Correct Answer - Option 3 : 67
Given:
Average of 10 numbers is 72.8
Average of first 6 numbers is 88.5
Average of last five numbers is 64.4
Formula Used:
Average = Sum of all observations/Total number of observations
Calculations:
Average of 10 numbers is 72.8
⇒ 72.8 = Sum of all 10 numbers/10
⇒ Sum of all 10 numbers = 72.8 × 10
⇒ Sum of all 10 numbers = 728
Average of first 6 numbers is 88.5
⇒ 88.5 = Sum of first 6 numbers/6
⇒ Sum of first 6 numbers = 88.5 × 6
⇒ Sum of first 6 numbers = 531
Average of last five numbers is 64.4
⇒ 64.4 = Sum of last 5 numbers/5
⇒ Sum of last 5 numbers = 322
Sum of total 11 numbers = Sum of first 6 numbers + Sum of last 5 numbers
⇒ Sum of total 11 numbers = 531 + 322
⇒ Sum of total 11 numbers = 853
But Sum of 10 numbers is 728
Number 6 is counted twice,
⇒ Number 6 = 853 – 728
⇒ Number 6 = 125
Now number 6 is excluded ,
⇒ New sum = 728 – 125
⇒ New sum = 603
Average of remaining 9 numbers,
⇒ Average = Sum of 9 numbers/ 9
⇒ Average = 603/9
⇒ Average = 67
∴ The average remaining 9 numbers is 67.
