Correct Answer - Option 3 : 118
Given:
Average of 16 numbers is 68.5
54 and 37 are replaced by 45 and 73
Concept Used:
Average = Sum of all observations/Total number of observations
Calculation:
Sum of all observations = Average × Total number of observations
⇒ Sum of all observations = 68.5 × 16
⇒ Sum of all observations = 1096
54 and 37 are replaced by 45 and 73
⇒ 54 + 37 = 91 replaced by 45 + 73 = 118
91 is replaced by 118, and one more number, i.e. x is excluded
⇒ 118 – 91 = 27 and x is added to the total sum
New Sum = 1096 + 27 – x
⇒ New Sum = 1123 – x,
The average is decreased by 1.5
New average = 68.5 – 1.5
⇒ New average = 67
Total numbers = 16 – 1
⇒ Total numbers = 15
New sum of all observations = 67 × 15
⇒ New sum of all observations = 1005
⇒ x = New Sum –Sum
⇒ x = 1123 – 1005
⇒ x = 118
∴ The value of x is 118.