Question

In a mathematics test given to 20 students, the marks obtained by students out of 100 are 41, 39, 58, 69, 49, 63, 96, 52, 93, 48, 52, 46, 62, 54, 40, 98, 40, 42, 52 and 60
Find the mean, median and mode of this data.

• A. Mean = 57 & Mode = 51
• B. Mean = 57.7 & Median = 52
• C. Median = 52 & Mode = 52
• D. Mode = 57.7 & Mean = 52

Answer 1

Answer: (B), (C)

The correct options are
B Mean = 57.7 & Median = 52
C Median = 52 & Mode = 52

Arranging the given marks in ascending order,
39, 40, 40, 41, 42, 48, 46, 49, 52, 52, 52, 54, 58, 60, 62, 63, 69, 93, 96, 98.

Now mean,
= $\frac{Sumofobservations}{Numberofobservations}$
$=\frac{39+40+40+41+42+46+48+49+52+52+52+54+58+60+62+63+69+93+96+98}{20}$
$=\frac{1154}{20}$
$=57.7$

For Median,
There are 20 terms
[even number of observations]

Median for even number of observations is the average of $(\frac{n}{2}{)}^{th}$ and $(\frac{n}{2}+1{)}^{th}$ term.
i.e. $(\frac{20}{2}{)}^{th}$ and $(\frac{20}{2}+1{)}^{th}$ term.
which is ${10}^{th}$ and ${11}^{th}$ terms respectively.
$=\frac{Sumof10thand11thterm}{2}$
$=\frac{52+52}{2}$
$=\frac{104}{2}$
$=52$

For Mode,
Mode is a quantity which have highest frequency. So, in the given marks 52 is the mode.