Question

The marks of 30 students of a class, obtained in a test (out of 75) are given below: -
4, 21, 50, 37, 68, 42, 37, 38, 42, 49, 52, 38, 53, 57, 47, 29, 64, 29, 63, 33, 17, 17, 39, 44, 42, 7, 27, 19, 54, 51.
Form a frequency table with equal class intervals.

Answer 1

Hint: First understand the term ‘frequency table’. Observe the lowest and highest marks so that one can decide the proper range of intervals. Form a table with two columns. Column 1 will have the interval of marks and column 2 will have frequency or the number of students. Take the interval of marks as 10, i.e. like 0 – 10, 11 – 20, 21 – 30 and so on.

Complete step by step answer:
We have been given marks of 30 students and we have to form a frequency table. First let us see what is the meaning of the term frequency table.
In statistics, a frequency distribution / table is a list, table or graph that displays the frequencies of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a practical group or interval. A frequency distribution shows us a summarized group of data divided into mutually exclusive classes and the number of occurrences in a class.
Now, let us come to the question. Here, we must check the lowest and height marks so that we can take proper intervals of marks.
On observing the list given in the question, we find that the lowest marks are 4 and highest marks are 68, while 75 is the total marks. So, let us form a table having two columns. Column 1 will contain an interval of marks, which we are going to consider as an interval of 10, i.e. 0 – 10, 11 – 20, 21 – 30 …… and column 2 will contain a number of students whose marks lie in that particular interval, also called frequency. So, the table would look like: -

Marks	No. of students (frequency)
0 – 10	2
11 – 20	3
21 – 30	4
31 – 40	6
41 – 50	7
51 – 60	5
61 – 70	3
71 – 80	0
Total	30

Note: One may note that we have taken the marks intervals as 0 – 10, 11 – 20, 21 – 30 and so on. We can also take it as 0 – 10, 10 – 20, 20 – 30 and so on. Actually there is not any particular difference between them but only the term name differs. First type of interval is known as inclusive class interval in which upper and lower limit both are considered while the latter type of interval is known as exclusive class interval where lower limit is considered but upper limit is not considered. In the solution, we have used inclusive class intervals. You can use exclusive also.