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# The average of five consecutive numbers is n. If the next two numbers are also included the average will A) increase by 1.4B) increase by 2C) increase by 1D) remain the same

Last updated date: 10th Sep 2024
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Hint: Assume the number to be $x$ and then note the next numbers and then accordingly find the new average. Apply an average formula.

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.
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.