Variance Calculator
Results:
What is Variance Calculator?
A variance calculator computes the measure of how spread out data points are from the mean. Variance quantifies the average squared deviation from the mean, helping you understand data distribution and variability.
Population Variance (σ²):
σ² = Σ(x-μ)²/n
Used when you have data for the entire population
Sample Variance (s²):
s² = Σ(x-μ)²/(n-1)
Used when you have a sample from a larger population
How It Works
Enter Data
Input comma-separated values
Choose Type
Select population or sample
Calculate Mean
Find average of all values
Get Variance
Calculate squared deviations
Common Examples
Test Scores
Student scores: 85, 90, 78, 92, 88
- • Mean: 86.6
- • Population Variance: 24.64
- • Standard Deviation: 4.96
Sales Data
Monthly sales: 100, 120, 95, 110, 105
- • Mean: 106
- • Sample Variance: 93.75
- • Standard Deviation: 9.68
Calculation Table
| Data Set | Mean | Population Variance | Sample Variance |
|---|---|---|---|
| 1, 2, 3, 4, 5 | 3.0 | 2.0 | 2.5 |
| 10, 20, 30 | 20.0 | 66.67 | 100.0 |
| 5, 5, 5, 5 | 5.0 | 0.0 | 0.0 |
| 2, 4, 6, 8, 10 | 6.0 | 8.0 | 10.0 |
Social Media & Sharing
Share this variance calculator with others:
Frequently Asked Questions
What's the difference between population and sample variance?
Population variance uses n in the denominator (entire population), while sample variance uses n-1 (Bessel's correction) to account for sampling bias.
How do I interpret variance results?
Higher variance means data points are more spread out from the mean. Lower variance indicates data points are closer to the mean. Zero variance means all values are identical.
What's the relationship between variance and standard deviation?
Standard deviation is the square root of variance. While variance is in squared units, standard deviation is in the same units as the original data.
Can variance be negative?
No, variance is always non-negative because it's calculated using squared differences. The minimum value is zero (when all data points are identical).
How many data points do I need for sample variance?
You need at least 2 data points for sample variance calculation since the formula uses n-1 in the denominator. With only 1 point, the denominator would be zero.