Question

The following data shows the runs scored by different batsmen. Find the modal number of runs scored by the batsmen.
$$\begin{array}{cc}\text{Runs Scored}& \text{Number of batsmen}\\ 3000-4000& 4\\ 4000-5000& 18\\ 5000-6000& 9\\ 6000-7000& 7\\ 7000-8000& 6\\ 8000-9000& 3\\ 9000-10000& 1\\ 10000-11000& 1\end{array}$$

• A. 4608.69
• B. 4000
• C. 5000
• D. 4300

Answer 1

The correct option is A 4608.69

Modal calss is the class with the highest frequency. So, the modal class for the given data is 4000-5000.
$\because \text{Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$
where $f_1$ represents the frequency of the modal class.
Also,
$l=$lower boundary of the modal class
$h=$ size of the modal class interval
$f_0=$ frequency of the class preceding the modal class
$f_2=$ frequency of the class succeeding the modal class
$\therefore \text{Mode}=4000+\left[(\frac{18-4}{2\left(18\right)-4-9})\right]\times 1000$
$=4000+\left[(\frac{18-4}{36-4-9})\right]\times 1000=4000+\left[(\frac{14}{23})\right]\times 1000=4608.69$