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As far as I know variance is calculated as $$\text{variance} = \frac{(x-\text{mean})^2}{n}$$ while $$\text{Empirical Variance} = \frac{(x-\text{mean})^2}{n(n-1)} $$ Is it correct? Or is there some other definition? Kindly explain with example or any refence for reading on this topic |
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In your expression for the variance, you need to take a sum (or integral) across the population $$\text{variance} = \frac{\sum_i(x_i-\text{mean})^2}{n}$$ If your data is a sample from the population then this expression will give you a biased estimate of the population variance. An unbiased estimate would be as follows (note the change in the denominator from your expression), often called the sample variance $$\text{Sample variance} = \frac{\sum_i(x_i-\text{mean})^2}{n-1} $$ If on the other hand you were trying to estimate the variance of the sample mean, then you vould have a smaller number, closer to your expression. The square root of this is called the standard error of the mean and a reasonable estimate is $$\text{Standard error} = \sqrt{\frac{\sum_i (x_i-\text{mean})^2}{n(n-1)}} $$ |
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