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's know the meaning of the terms "Mode" and "Median"

Mode = The no. which is occurring most frequently in a set of numbers is called Mode

Median = Median refers to the value which lie in the middle of the set of numbers (When arranged in ascending or descending order).

Now Coming to the question :-

First we will find the mode of the data :- 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20

20 have occurred 4 times ∴

The most frequently occurring value =  20                                                                     Therefore the mode of the given set of data is 20

Now Median;

Numbers arranged in ascending order  = 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25

So the middle value here is 20.

$\therefore$ Median and Mode both are same.

Answer 2

Concept:

Mode = The no. with the highest frequency is called mode

Median = Median refers to the middlemost value in a set of numbers (When arranged in ascending or descending order).

Given:

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

Solution:

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

20 have occurred 4 times ∴

maximum frequency value =  20                                                                     Therefore the mode of the given set of data is 20

Median;

Numbers arranged in ascending order  = 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25

So the  median is 20.

Therefore, Median and Mode both are same

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