Question

The median class for the given data is

$$\begin{array}{ccccccc}\text{Height (in cm)}& \text{Less than 140}& \text{Less than 145}& \text{Less than 150}& \text{Less than 155}& \text{Less than 160}& \text{Less than 165}\\ \text{No. of girls}& 4& 11& 29& 40& 46& 51\end{array}$$

• A. 145 - 150
• B. 150 - 155
• C. 155 - 160
• D. 160 - 165

Answer 1

The correct option is A

145 - 150

The given table can be written as:
$$\begin{array}{ccccccc}\text{Height (in cm)}& \text{Less than 140}& \text{Less than 145}& \text{Less than 150}& \text{Less than 155}& \text{Less than 160}& \text{Less than 165}\\ \text{No. of girls}& 4& 11& 29& 40& 46& 51\end{array}$$

$$\begin{array}{ccccccc}\text{Height (in cm)}& \text{Less than 140}& 140-145& 145-150& 150-155& 155-160& 160-165\\ \text{Cumulative Frequency}& 4& 11& 29& 40& 46& 51\end{array}$$

n = 51

$\therefore \frac{n}{2}=\frac{51}{2}$
= 25.5

Since there are a total of 51 observations, the median class is the one whose cumulative frequency is closest to and greater than 25.5. The cumulative frequency for the class '145 - 150' is 29 which is greater than 25.5. The median class is '140 - 145'. Thus, the class interval '145 - 150' is the required answer.