Population or sample — which do I need?

Use sample (n−1) when your data is a sample of a larger group, and population (n) when it is the whole set.

What does standard deviation tell me?

It measures how spread out the values are around the mean — larger means more variability.

Standard Deviation Calculator

Calculate standard deviation, variance, mean, and z-scores with step-by-step work.

Input Numbers

8 numbers parsed

Results

Count (N)8

Sum144

Mean18

Min10

Max23

Range13

Population Variance24

Population Std Dev4.898979

Sample Variance27.428571

Sample Std Dev5.237229

Step-by-Step Work

Step 1: Mean = Sum / N = 144 / 8 = 18

Step 2: Squared differences from mean:

(10 - 18)^2 = 64

(12 - 18)^2 = 36

(23 - 18)^2 = 25

(16 - 18)^2 = 4

(23 - 18)^2 = 25

(21 - 18)^2 = 9

(16 - 18)^2 = 4

Step 3: Sum of squared diffs = 192

Step 4 (Population): Variance = 192 / 8 = 24

Population Std Dev = sqrt(24) = 4.898979

Step 4 (Sample): Variance = 192 / 7 = 27.428571

Sample Std Dev = sqrt(27.428571) = 5.237229

Z-Scores (Population)

x = 10

z = -1.632993

x = 12

z = -1.224745

x = 23

z = 1.020621

x = 23

z = 1.020621

x = 16

z = -0.408248

x = 23

z = 1.020621

x = 21

z = 0.612372

x = 16

z = -0.408248

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About Standard Deviation Calculator

Calculate the mean, variance, and standard deviation of a set of numbers, with both population and sample formulas. Useful for quick statistics without a spreadsheet.

How to use

Paste your numbers separated by commas, spaces, or new lines.
Choose population or sample standard deviation.
Read the mean, variance, and standard deviation.

Frequently asked questions

Population or sample — which do I need?: Use sample (n−1) when your data is a sample of a larger group, and population (n) when it is the whole set.
What does standard deviation tell me?: It measures how spread out the values are around the mean — larger means more variability.