Question

In the given frequency table, the frequency of class-interval 20 - 30 is 4 greater than the frequency of class-interval 40 - 50.

$\begin{array}{cc}\text{Marks}& \text{Cumulative frequency}\\ \text{Less than 10}& 5\\ \text{Less than 20}& 16\\ \text{Less than 30}& 35\\ \text{Less than 40}& K\\ \text{Less than 50}& 80\end{array}$
The value of ‘K’ and the frequency of class-interval 30 - 40 respectively are

• A. 65, 30
• B. 30, 65
• C. 50,30
• D. 65, 35

Answer 1

The correct option is A 65, 30

$\begin{array}{cccc}\text{Class intervals}& \text{Frequency}& \text{Cumulative frequency}& \\ 0-10& 5& 5& \\ 10-20& 11& 16& \\ 20-30& 19& 35& \\ 30-40& K-35& K& \\ 40-50& 80-K& 80& \\ & {\sum }_{i=1}^5{f}_i=80& & \end{array}$

Now, the frequency of class-interval 20 - 30 is 4 greater than the frequency of class-interval 40 - 50.
$\Rightarrow 19–4=80–K$
$\Rightarrow 15=80–K$
$\Rightarrow K=65$
Frequency of class-interval 30 - 40 = K – 35
= 65 – 35
= 30
Therefore, the value of K is 65 and the frequency of class-interval 30 - 40 is 30.
Hence, the correct answer is option (a).