Question

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

$$\begin{array}{cc}Marksobtained& Numberofstudents\left(Frequency\right)\\ 20& 6\\ 25& 20\\ 28& 24\\ 29& 28\\ 33& 15\\ 38& 4\\ 42& 2\\ 43& 1\end{array}$$

• A. 50^th term and 49^th term
• B. 61^st term and 49^th term
• C. 50^th term and 51^st term
• D. Cannot be determined

Answer 1

The correct option is C

50^th term and 51^st term

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

$$\begin{array}{ccc}Marksobtained& Numberofstudents\left(Frequency\right)& Cumulativefrequency\\ 20& 6& 6\\ 25& 20& 26\\ 28& 24& 50\\ 29& 28& 78\\ 33& 15& 93\\ 38& 4& 97\\ 42& 2& 99\\ 43& 1& 100\end{array}$$

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 ${50}^{th}$ and ${51}^{st}$ terms