Variance Calculator Formula

Understand the math behind the variance calculator. Each variable explained with a worked example.

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Formulas Used

Population Variance

pop_variance = ss / 5

Sample Variance

samp_variance = ss / 4

Mean

data_mean = mn

Variables

VariableDescriptionDefault
v1Value 14
v2Value 28
v3Value 36
v4Value 45
v5Value 57
mnDerived value= (v1 + v2 + v3 + v4 + v5) / 5calculated
ssDerived value= pow(v1 - mn, 2) + pow(v2 - mn, 2) + pow(v3 - mn, 2) + pow(v4 - mn, 2) + pow(v5 - mn, 2)calculated

How It Works

How to Calculate Variance

Population Variance

sigma^2 = Sum of (xi - mean)^2 / N

Sample Variance

s^2 = Sum of (xi - mean)^2 / (n - 1)

Variance measures the average squared distance of each data point from the mean. The sample variance divides by (n-1) instead of n to correct for the bias introduced by estimating the population mean from the sample (Bessel's correction).

Worked Example

Find the variance of 4, 8, 6, 5, 7.

v1 = 4v2 = 8v3 = 6v4 = 5v5 = 7
  1. 01Mean = (4 + 8 + 6 + 5 + 7) / 5 = 30 / 5 = 6
  2. 02Squared deviations: (4-6)^2=4, (8-6)^2=4, (6-6)^2=0, (5-6)^2=1, (7-6)^2=1
  3. 03Sum of squares = 4 + 4 + 0 + 1 + 1 = 10
  4. 04Population Variance = 10 / 5 = 2
  5. 05Sample Variance = 10 / 4 = 2.5

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