# What does the standard deviation of a data set describe?

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Oct 22, 2015

The standard deviation of a data set describes how much do the data differ from their mean.

#### Explanation:

The standard deviation of a data set describes the difference between the data in the set and their mean. The simpliest interpretation could be: "The higher deviation, the more differences there are in the data set". It is rarely non-zero. In fact, as far as I know, the only possibility for a data set to have zero deviation is when it contains only the same numbers.

Example

Let there be 2 companies A and B.

In company A the mean salary is $3,000 and the deviation$50.
In company B the mean salary is $2,800 and the deviation$300.

The interpretation of these values is that in company A the salary is between $2,950 and$3,050, while in B it is between $2,500 and$3,100.

The difference in deviation shows, that in A salaries are close to the mean, while in B the range of salaries is much bigger.

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