Question

Forty candidates from $10^{th}$ class of a school appear for a test. The number of questions (out of 60) attempted by them in forty-five minutes is given here.
52, 42, 40, 36, 12, 28, 15, 37, 35, 22, 39, 50, 54, 39, 21, 34, 46, 31, 10, 09, 13, 24, 29, 31, 49, 58, 40, 44, 37, 28, 13, 16, 29, 36, 39, 41, 47, 55, 52, 09.
Prepare a frequency distribution table with the class size 10 and answer the following:
(i) Which class has the highest frequency?
(ii) Which class has the lowest frequency?
(iii) Write the upper and lower limits of the class (20-29)
(iv) Which two classes have the same frequency?

Answer 1

Hint: Firstly, to solve this question, we will need to draw a frequency table, which we will make by using the class size of 10. After that, we will observe and find out the class which has the highest frequency, the lowest frequency, and will find an adjusted frequency table to answer the upper and lower limits of the class (20-29), and also we will find the classes with the same frequency.

Complete step-by-step solution:
Let us prepare the frequency distribution table for the given data in question.
Now, from the data, we can see that we have the lowest data as 09 and the largest data entry as 58, and in question, we are asked to take the class size as 10. So, we can take first-class as 0-9, the next class as 10-19, and so on up to 50-59.
So, the frequency distribution table for the class size of 10, for given data will show the number of data elements appearing in the particular interval.
Thus, the frequency data table is,

Class Interval	Frequency
0 – 9	2
10 – 19	6
20 – 29	7
30 – 39	11
40 - 49	8
50 – 59	6
Total	40

Using this table, we can observe and answer the following questions:
( i ) (30-39) has the highest frequency as from the table we can see that the frequency of class (30-39) is 11.
( ii ) (0-9) has the lowest frequency as from the table we can see that frequency of class (0-9) is 2.
( iii ) Now, the lower limit and upper limit of any of the corresponding classes is not the same. So, we will find the adjusted class limit which will be the same for each class.
So, to adjust the class limit we will subtract 0.5 from the lower limit of each class except in class 0-9 as marks can not be negative and will add 0.5 in the upper limit of each class.
So, we will have an updated frequency distribution table with adjusted class limits as,

Class Interval	Frequency
0 – 9.5	2
9.5 – 19.5	6
19.5 – 29.5	7
29.5 – 39.5	11
39.5 – 49.5	8
49.5 – 59.5	6
Total	40

So, the upper limit of class (20-29) is 29.5 and the lower limit is 19.5.
( iv ) (10-19) and (50-59) have the same frequency, which is equal to 6.

Note: While making the frequency table, most importantly cross-check that the total number of data elements is equal to the total of frequency in the table of the frequency distribution. Also, you can add columns of Tally marks to the frequency distribution table. Do not forget to make an adjusted class frequency table for solving the third part of the question.