Find Variance Calculator

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One frequency per data value, for grouped or frequency-table data. Leave blank for raw data.
A sample of a larger group uses n − 1; a complete population uses N.
Variance
4.571429
Standard Deviation Calculator
Standard deviation
2.13809
Sample standard deviation (s)
2.13809
Sample variance (s²)
4.571429
Population standard deviation (σ)
2
Population variance (σ²)
4
Mean
5
Data points entered
8
Sample size (n)
8
Sum of values
40
Sum of squared deviations
32
Degrees of freedom (n − 1)
7
Divisor used
7
Standard error of the mean
0.755929
Coefficient of variation
42.761799 %
Estimator used
Sample (÷ n − 1)
Worked out from OpenStax, Introductory Statistics 2e, section 2.7 "Measures of the Spread of the Data" and 1 other source.

How this is worked out

5 steps
  1. n = 8, Σx = 40
  2. Mean = 40 / 8 = 5
  3. Σ(x − mean)² = 32
  4. s² = 32 / (8 − 1) = 4.571429
  5. s = sqrt(4.571429) = 2.13809
Deviation tabletable
valuefrequencydeviationsquaredDeviation
21-39
41-11
41-11
41-11
5100
5100
7124
91416

Results are general information, not financial, tax, legal, medical or engineering advice.