Question

For the positive numbers, $n,n+1,n+2,n+4$ and $n+8$, the mean is how much greater than the median?

• A. $0$
• B. $1$
• C. $n+1$
• D. $n+2$
• E. $n+3$

Answer 1

Answer: (B)

$1$

Mean is the sum of the values divided by the total number of values in the data set.

Median is the middle value of the data values after arranging the data values in the ascending or descending order.

If $n$ is odd, then the median is $(\frac{n+1}{2}{)}^{th}$ value.

If $n$ is even, then the median is ${\frac{(\frac{n}{2}{)}^{th}+(\frac{n}{2}+1)}{2}}^{th}$ value.

Given data set is $n,n+1,n+2,n+4,n+8$

Therefore, mean is $\frac{n+n+1+n+2+n+4+n+8}{5}=\frac{5n+15}{5}=n+3$

Total number of values is $n=5$ (odd) then

the median is$(\frac{5+1}{2}{)}^{th}$ value $=3^{rd}$ value $=n+2$

$Mean-Median=(n+3)-(n+2)=1$

Therefore, Mean is one more than the Median.