Frequency Distribution Table: When the number of observations in an experiment is large then we can convert it into the tabular form which is called a Frequency Distribution Table.

Ungrouped Frequency Distribution Table: When the frequency of each class interval is not arranged or organized in any manner.

Grouped Frequency Distribution Table: The frequencies of the corresponding class intervals are organised or arranged in a particular manner, either ascending or descending. 

Inclusive or discontinuous Frequency Distribution: A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.

Exclusive or continuous Frequency Distribution: A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution.

Frequency Distribution table:

• Presentation of data in ascending or descending order can be quite time-consuming.

• When the number of observations in an experiment is large then we can convert it into the tabular form which is called a Frequency Distribution Table.

• A frequency table shows the list of categories or groups of things, together with the number of times the items occur.

• There are two types of frequency distribution table:
  (i) Ungrouped Frequency Distribution Table
  (ii) Grouped Frequency Distribution Table

A. Ungrouped frequency distribution table:

When the frequency of each class interval is not arranged or organised in any manner.

Consider the marks obtained (out of 100 marks) by 30 students of Class IX of a school:
10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88, 80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60, 88.

B. Grouped Frequency Distribution Table:

• Raw data can be ‘grouped’ and presented systematically through ‘grouped frequency distribution’.

• Presenting data in this form simplifies and condenses data and enables us to observe certain important features at a glance. This is called a grouped frequency distribution table.

Grouped data could be of two types as below:-

1. Inclusive or discontinuous Frequency Distribution:-

A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.

While analysing a frequency distribution, if there are inclusive type of class intervals they must be converted into exclusive type. This can be done by extending the class intervals from both the ends.

2. Exclusive or continuous Frequency Distribution:-

A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution.

1) 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.

• Each of the groups 0-10, 10-20, 20-30, etc., is called a Class Interval.

• In the class interval, 10-20, 10 is called the lower class limit and 20 is called the upper-class limit.

• This 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) is called the width or size of the class interval.

2) Let us now consider the following frequency distribution table which gives the weights of 38 students of a class:

In this class, we cannot added new students with 35.5 kg and 40.5 kg because there are gaps in between the upper and lower limits of two consecutive classes. So, we need to divide the intervals so that the upper and lower limits of consecutive intervals are the same. For this, we find the difference between the upper limit of a class and the lower limit of its succeeding class. We then add half of this difference to each of the upper limits and subtract the same from each of the lower limits.

So, the new class interval formed from 31-35 is (31 – 0.5) - (35 + 0.5), i.e., 30.5-35.5.

Now it is possible for us to include the weights of the new students in these classes. But, another problem crops up because 35.5 appears in both the classes 30.5-35.5 and 35.5-40.5.

By convention, we consider 35.5 in the class 35.5-40.5 and not in 30.5-35.5.

Now, with these assumptions, the new frequency distribution table will be as shown below: