Statistics

Variance

Formula

σ² = Σ(xᵢ − μ)² / N

What is Variance?

Variance measures the average squared deviation of each data point from the mean. It is the square of the standard deviation and quantifies how spread out the data is.

Variables

σ
σ² — Variance (population)
x
xᵢ — Each data value
μ
μ — Mean
N
N — Number of data values

Worked Examples

Example 1

Find the variance of 4, 8, 12.

Solution:

Mean = 8. Deviations: −4, 0, 4. Squared: 16, 0, 16. Sum = 32. σ² = 32/3 ≈ 10.67

Frequently Asked Questions

Related Formulas

Mean = (Sum of all values) / (Number of values)

Median = Middle value of sorted data

Mode = Most frequently occurring value

Range = Maximum value − Minimum value

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