What is the formula of variance?
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The formula of variance
σ^2 = (1/N) ∑(x_i – μ)^2
Where:
- σ^2 is the population variance,
- N is the number of elements in the population,
- x_i is the i-th value of the population,
- μ is the mean (average) of the population, and
- ∑(x_i – μ)^2 is the sum of the squared deviations from the mean.
The formula to calculate the variance of a sample is slightly different:
s^2 = (1/(n-1)) ∑(x_i – x̄)^2
Where:
- s^2 is the sample variance,
- n is the number of elements in the sample,
- x_i is the i-th value of the sample,
- x̄ is the mean (average) of the sample, and
- ∑(x_i – x̄)^2 is the sum of the squared deviations from the mean.
The difference between the population variance and sample variance lies in the denominator of the formula.
The denominator of the population variance is N, whereas the denominator of the sample variance is n-1. This difference is due to the fact that the sample variance is an estimate of the population variance and is subject to sampling error. By using n-1 instead of n in the denominator, the sample variance corrects for this error and gives a more accurate estimate of the population variance.