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