#### description

- Grouped Frequency Distribution,
- Class Interval,
- Lower class limit, Upper class limit

#### notes

The data regarding choice of subjects showed the occurrence of each of the entries several times.

For example, Art is liked by 7 students, Mathematics is liked by 5 students and so on . This information can be displayed graphically using a pictograph or a bargraph. Sometimes, however, we have to deal with a large data.

For example, consider the following marks (out of 50) obtained in Mathematics by 60 students of Class VIII:

21, 10, 30, 22, 33, 5, 37, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 36, 18, 20, 38, 22, 44, 16, 24, 10, 27, 39, 28, 49, 29, 32, 23, 31, 21, 34, 22, 23, 36, 24, 36, 33, 47, 48, 50, 39, 20, 7, 16, 36, 45, 47, 30, 22, 17.

If we make a frequency distribution table for each observation, then the table would be too long, so, for convenience, we make groups of observations say, 0-10, 10-20 and so on, and obtain a frequency distribution of the number of observations falling in each group.

Thus, the frequency distribution table for the above data can be.

Data presented in this manner is said to be grouped and the distribution obtained is called grouped frequency distribution.

(1) Most of the students have scored between 20 and 40.

(2) Eight students have scored more than 40 marks out of 50 and so on. Each of the groups 0-10, 10-20, 20-30, etc., is called a** Class Interval.**

Observe that 10 occurs in both the classes, i.e., 0-10 as well as 10-20. But it is not possible that an observation (say 10 or 20) can belong simultaneously to two classes.

To avoid this, we adopt the convention that the common observation will belong to the higher class, i.e., 10 belongs to the class interval 10-20 (and not to 0-10). Similarly, 20 belongs to 20-30 (and not to 10-20).

In the class interval, 10-20, 10 is called the **lower class** limit and 20 is called the** upper class limit.** The difference between the upper class limit and lower class limit is called the width or size of the class interval.