Question

Sam’s test scores are history 76, geography 74, maths 92, English 81 and chemistry $80$ , if average $($arithmetic mean$)$ score is M and median score is m. What is the value of M-m
(A) 0.4
(B) 0.5
(C) 0.6
(D) 0.8

Answer 1

Hint: First we will find the mean of the above data by using formula for average mean and then we will average the given data in increasing order to find median of data. Then we will subtract median from mean. But before solving the question we should know about mean and median.
The mean $($average$)$ of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle number in a sorted, ascending or descending list of given data.

Complete step-by-step answer:
MEAN, $m = \dfrac{{Sum\,of\,all\,the\,data\,}}{{Number\,of\,data}}$
Median, m $ = $ middle data of sorted data
MEAN, $M = \dfrac{{Sum\,of\,all\,the\,data\,}}{{Number\,of\,data}}$
$M = \dfrac{{76 + 92 + 81 + 80 + 74}}{5}$
$M = \dfrac{{329 + 74}}{5}$
$M = \dfrac{{403}}{5}$
$M = 80.6$
Median, m is middle data so, in 74, 76, 80, 81, 92
80 is the median m,
According to question $M - m$
$ = 80.6 - 80$
$ = 0.6$
Therefore option (C) i.e. 0.6 is the correct option
So, the correct answer is “Option C”.

Note: One should arrange the given data in increasing or decreasing order, before solving for median. The median is the middle number in a sorted, ascending or descending list of given data.