Question

The scores in mathematics test (out of$25$) of $15$ students is as follows:$19,25,23,20,9,20,15,10,5,16,25,20,24,12,20$ Find the mode and median of this data. Are they same?

Answer 1

Let us first arrange the given scores in ascending order, we

$5,9,10,12,15,16,19,20,20,20,20,23,24,25,25$

Mode: Mode is the value of the variable that occurs most frequently.

Clearly, $20$ occurs a maximum number of times.

Hence, the mode of the given sores is $20$

Median: The value of the middle-most observation is called the median of the data.

Here$n=15,$ which is odd.

Where, $n$ is the number of the students.

$\begin{array}{rcl}\therefore \mathrm{median}& =& \mathrm{value}\mathrm{of}{\left(\frac{\mathrm{n}+1}{2}\right)}^{\mathrm{th}}\mathrm{term}\\ & =& \mathrm{value}\mathrm{of}{\left(\frac{15+1}{2}\right)}^{\mathrm{th}}\mathrm{term}\\ & =& \mathrm{value}\mathrm{of}{8}^{\mathrm{th}}\mathrm{term}\\ & =& 20\end{array}$

Hence, median is also $20$

Yes both are same