# Constructing Data

Let us consider the following example to understand the concept of constructing data.

Class X has 60 students. Their marks in the Maths subject have been taken into consideration.

36, 33, 47, 48, 50, 39, 20, 7, 16, 36, 45, 47, 30, 22, 17.21, 10, 30, 22, 33, 5, 37, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 20, 38, 22, 44, 16, 24, 10, 27, 39, 36, 18, 28, 49, 29, 32, 23, 31, 21, 34, 22, 23, 36, 24,

Let us make a frequency distribution table by grouping the data.

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

This table helps us to understand,

• Most of the students have scored between 20 and 40.
• 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. Similarly, 20 occurs in classes 10-20 and 20-30. 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.

Similarly, in the class interval 20-30, 20 is the lower class limit and 30 is the upper class limit.

Observe that the difference between the upper class limit and lower class limit for each of the class intervals 0-10, 10-20, 20-30 etc., is equal, (10 in this case). This difference between the upper class limit and lower class limit is called the width or size of the class interval.