Questions & Answers

Question

Answers

A) increase by 1.4

B) increase by 2

C) increase by 1

D) remain the same

Answer
Verified

Let us assume the first number to be $x$. Therefore the next four consecutive numbers are $x + 1,x + 2,x + 3,x + 4$. Average is the sum of observations divided by the number of observations.

Average = Sum of Observations/ Number of Observations

Applying this concept, we get $\dfrac {{x + x + 1 + x + 2 + x + 3 + x + 4}}{5} = \dfrac {{5x + 10}}{5} = n$

Therefore $5x + 10 = 5n$ and after solving this equation we get $x = n - 2$. When we add the next two numbers, we get $5x + 10 + x + 5 + x + 6 = 7x + 21$. Therefore, the new average is $\dfrac {{7x + 21}}{7} = x + 3$. Substituting the value of $x = n - 2$, the value of the new average in terms of n is $n - 2 + 3 = n + 1$.

The previous average of numbers is $n$ and the new average is $n + 1$. So, the average increases by 1.