The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last is 11.4, then find the sixth number?
Answer: 11.5
Explanation
Let's denote the sum of all 11 numbers as S.
Given:
Average of 11 numbers = 10.9
S / 11 = 10.9
S = 10.9 × 11 = 119.9
Average of first 6 numbers = 10.5
Sum of first 6 numbers = 10.5 × 6 = 63
Average of last 6 numbers = 11.4
Sum of last 6 numbers = 11.4 × 6 = 68.4
Let's denote the 6th number as x. The sum of all 11 numbers can also be calculated as:
Sum of first 6 numbers + Sum of last 6 numbers - x = S
63 + 68.4 - x = 119.9
131.4 - x = 119.9
x = 11.5
