Question

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 6th number.

Answer 1

Mean of 11 numbers = 42
Sum of 11 numbers = 42$\times$11 = 462
Mean of the first 6 numbers = 37
Sum of the first 6 numbers = 37$\times$6 = 222
Mean of the last 6 numbers = 46
Sum of the last 6 numbers = 46$\times$6 = 276
∴ 6th number = [(Sum of the first 6 numbers + Sum of the last 6 numbers) $-$ Sum of 11 numbers]
= [(222 + 276) $-$ 462]
= [498 $-$ 462]
= 36
Hence, the 6th number is 36.