FRAME 40.

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

s =

n-1

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.

QUESTION:

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 __________

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