Question

The average of five consecutive natural numbers is $m$ . If the next three natural numbers are also included, how much more than $m$ will the average of these $8$ number be ?

• A. $1$
• B. $1.5$
• C. $1.4$
• D. $2$

Answer 1

Answer: (B)

$1.5$

Average is the sum of the data values divided by the total number of data values.

Given that, average of $5$ consecutive natural numbers is $m$

Let the $5$ consecutive natural be $(x-2),(x-1),x,(x+1),(x+2)$

Therefore, average is $\frac{(x-2)+(x-1)+x+(x+1)+(x+2)}{5}$

$⟹m=\frac{5x}{5}⟹x=m$ -------(1)

Given that next three natural numbers are included. Therefore, the next three natural numbers will be $(x+3),(x+4),(x+5)$

Therefore, the average of all the $8$ numbers

$=\frac{(x-2)+(x-1)+x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)}{8}$

$=\frac{8x+12}{8}$

$=x+\frac{12}{8}$

$=m+1.5$ (from (1))

Therefore the average of the $8$ numbers is $1.5$ more than $m$