Question

The average of a ten numbers is 72.8. The average of the first six numbers is 88.5 and the average of the last five numbers is 64.4. If the 6th number is excluded, then what is the average of the remaining numbers?

• A. 65.8
• B. 66.5
• C. 67
• D. 66

Answer 1

Answer:

C. 67

Solution: 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: ⇒ Sum of all 10 numbers = 72.8 × 10 = 728 ⇒ Sum of first 6 numbers = 88.5 × 6 = 531 ⇒ Sum of last 5 numbers = 64.4 × 5 = 322 Sum of total 11 numbers = Sum of first 6 numbers + Sum of last 5 numbers ⇒ Sum of total 11 numbers = 531 + 322 = 853 But Sum of 10 numbers is 728 Number 6 is counted twice, ⇒ Number 6 = 853 – 728 = 125 Now number 6 is excluded , ⇒ New sum = 728 – 125 = 603 Average of remaining 9 numbers, ⇒ Average = Sum of 9 numbers/ 9 ⇒ Average = 603/9 = 67 ∴ The average remaining 9 numbers is 67.