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

Given the scores in mathematics test (out of 25) of 15 students is as follows

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

Mode means which observation is most frequently occurred

Here observe that 20 is most frequently occurred so mode is 20. __(1)

first of all average the data in ascending order

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

Here observe that no of observations $\left(n\right)=15$

So median is ${\frac{N+1}{2}}^{th}$ term

median $={\frac{15+1}{2}}^{th}$ term

$={\frac{16}{2}}^{th}$ term $=8^{th}$ term

$\text{median}$ $=20$ __(2)

from (1) & (2)

mode = median

(Both are same)