How to calculate a standard deviation

Not all the data found in the research appear exactly as they should from a theoretical perspective. The standard deviation can help explain how far from certain data points they are, from the average data point, without having to make an approximate calculation. Knowing how to calculate the standard deviation is not only an important part of problem solving and numerical analysis, it is often a necessary component to decipher these problems.

You will need to:
  • Calculator
  • Paper
  • Pen or pen
Steps to follow:

one

Take the number on which you want to measure the standard deviation, as well as the average or average of all the numbers and the number of numbers that exist. For example, if you are looking at the height of six men and you get 178, 183, 170, 179, 175 and 186, and you want to find out the standard deviation, the average is calculated by adding up all the numbers and dividing by the number of actual results, is 1071/6, or 178.5 centimeters. Your total number of grades is six. Your individual number will be each sample number.

two

Find the sum of all your individual results, minus the average score, all squared. In this example we are going to do (178 - 178, 5) squared, (183 - 178, 5) squared, (170 - 178, 5) squared, (179 - 178, 5) squared, (175 - 178), 5) and squared (186 - 178, 5) squared, and then add all the numbers. This gives you 0.25 + 20.25 + 72.25 + 0.25 + 12.25 + 56.25 = 161.5.

3

Subtract 1 from the total sample. In this case, it is 6 -1, which is 5.

4

Divide the sum of the numbers in step 2 by the total of the sample minus one, which in this case is 161.5 divided by 5, so it is 32.3.

5

Take the square root of the number obtained in step 4. In this case, it would be the square root of 32.3, which leaves 5.68. This is your standard deviation.

Tips
  • All these calculations can be done by hand, but it is much faster using a scientific calculator.