Average of 15 numbers is 68. Average of first 8 numbers is 63 and average of last 8 numbers is 70. Find out the eighth number.

Given:

Average of 15 numbers = 68

Average of first 8 numbers = 63

Average of last 8 numbers = 70

Concept:

The eighth number can be calculated by subtracting the sum of the first 7 numbers from the sum of the first 8 numbers, which all can be derived from their averages.

Calculation:

Sum of 15 numbers = Average × Number of terms ⇒ 68 × 15 = 1020

Sum of first 8 numbers = Average × Number of terms ⇒ 63 × 8 = 504

Sum of last 8 numbers = Average × Number of terms ⇒ 70 × 8 = 560

Now, the 8th number is a part of both series (first 8 numbers and last 8 numbers)

So, if we add the sums of the first 8 and last 8 numbers, we take the 8th number twice

To get the correct sum, Subtract the sum of 15 numbers from the sum obtained in step 5 ⇒ (504 + 560) - 1020 = 44

∴ The eighth number is 44.