Question

Find the median of the following data distribution.$$\begin{array}{ccccccccc}Marksobtained& 20& 29& 28& 33& 42& 38& 43& 25\\ Numberofstudents& 6& 28& 24& 15& 2& 4& 1& 20\end{array}$$

• A. 40
• B. 30
• C. 28.5
• D. 29

Answer 1

The correct option is C 28.5

First we arrange the marks in ascending order and prepare a frequency table as shown.
By adding number of students we know the total number of students in the class. This is 100.
The information shown in the right column is called cumulative frequency. $$\begin{array}{ccc}Marks& Number& Cumulative\\ obtained& ofstudents& frequency\\ 20& 6& 6\\ 25& 20& 26\\ 28& 24& 50\\ 29& 28& 78\\ 33& 15& 93\\ 38& 4& 97\\ 42& 2& 99\\ 43& 1& 100\end{array}$$

n = 100.
The median = average of ${50}^{th}$ and ${51}^{st}$ terms of distribution.
From the last column, we can observe that
Marks obtained by 50th student = 28 and
Marks obtained by 51st student = 29

The median is the average of these terms = 28.5.