Question

In a mathematics test given to$15$ students, the following marks (out of $100$) are recorded: $41,39,48,52,46,62,54,40,96,52,98,40,42,52,60$. Find the mean, median and mode of this data.

Answer 1

Step 1: Find the mean

Given data: $41,39,48,52,46,62,54,40,96,52,98,40,42,52,60$

The total number of students, $n=15$.

We know that when we have $n$ values in a set of data namely $x_1,x_2,.....,x_n$. then the mean of the given data is given by

$\overline{x}=\frac{x_1+x_2+....+x_n}{n}=\frac{1}{n}\underset{i=1}{\overset{n}{\sum x_i}}$

So, the mean of the given data$=\frac{41+39+48+52+46+62+54+40+96+52+98+40+42+52+60}{15}$

$$\begin{gathered} =\frac{822}{15} \\ =54.8 \end{gathered}$$

Therefore, the mean of the given data is $54.8$.

Step 2: Find the median

By arranging the given data in ascending order we get,

$39,40,40,41,42,46,48,52,52,52,54,60,62,96,98$

We have $n=15$,

We know that If the number of values or observation in the given set of data is odd, then the median $={\left(\frac{n+1}{2}\right)}^{th}$observation.

So, the median of the given data $={\left(\frac{15+1}{2}\right)}^{th}$observation

$={\left(\frac{16}{2}\right)}^{\mathrm{th}}$observation

$=8^{\mathrm{th}}$ observation

$=52$

Therefore, the median of the given data is $52$.

Step 3: Find the mode

We know that the most frequent number in the data set is known as mod.

In the data element $52$ occurs 3 times, which is the maximum number of times.

Therefore, the mode of the given data is $52$.

Hence, the mean of the given data is $54.8$, the median is $52$ and the mode is $52$.