## Calculating the standard deviation using Excel

Excel has functions to calculate the population and sample standard deviations. The appropriate commands are entered into the formula bar towards the top of the spreadsheet and the corresponding cells in the spreadsheet are updated to show the result.

For an example of calculating the population standard deviation, imagine you wish to know how fuel-efficient a new car that you have just purchased is. You calculate how many kilometres you have done per litre on your first five trips. This information is presented as column A of the spreadsheet (figure 5). As you have only made 5 trips you do not have any further information and you are therefore measuring the whole population at this point in time. The command to find the population standard deviation in Excel is **=STDEVP(VALUES)** and in this case the command is **=STDEVP(A2:A6)** which gives an answer of 0.49.

Basing your results on the population standard deviation and assuming that your first 5 trips in your new car have been typical of your usual journeys, you can be 99% confident that your new car will do between 14.75 **(MEAN-3SD)** and 17.69 **(MEAN+3SD)** kilometres per litre .

The same data can be used to demonstrate how to calculate the sample standard deviation in Excel. In this case, imagine that the data in column A represent the kilometres per litre found for a sample of 5 new cars tested by the manufacturer. The population standard deviation is calculated using **=STDEV(VALUES)** and in this case the command is **=STDEV(A2:A6)** which produces an answer of 0.55.

The sample standard deviation will always be greater than the population standard deviation when they are calculated for the same dataset. This is because the formula for the sample standard deviation has to take into account the possibility of there being more variation in the true population than has been measured in the sample.

Based on their sample of 5 cars, and therefore using the sample standard deviation, the manufacturers could state with 99% confidence that similar cars will do between 14.57 **(MEAN-3SD)** and 17.87 **(MEAN+3SD)** kilometres per litre .

These examples show the quick method of calculating standard deviations using a cell range. Each of the commands can also be written out in a longer format with the individual kilometres/litre entered.

For example entering: **=STDEV(16.13,16.40,15.81,17.07,15.69)** produces an identical result to **=STDEV(A2:A6)**.However, if one of the values in column A was found to be incorrect and adjusted, the cell range method would automatically update the calculation of the standard deviation whereas the longer format will require manual adjustment of the command.