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If we prepare an ungrouped frequency distribution table of this data as done earlier, it would
occupy a large space and take a lot of our time. In such a case, we condense the data into several
groups called class intervals or classes.
For making a grouped frequency distribution, let us first decide the width or size of the classes.
Here, the data ranges from 5 to 69, i.e., 69 – 5 = 64. If we take the class size 10, then there will be
64 = 64 . , i.e., 7 classes as 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, and 60-70.
10
Thus, we can arrange the above data into classes as shown below.

Class Tally marks Frequency Note that a class interval includes
the lower-class limit, not the upper-
0-10 ||| 3 class limit. In class interval 0-10, all the

10-20 |||| |||| 9 observations from 0 to 9 (10 not included)
are taken.
20-30 |||| |||| ||| 13
Similarly, in class interval 10-20, all the
30-40 |||| |||| 10 observations from 10 to 19 (20 not included)
40-50 |||| |||| |||| 14 are taken.
Here, the classes 0-10, 10-20, 20-30, 30-40,
50-60 |||| || 7 40-50, 50-60 and 60-70 are continuous. Such
60-70 |||| 4 a type of distribution is called continuous
distribution.
Total 60
Data represented in this manner is called grouped and the distribution obtained is called grouped
frequency distribution.
In a class interval like 60-70, 60 is called the lower limit and 70 is called the upper limit. The
difference between the upper limit and the lower limit is called the class size or class width.
Class size = Upper limit – Lower limit

The midpoint of the class is called its class mark which is given by
Lower limit + Upper limit
Class mark =
2
60 + 70 130
Therefore, the class mark of 60-70 = 2 = 2 = 65

Consider two successive classes say 0 -10 and 10 -20. Their class marks are 0 + 10 = 5 and 10 + 20 = 15
Note: 2 2
respectively. The difference between these two class marks = 15 – 5 = 10, which is same as the class
width of 0 -10 or 10 - 20. The same is true for any two successive classes.

There is another way of classifying the above given raw data into groups. We can also choose the
classes as 0-9, 10-19, 20-29, 30-39, and so on. In such cases, the class 0-9 includes all the observations
from 0 to 9 (i.e., 9 included). Similarly, 10-19 includes all the observations from 10 to 19 (i.e., 19
included) and so on.

Class Tally marks Frequency

0-9 ||| 3
10-19 |||| |||| 9

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