Question

If the cumulative frequency for the class interval (30-40) is 70 and for class interval (50-60) is 150 , then the value of y =

$\begin{array}{ccccccc}\text{Class Interval}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Frequency}& 12& 20& x& 18& 10& y\end{array}$

• A. 20
• B. 80
• C. 70
• D. 50

Answer 1

The correct option is C

70

The cumulative frequency table for the given distribution is

$\begin{array}{ccc}\text{Class Interval}& \text{Frequency}& \text{Cumulative Frequency}\\ 0-10& 12& 12\\ 10-20& 20& 32\\ 20-30& x& (32+x)\\ 30-40& 18& (50+x)\\ 40-50& 10& (60+x)\\ 50-60& y& (60+x+y)\end{array}$

$\therefore \text{Cumulative frequency for class interval (30 - 40) is 70}$

$\Rightarrow 50+x=70$

$\Rightarrow x=70-50$

$\Rightarrow x=20$

$\text{Cumulative frequency for class interval (50 - 60) is 150}$

$\Rightarrow 60+x+y=150$

$\Rightarrow 60+20+y=150$

$\Rightarrow y=150-(60+20)$

$\Rightarrow y=150-80$

$\Rightarrow y=70$