Question

If $m$ is the average (arithmetic mean) of the first $10$ positive multiples of $5$ and if $M$ is the median of the first $10$ positive multiples of 5, what is the value of $M-m$?

• A. $-5$
• B. $0$
• C. $5$
• D. $25$
• E. $27.5$

Answer 1

Answer: (B)

$0$

Mean is the sum of the data 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.

The first $10$ positive multiples of $5$ are $5,10,15,20,25,30,35,40,45,50$

Given that mean is $m$

Therefore, $m=\frac{5+10+15+20+25+30+35+40+45+50}{10}$

$m=\frac{275}{10}=27.5$

Given that median is $M$

Total number of values is $n=10$ (even) then

the median is $M={\frac{(\frac{10}{2}{)}^{th}+(\frac{10}{2}+1)}{2}}^{th}$ value

$M=\frac{5^{th}value+6^{th}value}{2}$

$M=\frac{25+30}{2}=\frac{55}{2}=27.5$

Therefore, $m-M=27.5-27.5=0$