When calculating sample variance ($s^2$), why is the sum of squares divided by $n-1$ instead of $n$?
Answer
This adjustment, known as Bessel's correction, prevents underestimating the true variance of the larger population.
Dividing by $n-1$ instead of $n$ when working with a sample is a correction applied because using $n$ would generally result in an underestimate of the variance belonging to the complete population from which the sample was drawn.
Related Questions
What fundamental question does variance provide a precise mathematical answer to?If you summed the deviations of every data point from the mean ($x_i - ar{x}$), what result would you always obtain?What is the primary statistical purpose served by squaring each deviation from the mean?What divisor is used when calculating the variance for an entire population ($\sigma^2$)?When calculating sample variance ($s^2$), why is the sum of squares divided by $n-1$ instead of $n$?If house prices are measured in dollars, what unit will the calculated variance be expressed in?What operation yields the standard deviation from the variance?Which key mathematical property makes variance especially useful for creating and testing complex statistical models?Compared to variance, what is the primary weakness of the Range as a measure of spread?In statistical analysis, which measure of spread is typically preferred for building models or performing hypothesis tests due to its mathematical properties?