Question

What is the modal class for the following table given below?

Fruits	100-90	90-80	80-70	70-60	60-50	50-40	40-30
Boxes	12	34	56	78	98	65	70

(a) 100-90
(b) 40-30
(c) 80-70
(d) 60-50

Answer 1

Hint: Mode is the number which appears most often. Since the marks have been grouped, we will first find the midpoints of the given groups. Then we will look at the range of marks in which the most number of students have scored. We will make a table that has the groups, its midpoint and the frequency. The midpoint for this range will be the mode for the given data.

Complete step by step answer:
We will first arrange the given frequencies in an ascending order. Then, we will look for the class that corresponds to the highest frequency. This class contains the mode of the given frequencies. This class will be the modal class for the given data. The modal class is the class with the highest frequency.
We know that the mode is the number or observation that most often appears. So, the modal class is the class in a grouped data that contains the mode. That means, the class that has the highest frequency is the modal class of the grouped data. Now, let us list all the frequencies given in the following manner,
12, 34, 56, 78, 98, 65, 70.
Next, we will arrange these given frequencies in ascending order so that we can find the highest frequency. The ascending order of the frequencies is given as,
12, 34, 56, 65, 70, 78, 98.
We can see that the frequency 98 is the highest. The class that has the frequency as 98 is 60-50. Hence, the modal class is 60-50.
The correct option is (d).
Note:
It is important to arrange the frequencies in an ascending order. There can be multiple classes that have the same frequency. There is also the possibility that the number of classes is so large that we cannot determine the highest frequency in one glance. Hence, the process of arranging the frequencies in ascending order will definitely work for either of these two cases.