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How to Find Standard Deviation

Arjun Kulkarni Feb 17, 2019
Standard deviation is one of the most important tools for statistical analysis. Here are some methods on how to find standard deviation.
The title itself will tell you that the term in question has something to do with a change or difference. Now, suppose you find the mean for some data. If you want to know the difference of each individual number from the mean, what you need is to find the standard deviation.
So, in a nutshell, it is the difference of an amount from the mean of the total collection of data. This piece of information enlists a couple of methods of how to find standard deviation.

Vital Information

This value tells you how spread out the numbers are in your set. It is represented by the Greek letter 'σ'. To find this, you need to go through a couple of calculations first. In simple terms, it is the square root of the variance. Variance is defined as the average of the squared differences from the mean.
To calculate it, you need to find out the simple average of the numbers first. Then, for each and every number, you need to subtract the mean and square the result. This is called a 'squared difference'. The final step is to find out the average of those squared differences. There are three important ways of finding this value, and those are enlisted here.

By Hand

Step 1
The first step is to add all the numbers. Consider the numbers 12, 15, 19, and 24. Add them all, and you will get the result as 70. Keep it aside.

Step 2
The second step is to divide the resulting number by the number of terms in the sequence. Therefore, the mean of the above numbers is: 70/4, i.e., 17.5. Hence, the mean of 12, 15, 19, 24 is 17.5.
Step 3
Here, you have to calculate the difference between each individual piece of data and the mean. So now, you will have:

12 - 17.5 = -5.5
15 - 17.5 = -2.5
19 - 17.5 = 1.5
24 - 17.5 = 6.5
Step 4
Now, square each individual deviation and add them up. So we have:

(-5.5) * (-5.5) = 30.25
(-2.5) * (-2.5) = 6.25
(1.5) * (1.5) = 2.25
(6.5) * (6.5) = 42.25

And, 30.25 + 6.25 + 2.25 + 42.25 = 81
Step 5
The next step is to divide 81 by one less than the total number of terms given, i.e., 3.

Thus, 81/3 = 27

Step 6
The last step is to find the square root of the result.

Thus, 271/2 = 5.2

In Excel

  • This is a very simple process. Enter all the numbers in one column of the excel sheet.
  • Now, click on the formula wizard, and select AVERAGE.
  • In the formula, enter the first and last cell number of the range, separated by a colon and press enter. This will give you the mean for the sequence of numbers.
  • Then go back to the formula wizard and select STDEV.
  • Then, in the formula, again type the first and last cell numbers of the data, separated by a colon. This will give you the result you need.

On a Calculator

Since the Ti-83 is the most common calculator, it would be better to do this on that calculator itself.
  • The first step is to press the '2nd' button, and then press '0'.
  • Then, you have to select 'LN' and using the arrow key, scroll down to the stdDEV, select this function.
  • Now, enter the numbers for which you want to calculate the standard deviation, and enter them in curly brackets. Press enter, you will get your answer.
So, this was all about finding the standard deviation manually, in excel, and on a calculator. Now, hope you know how to calculate this value, and complete your works without too much hassle!