In the graph on the left, the standard deviation of both sets of data is the same. This is observed by the same spread. The graph on the right shows two sets of data with very different standard deviations. The taller graph represents a smaller standard deviation than the shorter graph.
The formula for the standard deviation, , is
where is the number of data values (sample size) and is the sample mean.
This means that the standard deviation is an average of the squared deviations of each data value from the mean.
If a data set is small, a rule for estimating the standard deviation for small data sets is
standard deviation or
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