Without some correction sample variability is said to be bia

Without some correction, sample variability is said to be “biased.” Define the term \"biased\", and explain how this bias is corrected in the formula for sample variance and sample standard deviation.

Solution

It is biased because true sample values are closer to sample mean than true mean. The sample variance is calculated as squared deviations from sample mean rather than population mean, and thus sample variance would under estimate population variance (biased). This is corrected by dividing sum of squared deviations by (n-1) rather than by (n). Similarly, sample standardard deviation is taken square root of (sum of squared deviaitons divided by (n-1))