Statistics

The Standard deviation is simply the square root of the variance and gives the spread of the sample or population about the mean.

For the sample data the standard deviation is denoted by S and is defined as:
For a population data the standard deviation is denoted by and is defined as:

That is,

The standard deviation plays a dominating role for the study of variation in the data. It is a very widely used measure of dispersion. As far as the important statistical tools are concerned, the first important tool is the mean and the second important tool is the standard deviation.

A couple has six children whose ages are 6, 8, 10, 12, 14 and 16. Find the standard deviation in ages.

1. The population mean is:

2. For each number subtract the mean and then square the result. Work out the average of those squared differences.

3. Find the positive square root of the variance:

Properties:

The standard deviation is in the same units as the units of the original observations.
Standard deviation is independent of change of origin but not of scale (Proof).