The mean of 11 numbers is 42. If the mean of the first 6 numbers is 37 and that of the last 6 numbers is 46, find the 6^th number.

Given,

Mean of 11 number = 42

So, Sum of numbers = 11 × 42 = 462.

Mean of first 6 numbers = 37.

Hence, sum of first six numbers = 6 × 37 = 222.

Mean of last 6 numbers = 46

Sum of last 6 numbers = 6 × 46 = 276.

So,

The 6^th number = (sum of first 6 numbers and last 6 numbers) – (Sum of 11 numbers)

= (222 + 276) – 462 = 498 – 462 = 36.

The 6^th number is 36.