Question

the marks obtained by 8 students in an examination out of hundred or 80,87 ,81,92 ,87,87 ,83,95 find the median and mode of the data

Answer 1

Arranging the marks obtained in ascending order :

80, 81, 83, 87, 87, 87, 92, 95
There are 8 terms so there are two middle numbers i.e the 87 + 87/2 = 84.
Median = 84.

Mode is the value that occurs more frequently..
Here 87 occurs more frequently so the mode is 87.

Answer 2

Given

Marks obtained by 8 student out of hundred


= 80 , 87 , 81 , 92 , 87 , 87 , 83 , 95

Observation in accending order :-

= 80 , 81 , 83 , 87 , 87 , 87 , 92 , 95

Now as there are even number of data then Median

$= \frac{ \frac{n}{2}th \: observation\: + (\frac{n}{2} + 1) \: observation \: }{2}$
=
$= \frac{ \frac{8}{2} + ( \frac{8}{2} + 1) \: observation }{2} \\ \\ = \frac{4th \: + 5th \: observation}{2}$
which is equal to

$\frac{87 + 87}{2} \\ \\ = 87$

Now Mode = the number with higher frequency

= 87


Hope it helps