A standard deviation is a statistical tool that tells you roughly how far, on average, each number in a list of data values varies from the average value or arithmetic mean of the list itself.

For example, for the numbers 1 and 2, the average is 1.5 (add the numbers together and divide by two). The distance away from this mean (the standard deviation) of 1.5 for the numbers 1 and 2, is 0.5 (each number is either 0.5 greater or lesser in value than 1.5).

The STDEV function, however, gives only an estimate of the standard deviation. The function assumes that the entered numbers represent only a small portion or *sample* of the total *population* being studied.

As a result, the STDEV function does not return the exact standard deviation. For example, for the numbers 1 and 2 the STDEV function in Excel returns an estimated value of 0.71 rather than the exact standard deviation of 0.5.

### STDEV Function Uses

Even though it only estimates the standard deviation, the function still has its uses when only a small part of a total population is being tested.

For example, when testing manufactured products for conformity to the mean — for measures like size or durability — not every unit is tested. Only a certain number are tested and from this an estimate of how much each unit in the entire population varies from the mean can be gained using STDEV.

To show how close the results for STDEV can be to the actual standard deviation, in the image above, the sample size used for the function was less than one-third of the total amount of data yet the difference between the estimated and actual standard deviation is only 0.02.

### The STDEV Function's Syntax and Arguments

A function's syntax refers to the layout of the function and includes the function's name, brackets, comma separators, and arguments.

This is the syntax for the Standard Deviation function:

= STDEV ( Number1, Number2, ... Number255)

**Number1**: This is required. It can be actual numbers, a named range, or cell references to the location of data in a worksheet. If cell references are used, empty cells, Boolean values, text data, or error values in the range of cell references are ignored.

**Number2, ... Number255**: This is optional. Up to 255 numbers can be entered

### Example Using Excel's STDEV

In the image above, the STDEV function is used to estimate the standard deviation for the data in cells A1 to D10.

The sample of data used for the function's *Number *argument is located in cells A5 to D7.

For comparison purposes, the standard deviation and the average for the complete data range A1 to D10 is included

### Enter the STDEV Function

If you're using Excel 2016, 2013, 2010, Excel for Mac, or Excel Online, type the formula manually.

- Click cell D12 to make it the active cell, which is the location where the results for the STDEV function will be displayed
- Type
**=STDEV(A5:D7)**and press**Enter**. - Notice the value in D12 change to 2.37.
- This number represents the estimated standard deviation of each number in the list from the average value of 4.5

For older versions of Excel, you can type the formula manually or click in D12 and then open the visual data selector via **Formulas **> **More Functions** > **STDEV**.