Question

Identify the modal class for the following data:

Farm	20-30	30-40	40-50	50-60	60-70
Animals	12	14	21	34	15

(A) 60-70
(B) 50-60
(C) 30-40
(D) 20-30

Answer 1

The mode of any given data set is the value which appears the highest number of times in a given data set. The term “Modal Class” is used for when there are grouped data sets with ranges in place of values. Modal class is the range of data with the highest frequency in the table of values.

Complete step by step solution:
Mode is the number which appears most often in a given data set. Since the number of animals is grouped, we will first arrange the frequency in the increasing order of their value. Then, we will look at the range of farms with the greatest number of animals. This range of farms will be the modal class of the required data set.
We have our data set given to us as:

Farm	20-30	30-40	40-50	50-60	60-70
Animals	12	14	21	34	15

The frequencies of this data set are 12, 14, 21, 34, 15. Here, we can see the frequency is discretely distributed. Arranging this set of frequencies in the ascending order, we get the series:
12, 14, 15, 21, 34
Now, from the above ascending series of frequencies, we can see that the frequency with the highest value is 34. Now, we will find the range of data in which this frequency lies.
This can be observed in the second last column in the following data set diagram:

Farm	20-30	30-40	40-50	50-60	60-70
Animals	12	14	21	34	15

Thus, the class of 50-60 has the highest frequency.
Hence, the modal class for the data set given to us is 34.

Note: It is very important to arrange the frequencies in ascending order. This is because there may be some cases when the group of data is so large that we couldn’t just find the class with the highest frequency. This is where arranging the frequencies in increasing order helps us find the highest frequency, and thus the corresponding modal class.