Variance Calculator
Calculate the sample and population variance to measure how spread out values are from the mean.
Sample Variance
2.5000
Sample Variance vs Value 1
Formula
## How to Calculate Variance ### Population Variance **sigma^2 = Sum of (xi - mean)^2 / N** ### Sample Variance **s^2 = Sum of (xi - mean)^2 / (n - 1)** Variance measures the average squared distance of each data point from the mean. The sample variance divides by (n-1) instead of n to correct for the bias introduced by estimating the population mean from the sample (Bessel's correction).
Esempio Risolto
Find the variance of 4, 8, 6, 5, 7.
- 01Mean = (4 + 8 + 6 + 5 + 7) / 5 = 30 / 5 = 6
- 02Squared deviations: (4-6)^2=4, (8-6)^2=4, (6-6)^2=0, (5-6)^2=1, (7-6)^2=1
- 03Sum of squares = 4 + 4 + 0 + 1 + 1 = 10
- 04Population Variance = 10 / 5 = 2
- 05Sample Variance = 10 / 4 = 2.5
Domande Frequenti
When should I use sample vs. population variance?
Use population variance when you have data for the entire group of interest. Use sample variance when your data is a subset drawn from a larger population, which is the more common scenario.
Why divide by n-1 for the sample variance?
Dividing by n-1 (Bessel's correction) produces an unbiased estimator of the population variance. Dividing by n would systematically underestimate the true variance.
What are the units of variance?
Variance is measured in squared units of the original data. If values are in meters, variance is in meters squared. Take the square root to get the standard deviation in original units.
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