Question

The mean of 11 numbers is 35. If the mean of first 6 numbers is 32 and that of last 6 numbers is 37, find the 6th number.

Answer 1

Let the 6^th number be x

Given that mean of 11 results = 35

∴ sum of 11 numbers = 11 × 35 = 385

Mean of the first 6 results = 32

Sum of first 6 numbers = 6 × 32 = 192

Mean of the last 6 results = 37

Sum of the last 6 results = 6 × 37 = 222

Therefore,

Sum of first 6 numbers + sum of last 6 numbers – 6^th number = sum of 11 numbers

192 + 222 - x = 385

⇒ 414 – x = 385

⇒ x = 29