CalculatorHandy

Math Calculators

Standard Deviation Calculator

Measure how spread out a set of numbers is. Choose sample if your data is a subset of a larger group (most surveys and experiments), or population if it includes every member.

Separate numbers with commas, spaces or new lines.

Data is a
Sample standard deviation2.03101s
Variance
4.125
Mean
5.875
Count
8
Sum of squares
28.875
Coefficient of variation
34.57%
Step-by-step working
  1. Mean = 47 ÷ 8 = 5.875
  2. Square each deviation from the mean and add them: Σ(x − mean)² = 28.875
  3. Divide by n − 1 = 7: variance = 4.125
  4. Square root: 2.03101

Deviation table

xx − mean(x − mean)²
4-1.8753.515625
82.1254.515625
60.1250.015625
5-0.8750.765625
3-2.8758.265625
71.1251.265625
93.1259.765625
5-0.8750.765625

How to use the Standard Deviation Calculator

  1. Paste or type the numbers.
  2. Choose sample or population.
  3. Press Calculate. A deviation table appears below the calculator.

Formula

Population: σ = √( Σ(x − μ)² ÷ N )

Sample: s = √( Σ(x − x̄)² ÷ (n − 1) )

Dividing by n − 1 (Bessel’s correction) corrects the tendency of a sample to underestimate the true spread.

Examples

  • Data 4, 8, 6, 5, 3, 7, 9, 5: mean 5.875, sample SD ≈ 2.031, population SD ≈ 1.900.

Frequently asked questions

Which should I choose, sample or population?

If you measured every member of the group you care about, use population. If you measured some to learn about all, use sample.

What is a “good” standard deviation?

It depends on the scale. Compare it with the mean using the coefficient of variation: below about 10% is usually considered low spread.

Related calculators