How to Calculate Standard Deviation

The standard deviation is the average of all the averages of several sets of data. Statisticians use the standard deviation to calculate how close the various sets of data are to the mean of all the data sets. Standard deviation is often associated with the mean of test scores in schools.

Difficulty: Moderate

Instructions

Things You'll Need:

• Graphing calculator

Calculate standard deviation by hand

1. Compute the mean of the data set. Do this by adding all the numbers in the data set together and dividing by the amount of pieces of data. For example, if you have added 27 numbers together, divide that total by 27. This is the mean of the data set.

2. Calculate the deviance of each piece of data from the mean of the data set. This is done by subtracting the total mean from each individual number.

3. Square each of the individual deviations.

4. Add these squared differences.

5. Divide the number you got from adding the squared differences together by one less than the data set. If there are 27 numbers, divide by 26.

6. Calculate the square root of the result of the previous step. The result of this calculation is the standard deviation.

Calculate standard deviation using a graphing calculator

7. Turn on your graphing calculator, go to the stats/editor screen and enter your data set into list1. Once this is done, return to your home page by hitting the home button.

8. Push the catalog button and scroll through the applications until you find "stdDev(". Place the arrow next to it and press enter.

9. Type the word "list1" into the open parenthesis. After you have put that in, close the parenthesis so you calculator doesn't show an error message.

10. Press the enter button. The calculator has done the calculations and you now have the standard deviation of your data set.

Tips & Warnings

• Using 1-var stats in the stats/editor screen will also give you the standard deviation. Using that function will also give you other information associated with your data set.

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[thomasrm]

on 2/19/2008 I wish I could remove my answers, but can't find that function. So, here goes a clarification to my earlier post. This was a good article, but it could also have specified in the introduction that it is a guide for calculating ST.DEV for the POPULATION based on a sample(all data sets - which is says, but doesn't use the word population), instead of ST. DEV for the SAMPLE itself. For the sample, you would in Step 5, divide with the number of respondents/data units (N), instead of n-1.
Hope this was useful.

[thomasrm]

on 2/19/2008 Nice guide(!), but I have seen other places that in Step 5, others would divide with N, instead of n-1? Is this the difference between calculating using the population (N) compared to the sample (n-1)? wikipedia is one of the instances.

[thomasrm]

on 2/19/2008 Nice guide(!), but I have seen other places that in Step 5, others would divide with N, instead of n-1? Is this the difference between calculating using the population (N) compared to the sample (n-1)? wikipedia is one of the instances.

[thomasrm]

on 2/19/2008 Very nice step-by-step, but other places I've seen that in Step 5, you should divide by the actual N, not n-1. Any comments? Or is n-1 based on sample size calculation, compared to population calculation (N)?