Question

Find the mean of 28,24,37,42,56,59,67. What is the new value of the mean
if each observation is i) multiplied by 2 ii) decreased by 30%.?​

Answer 1

Answer:

I hope it will help you...

Answer 2

The mean of the given set of observations is 44.71.

i) The new mean obtained on multiplying each observation by 2 = 89.42

ii) The mean obtained on decreasing each observation by 30 % = 31.3

• The mean of a given set of observations = Sum of all observations / Total number of observations in the set

• Given numbers are 28, 24, 37, 42, 56, 59, 67.

Total number of observations in the set = 7

∴  Mean = ( 28 + 24 + 37 + 42 + 56 + 59 + 67 ) / 7

Or, Mean = 313 / 7

Or, Mean = 44.71

i) If each observation is multiplied by 2, the sum also gets multiplied by 2.

=> New sum = 313 × 2 = 626

∴  New Mean = New Sum / 7

Or, Mean = 626 / 7

Or, Mean = 89.42

ii) If each observation is decreased by 30 %,  the sum also gets decreased by 30 % on the whole.

=> New Sum = Original sum - 30 % of the original sum

=> New Sum = 313 - 30 % of 313

=> New Sum = 313 - ( 30 / 100 ) × 313

=> New Sum = 313 { 1 - ( 3 / 10 ) }

=> New Sum = 313 { ( 10 - 3 ) / 10 }

=> New Sum = 313 × (7 / 10)

=> New Sum = ( 313 × 7 ) / 10

=> New Sum = 219.1

∴   New Mean = 219.1 / 7

Or, New Mean = 31.3