Question

The scores in mathematics test (out of 25) of 15 students are as follows:
19, 25, 23, 20, 19, 15, 20, 18, 7, 9, 8, 15, 20, 25, 20.
Find the mode and median of the given data. Are they same?
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Answer 1

Mode = 20.

Median = 19.

Step-by-step explanation:

Mode is the most frequently repeated score of given observations, so

according to given data,

19 repeated 2 times

25 repeated 2 times

23 only 1 time

20 repeated 4 times

15 repeated 2 times

18 only 1 time

7 only 1 time

9 only 1 time

8 only 1 time.

So the frequently repeated score is 20.

20 is the mode of the data.

Median is the middle observation of given data when it is arranged in a ascending order or descending order.

Ascending order of given data:

7,8,9,15,15,18,19,19,20,20,20,20,23,25,25

the middle value by cancelling each term from left and right is 19.

Or by formula, when the data has 'n' observations and if 'n' is odd then the median will be (n+1/2) th observation.

Here 'n' is 15, so (15+1/2)

=(16/2)

=8

So the median will be 8th observation when the data is arranged in ascending order.

The median will be 19.