Correct Answer - Option 2 : 58.7
Given:
Average of 31 numbers = 59
Average of 1st 11 numbers = 53.9
Average of last 21 numbers = 62.1
Concept:
To find the 11th numbers, subtract the sum of all 31 numbers from the sum of 1st 11 numbers and the last 21 numbers from.
Formula used:
Average of 'n' numbers = Sum of n numbers/n
Sum of 'n' numbers = (Average of 'n' numbers) × (n)
Calculation:
∵ Average of 31 numbers = 59
∴ Sum of 31 numbers = 59 × 31
= 1,829
∵ Average of 1st 11 numbers = 53.9
∴ Sum of 1st 11 numbers = 53.9 × 11
= 592.9
∵ Average of last 21 numbers = 62.1
∴ Sum of last 21 numbers = 62.1 × 21
= 1304.1
∴ The 11th numbers = (Sum of 1st 11 numbers + Sum of last 21 numbers) - (Sum of 31 numbers)
= (592.9 + 1304.1) - 1,829
= 1897 - 1829
= 68
∴ Excluding the 11th number from the sum of 31 numbers = 1829 - 68
= 1761
∴ Average of the remaining 30 numbers = (Sum of 30 numbers)/30
= 1761/30
= 58.7
