Last updated at May 29, 2018 by Teachoo
Transcript
Example 16 The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations. Let the observations be 1 , 2 , 3 , ..., 20 and be their mean. Given that Variance = 5 and n = 20. We know that Variance = 1 n ( ) 2 5 = 1 20 ( ) 2 5 20 = ( ) 2 100 = ( ) 2 ( ) 2 = 100 If each observation is multiplied by 2 , we get new observations, Let the new observations be 1 , 2 , 3 , ..., 20 where = 2 ( ) We need to find variance of the new observations i.e. New Variance = 1 n ( ) 2 Now, We know = 2 ( ) Calculating in terms of = 1 = 1 20 2 = 2 ( 1 20 ) = 2 From (1) ( ) 2 = 100 ( 1 2 1 2 ) 2 = 100 ( 1 2 ( )) 2 = 100 1 2 2 ( ) 2 = 100 1 2 2 ( ) 2 = 100 ( ) 2 = 100 4 ( ) 2 = 400 Now, New Variance = 1 n ( ) 2 = 1 20 400 = 20
Examples
Example 2
Example 3 Important
Example 4
Example 5 Important
Example 6 (Normal Method)
Example 6 (Shortcut Method) Important
Example 7 Important
Example 8
Example 9 Important
Example 10 Important
Example 11
Example 12 Important
Example 13 Deleted for CBSE Board 2022 Exams
Example 14 Important
Example 15 Important Deleted for CBSE Board 2022 Exams
Example 16 You are here
Example 17 Important
Example 18
Example 19 Important
Examples
About the Author