# 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, 20Find the mode and median of this data. Are they same?

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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).

Updated on 10-Oct-2022 13:33:20