Summarize this article:

The standard deviation is a measure of how spread out your data is. It gives you information on how similar each data point is within your sample, which helps you determine if the data is significant. At first glance, the equation may seem a bit complicated, but these steps will walk you through the process of the calculation. The formula is s = √∑((xi – µ)2/(N – 1)).  s is the standard deviation. ∑ indicates that you will sum all of the sample values collected. xi represents each individual value from your data. µ is the average (or mean) of your data for each group. N is the total sample number. To calculate the standard deviation, first you must take the average of the samples in the individual groups. The average is designated with the Greek letter mu or µ. To do this, simply add each sample together and then divide by the total number of samples.  For example, to find the average grade of the group that read the material before class, let’s look at some data. For simplicity, we will use a dataset of 5 points: 90, 91, 85, 83, and 94. Add all the samples together: 90 + 91 + 85 + 83 + 94 = 443. Divide the sum by the sample number, N = 5: 443/5 = 88.6. The average grade for this group is 88.6. The next part of the calculation involves the (xi – µ) portion of the equation. You will subtract each sample from the average just calculated. For our example you will end up with five subtractions.  (90 – 88.6), (91- 88.6), (85 – 88.6), (83 – 88.6), and (94 – 88.6). The calculated numbers are now 1.4, 2.4, -3.6, -5.6, and 5.4. Each of the new numbers you have just calculated will now be squared. This step will also take care of any negative signs. If you have a negative sign after this step or at the end of your calculation, you may have forgotten this step.  In our example, we are now working with 1.96, 5.76, 12.96, 31.36, and 29.16. Summing these squares together yields: 1.96 + 5.76 + 12.96 + 31.36 + 29.16 = 81.2. The formula divides by N – 1 because it is correcting for the fact that you haven’t counted an entire population; you are taking a sample of the population of all students to make an estimation.  Subtract: N – 1 = 5 – 1 = 4 Divide: 81.2/4 = 20.3 Once you have divided by the sample number minus one, take the square root of this final number. This is the last step in calculating the standard deviation. There are statistical programs that will do this calculation for you after inputting the raw data. For our example, the standard deviation of the final grades of students who read before class is: s =√20.3 = 4.51.
Define the formula for standard deviation. Average the samples in each group. Subtract each sample from the average. Square each of these numbers and add them together. Divide by the total sample number minus 1. Take the square root.