (Bessel correction). Use sample SD when your data is a subset of a larger population.

How do I interpret standard deviation?▼

In a normal distribution: ~68% of data falls within 1 SD of the mean, ~95% within 2 SDs, and ~99.7% within 3 SDs (the 68-95-99.7 rule).