The average of 19 numbers is 24. The average of the first 8 numbers is 26.5 and that of the last 12 numbers is 21.5. If the 8th number is excluded, then what will be the average (correct to one decimal point) of the remaining numbers?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 24.6.
Given:
The average of 19 numbers is 24.
The average of the first 8 numbers is 26.5 and that of the last 12 numbers is 21.5
Formula used:
Average = Sum of observations/number of observations ---- (1)
Calculations:
Sum of 19 numbers = 19 × 24 = 456
Sum of first 8 numbers = 26.5 × 8 = 212
Sum of last 12 numbers = 21.5 × 12 = 258
8th number = (Sum of first 8 numbers + Sum of last 12 numbers) - Sum of 19 numbers
8th number = (258 + 212) - 456
⇒ 470 - 456 = 14
Excluding 8th number, the required average
⇒ (456 - 14/18) = 442/18
⇒ 24.6