Indirect questions - Multiplication of observation
Indirect questions - Multiplication of observation
Last updated at April 16, 2024 by Teachoo
Example 13 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