The average of eleven consecutive positive integers is d. If the last two numbers are excluded, by how much will the average increase or decrease?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. will decrease by 1.
We know that,
Average = Sum of observations/Number of observations
Let the first integer be x and average be d
According to the question:
⇒ x + (x + 1) + (x + 2) + ..... + (x + 10) = 11 × d
⇒ 11x + 55 = 11d
⇒ x + 5 = d
⇒ x = d - 5
Let the new average be A
⇒ x + (x + 1) + (x + 2) + ..... + (x + 8) = 9 × A
⇒ 9x + 36 = 9A
⇒ x + 4 = A
on putting x = d - 5
⇒ d - 5 + 4 = A
⇒ A = d - 1
Hence, the new average will decrease by 1