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

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.

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

Total number of students = 100

So, middle terms are $(\frac{n}{2}{)}^{th}$ and $(\frac{n}{2}+1{)}^{th}$ terms.

Hence median terms are ${\frac{100}{2}}^{th}\text{term}$ and $(\frac{100}{2}+1{)}^{th}\text{term}$

= ${50}^{th}\text{term and}{51}^{st}\text{term}$