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?
Given:
The scores in mathematics test (out of 25) of students is as follows:
19,25,23,20,9,20,15,10,5,16,25,20,24,12,20
To do:
We have to find the mode and median of the given data.
Solution:
Arrange the data in ascending order,
$5 , 9 , 10 , 12 , 15 , 16 , 19 , 20 , 20 , 20 , 20 , 23 , 24 , 25 , 25$
Mode $=$ Most frequent data
Mode $= 20$ (20 occurs 4 times in the given data)
Median $= \frac{(n+1)}{2}$th term when $n$ is odd.
Number of observations $n = 15$
Median $=\frac{(15 + 1)}{2}$th term
$= \frac{16}{2}$th term
$= 8$th term
$8^{th}$ term is 20.
Therefore,
Median $= 20$
Mode and Median are the same value(20).
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