Variance of a Data Set

Introduction to variance of a data set:

Data is nothing but a set of information or collection of facts. We can analyze the data’s with the help of charts and graphs. The method of collecting or preparing the data’s is the data collection.
Variance is the term that  explains how average value of the data set vary from the measured data.

Variance of Data Set:

Following are the steps involved in finding the variance of data set:    

Step 1: First step is to find the Average, that is the arithmetic mean for the given set of numbers.

Mean = Sum of all values / Total number of elements

Step 2: To find the sum of squares for all the given values in the given data set.

Step 3: Divide the result we obtained in Step 2 over the total number of elements in the given data set.

Step 4: Find the difference between the square of mean and the result we obtained from step 3

Step 5: For finding the variance, take the square root of the number that  we obtained as a result from step 4.

Thus, using the above steps, we can easily calculate the variance of the given data set.

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Solved Examples for Finding Variance of a Data Set:

Ex1: Find the variance  of the given data set: { 5, 6, 9, 13, 19 }

Sol:

Step 1: Arithmetic mean             =  (5 +6 + 9+ 13 + 22) / 5

= 55 / 5

=  11

Step 2: Sum of squares               =  52 + 62 + 92 + 132 + 222

=  25 + 36 + 81 + 169 + 484

= 795

Step 3: Sum of squares / Total number of elements

= 795 / 5

= 159

Step 4: Result from Step 3 – square of mean value

= 159 – 112       

= 159 – 121

= 38

Step 5: Variance                        = square root ( 38 )

= 6.16

The variance of the given data set is 6.16

Ex 2: Find the variance  of the given data set: { 2, 3, 4, 5,16 }

Sol:

Step 1: Arithmetic mean             =  (2 +3 + 4+ 5 + 16) / 5

= 30 / 5

=  6

Step 2: Sum of squares               =  22 + 32 + 42 + 52 + 162

=  4 + 9 + 16 + 25 + 256

= 310

Step 3: Sum of squares / Total number of elements

= 310 / 5

= 62

Step 4: Result from Step 3 – square of mean value

= 62 – 62       

= 62 – 36

= 26

Step 5: Variance                        = square root ( 26 )

= 5.1

The variance of the given data set is 5.1