Just as we make a distinction between population mean (u) and sample mean (X), we also
make a distinction between population standard deviation (s) and sample standard deviation (s).
Sample standard deviation is computed using the formula:
Σ(X - X )2
where s represents sample standard deviation, n the number of observations in the sample, and X
the sample mean. The sum of the squared differences, Σ(X - X)2, is divided by n-1, rather than by
n alone. This adjustment is called degrees of freedom. Allowing for degrees of freedom (df) also
gives a better estimate of the sample standard deviation since not all data points were analyzed.
As a rule of thumb, you should do the following: When dealing with a population, use the
population mean and population standard deviation. When dealing with a sample, use the sample
mean and the sample standard deviation.
From the following data, what is the mean and standard deviation of the days of accumulated
leave for all ten people in an office: 6, 6, 7, 8,
9, 11, 13, 13, 13, 14?
mean = _________
standard deviation __________