How to Find Standard Deviation

What is standard deviation? The phrase 'standard deviation' and a bit of common sense applied around it will tell you that standard deviation has something to do with change or difference. Spot on. Now suppose you find the mean for some data. Now if you want to know what is the difference of each individual number from the mean, what you need is to find the standard deviation. So in a nutshell, the standard deviation is the difference of an amount from the mean of the total collection of data.

Finding Standard Deviation

Of course now there are many ways of finding the standard deviation on the calculator, on excel and manually as well. So let us look at how to find the standard deviation in each of the following ways.

Standard Deviation by Hand

Now the two parts in calculating standard deviation, as outlined in the previous paragraph are first, finding the mean, and second, finding the individual deviations. Now I firmly believe that learning the method by hand first is more important than proceeding to the calculators, as it helps you learn better.

Let me start with how to calculate the mean of numbers. The first step is to add all the numbers. The second step is to divide the resulting number by the number of terms in the sequence. So if you have four numbers: 12, 15, 19, 24, then the mean of the 4 numbers is 12+15+19+24 = 70, divided by the number of terms, i.e., 4. Hence, the mean of 12, 15, 19, 24 is 17.5.

Now to calculate the standard deviation, the next step is to calculate the difference between each individual piece of data and the mean. So now you have the numbers -5.5, -2.5, +1.5, +6.5.

Now this was the first step in calculating standard deviation. The second step is to square each individual deviation and add them up. So we have -

30.25 + 6.25 + 2.25 + 42.25.

= 81

The next step is to divide 81 by one less than the total number of terms given, i.e. 3.

81/3

= 27

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

= 27^1/₂

= 5.2

Standard Deviation in Excel

This too 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.

The next step is to 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 standard deviation of the sequence.

Standard Deviation on a Calculator

Since the Ti-83 is the most common calculator, I'll teach you directly how to find standard deviation on Ti-83.

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 standard deviation manually, in excel and on a calculator. Now I hope you know how to calculate standard deviation and will be able to complete your homework without too much hassle!