Averages do not tell us everything about a sample. Samples can be very uniform with the data all bunched around the mean (Figure 1) or they can be spread out a long way from the mean (Figure 2). The statistic that measures this spread is called the standard deviation. The wider the spread of scores, the larger the standard deviation.

For data that has a normal distribution, 68% of the data lies within one standard deviation of the mean.

How to Calculate the Standard Deviation: ​

1. Calculate the mean (x̅) of a set of data​

2. Subtract the mean from each point of data to determine (x-x̅). You'll do this for each data point, so you'll have multiple (x-x̅).

3. Square each of the resulting numbers to determine (x-x̅)^2. As in step 2, you'll do this for each data point, so you'll have multiple (x-x̅)^2.

4. Add the values from the previous step together to get ∑(x-x̅)^2. Now you should be working with a single value.

5. Calculate (n-1) by subtracting 1 from your sample size. Your sample size is the total number of data points you collected.

6. Divide the answer from step 4 by the answer from step 5

7. Calculate the square root of your previous answer to determine the standard deviation.

8. Be sure your standard deviation has the same number of units as your raw data, so you may need to round your answer.

9. The standard deviation should have the same unit as the raw data you collected. For example, SD = +/- 0.5 cm.

Using Excel 2016 to Calculate the Standard Deviation

• Use Excel to calculate the mean of your data.

• Click on the box in which you want the Standard Deviation to be placed

• Click the "Formulas" tab at the top of the screen

• Select the “Insert Function button”​

• Search to find the STDEV option, click OK​

• Highlight the data of which you want the SD to be calculated, click OK. Be sure not to select the mean as one of your data points for calculating standard deviation. This is a common mistake.

• Once you have the mean and standard deviation, you need to make sure that you set the values to the correct number of digits. EXCEL will default to giving you too many numbers after the decimal place. Your mean and standard deviation must have the same precision (number of digits after the decimal) as your data points. So, the example, the standard deviation should be a whole number. To do this, click the box which is displaying the standard deviation and on the "Home" tab click the decrease decimal button until you have the correct number of digits showing.