# What are the variance and standard deviation of {18, -9, -57, 30, 18, 5, 700, 7, 2, 1}?

##### 2 Answers

Assuming we are dealing with the entire population and not just a sample:

Variance

Standard Deviation

#### Explanation:

Most scientific calculators or spreadsheets will allow you to determine these values directly.

If you need to do it in a more methodical way:

- Determine the
**sum**of the given data values. - Calculate the
**mean**by dividing the sum by the number of data entries. - For each data value calculate its
**deviation from the mean**by subtracting the data value from the mean. - For each data value's deviation from the mean calculate the
**squared deviation from the mean**by squaring the deviation. - Determine the
**sum of the squared deviations** - Divide the sum of the squared deviations by the number of original data values to get the
**population variance** - Determine the square root of the population variance to get the
**population standard deviation**

If you want the **sample variance** and **sample standard deviation**:

in step 6. divide by 1 less than the number of original data values.

Here it is as a detailed spreadsheet image:

Note: I would normally simply used the functions

and

instead of all these details

Variance = 44383.45

Standard deviation

#### Explanation:

The mean is given by

The variance is given by

The standard deviation is given by