# What is the difference between the formulas for the standard deviation of a population and the standard deviation for a sample?

##### 1 Answer

Standard deviation of a population implies that the "mean" is a calculable value; standard deviation of a sample implies that the "mean" is an estimate (based on the average of the sample values).

#### Explanation:

The **standard deviation** (for both **population** and **sample** statistics) is based on the corresponding **variance**.

If all values of a **population** are known, then the average of these values is the **true mean** value.

The **population variance** can be calculated as the average of the squares of the differences between individual values and the **true mean**.

If only a **sample** of the entire population is known. We can not calculate the **true mean** and must settle for the **sample mean**. This means that besides the difference between the sample values and the **true mean** we have another source of deviation, the error between our estimated "sample mean** and the true mean.

As a result, in calculating the **sample variance** our deviation must be increased. This is done by dividing the sum of the squares of the individual deviations from the **sample mean** by one less than the number of sample values.