Variance Calculator

Variance is evaluated from Data Values and Variance Type. The calculation reports Mean, Variance and Standard Deviation.

Results

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About the Variance Calculator

Variance is treated here as a quantitative relation between Data Values and Variance Type and Mean, Variance, Standard Deviation and Sum of Squared Deviations.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
SS = Sigma(xᵢ - x̄)^2
sigma^2 = SS / N (population)
s^2 = SS / (n - 1) (sample)
SD = sqrtvariance

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

SS = Sigma(xᵢ - x̄)^2
sigma^2 = SS / N (population)
s^2 = SS / (n - 1) (sample)
SD = sqrtvariance

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Heights of 6 NBA Players (sample)

Inputs

data: 76, 78, 80, 80, 82, 84 type: sample
Mean: 80. Variance: 8. Standard Deviation: 2.828427. Sum of Squared Deviations: 40. Count: 6

With Data Values = 76, 78, 80, 80, 82, 84 and Variance Type = sample as the stated inputs, the result is Mean = 80, Variance = 8 and Standard Deviation = 2.828427. Each value corresponds to the declared output fields.

Example 2: Mutual Fund Returns (population)

Inputs

data: 8.5, 12.3, -4.1, 15.7, 3.2, -1.8, 9.6, 11.2 type: population
Mean: 6.825. Variance: 43.159375. Standard Deviation: 6.56958. Sum of Squared Deviations: 345.275. Count: 8

With Data Values = 8.5, 12.3, -4.1, 15.7, 3.2, -1.8, 9.6, 11.2 and Variance Type = population as the stated inputs, the result is Mean = 6.825, Variance = 43.159375 and Standard Deviation = 6.56958. Each value corresponds to the declared output fields.

Example 3: Student Quiz Scores

Inputs

data: 7, 8, 8, 9, 7, 10, 6, 9, 8, 8 type: sample
Mean: 8. Variance: 1.333333. Standard Deviation: 1.154701. Sum of Squared Deviations: 12. Count: 10

With Data Values = 7, 8, 8, 9, 7, 10, 6, 9, 8, 8 and Variance Type = sample as the stated inputs, the result is Mean = 8, Variance = 1.333333 and Standard Deviation = 1.154701. Each value corresponds to the declared output fields.

Example 4: ANOVA Context — SS Between Groups

Inputs

data: 5, 6, 7, 13, 14, 15 type: population
Mean: 10. Variance: 16.666667. Standard Deviation: 4.082483. Sum of Squared Deviations: 100. Count: 6

With Data Values = 5, 6, 7, 13, 14, 15 and Variance Type = population as the stated inputs, the result is Mean = 10, Variance = 16.666667 and Standard Deviation = 4.082483. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate data variability for hypothesis testing
  • Measure consistency of manufacturing processes
  • Compute variance in financial risk models
  • Determine sum of squares for ANOVA