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Question

In the given frequency distribution where the marks are ordered, which 2 observations (students) are the median observations?

Marks obtainedNumber of students(Frequency)2062520282429283315384422431


A

50th term and 49th term

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B

61st term and 49th term

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C

50th term and 51st term

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D

Cannot be determined

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Solution

The correct option is C

50th term and 51st term


First we need to find the total number of students. For this a cumulative frequency distribution should be used as shown below.

Marks obtainedNumber of students(Frequency)Cumulativefrequency20662520262824502928783315933849742299431100

How has the cumulative frequency distribution been made? We just found the number of students who did not score more than a particular mark. The number of students who did not score than the highest mark is the entire strength that took test = 100.

Hence, we know that number of terms is 100 because there are 100 mark sheets - one for each student. For 100 terms, since number of terms is even, the median terms are 50th and 51st terms


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