Question

The marks (out of $25$) of $10$ students are as follows :

$21,20,13,15,10,16,17,14,20,18$

Find the range, mean and median of the data.

Answer 1

Arrange the given marks in ascending order :

$10,13,14,15,16,17,18,20,20,21$

Here, highest observation $=21$

and, lowest observation $=10$

and, Range $=$ Highest observation $-$ lowest observation

$=21-10=11$

So, the range of the given marks is $\mathbf{11}$.

Now, sum of marks obtained $=10+13+14+15+16+17+18+20+20+21$

$=164$

Mean $=\frac{\text{Sum of marks obtained}}{\text{Total number of students}}$

$=\frac{164}{10}=16.4$

So, the mean of given marks is $\mathbf{16}\mathbf{.}\mathbf{4}$.

Now,

Here, n $=10$, which is even.

So, Median $=$$\frac{1}{2}\left\{{\left(\frac{n}{2}\right)}^{\text{th}}\text{observation}+{(\frac{n}{2}+1)}^{\text{th}}\text{observation}\right\}$

Median of given marks $=$ $\frac{1}{2}\left\{{\left(\frac{n}{2}\right)}^{\text{th}}\text{observation}+{(\frac{n}{2}+1)}^{\text{th}}\text{observation}\right\}$

$=$ $\frac{1}{2}\left\{{\left(\frac{10}{2}\right)}^{\text{th}}\text{observation}+{(\frac{10}{2}+1)}^{\text{th}}\text{observation}\right\}$

$=\frac{1}{2}\left(5^{\text{th}}{\text{observation + 6}}^{\text{th}}\text{observation}\right)$

$$\begin{gathered} =\frac{1}{2}(16+17) \\ =16.5 \end{gathered}$$

So, the median of the given marks is $\mathbf{16}\mathbf{.}\mathbf{5}$.