Enter numbers separated by commas (complete population data)
Result
Step-by-Step Derivation
Population Variance Formula
Population Variance σ² = Σ(x - μ)² / N
μ = Population Mean = Σx / N
σ = √σ² (Population Standard Deviation)
Population variance measures the spread of an entire population. Use when you have data from all members of a group.
⚠Population variance uses N (total count) in the denominator, not n-1. Use sample variance for incomplete data.
What is Population Variance?
Population variance (σ²) is a measure of how spread out the values in an entire population are. It quantifies the average squared distance from each data point to the population mean.
Population Mean (μ)
The average value of all data points in the population. μ = Σx / N
Population Variance (σ²)
Average squared deviation from the mean. Measures spread in squared units.
Population SD (σ)
Square root of variance. Most common measure of spread.
When to Use
Use when you have complete population data, not just a sample.
💡 Example: Population: 2, 3, 5, 7, 8, 10. Mean = 5.83, Variance = 7.47, Std Dev = 2.73.
Applications
Census DataQuality ControlGovernment StatisticsBusiness AnalyticsMarket Research
Frequently Asked Questions
What is population variance?▼
Population variance (σ²) measures the spread of an entire population. It is the average of the squared differences from the population mean μ. Formula: σ² = Σ(x - μ)² / N.
When should I use population variance?▼
Use population variance when you have data from the entire population (all members of a group), not just a sample. Example: test scores of all students in a class.
What is the difference between population and sample variance?▼
Population variance divides by N (total population size). Sample variance divides by n-1 (degrees of freedom) to correct estimation bias.
How is population variance related to standard deviation?▼
Population standard deviation (σ) is the square root of population variance (σ²). σ = √σ². Standard deviation is in the same units as the original data.
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