Variance Calculator Formula
Understand the math behind the variance calculator. Each variable explained with a worked example.
Formulas Used
Variance Pop
variance_pop = ((a - mean_val)^2 + (b - mean_val)^2 + (c - mean_val)^2) / 3Variance Sample
variance_sample = ((a - mean_val)^2 + (b - mean_val)^2 + (c - mean_val)^2) / 2Std Dev
std_dev = sqrt(((a - mean_val)^2 + (b - mean_val)^2 + (c - mean_val)^2) / 3)Mean
mean = mean_valVariables
| Variable | Description | Default |
|---|---|---|
a | Value 1 | 4 |
b | Value 2 | 8 |
c | Value 3 | 6 |
mean_val | Derived value= (a + b + c) / 3 | calculated |
How It Works
How to Calculate Variance
Formula (Population Variance)
σ² = Σ(xᵢ - μ)² / N
Steps
1. Find the mean (μ) 2. Subtract the mean from each value 3. Square each difference 4. Find the average of the squared differences
Variance is the square of the standard deviation.
Worked Example
Find the variance of 4, 8, and 6.
a = 4b = 8c = 6
- 01Mean = (4 + 8 + 6) / 3 = 6
- 02Squared differences: (4-6)² = 4, (8-6)² = 4, (6-6)² = 0
- 03Variance (population) = (4 + 4 + 0) / 3 = 2.6667
- 04Variance (sample) = (4 + 4 + 0) / 2 = 4
Ready to run the numbers?
Open Variance Calculator