The formula to calculate the corrected variance is:
\[ \sigma^2 = \frac{S}{N - 1} \]
Where:
Corrected variance, also known as sample variance, is a measure of the dispersion or spread of a set of values. It is calculated by taking the sum of the squared deviations of each value from the mean, and then dividing by the number of values minus one. This correction (dividing by \(N-1\) instead of \(N\)) is used to provide an unbiased estimate of the population variance when working with sample data. Corrected variance is commonly used in statistics to understand the variability within a dataset and to make inferences about the population from which the sample was drawn.
Example 1:
Using the formula:
\[ \sigma^2 = \frac{200}{10 - 1} = \frac{200}{9} \approx 22.22 \]
Example 2:
Using the formula:
\[ \sigma^2 = \frac{450}{15 - 1} = \frac{450}{14} \approx 32.14 \]
