Frequency Distribution Table Statistics

Frequency Distribution Table – Data Collection:

In our day to day life, recording of information is very crucial. A piece of information or representation of facts or ideas which can be further processed is known as data. Weather forecast, maintenance of records, dates, time everything is related to the collection of data.

The collection, presentation, analysis, organization and interpretation of observations or data is known as statistics. Using statistics, predictions about the nature of data can be made based on the previous data. Statistics is helpful when large amount of data is to be studied and observed.

The statistical data which is collected, can be represented by various methods such as tables, bar graphs, pie charts, histograms, frequency polygons etc.

In the upcoming discussion, collection of data through frequency distribution table is discussed.

Suppose the runs scored by the 11 players of Indian cricket team in a match are given as follows:

\(25, 65, 03, 12, 35, 46, 67, 56, 00, 31, 17\)

This type of data is in raw form and is known as raw data. The difference between the measure of highest and lowest value in a collection of data is known as the range. Here, the range is- \(|67 – 00|, i.e. 67\)

When number of observations increase, this type of representation is quite hectic and the calculations based on this could be quite complex. As statistics is about presentation of data in organized form, the representation of data in tabular form is more convenient.

Considering another example: In a quiz, the marks obtained by 20 students out of 30 are given as:

\(12, 15, 15, 29, 30, 21, 30, 30, 15, 17, 19, 15, 20, 20, 16, 21, 23, 24, 23, 21\)

This data can be represented in tabular form as follows:

Table 1: Frequency Distribution Table (Ungrouped)

Marks obtained in quiz Number of students(Frequency)
12 1
15 4
16 1
17 1
19 1
20 2
21 3
23 2
24 1
29 1
30 3
Total 20

The number of times a data occurs in a data set is known as frequency of data. In above example, frequency is the number of students who scored various marks as tabulated. This type of tabular data collection is known as ungrouped frequency table.

What happens if instead of 20 students 200 students took the same test. Would it have been easy to represent such data in format of ungrouped frequency distribution table? Well, obviously no. To represent huge amount of information, the data is subdivided into groups of similar sizes known as class or class intervals and the size of each class is known as class width or class size.

For better understanding, consider the following table which represents the height of 200 students of high school.

Table 2: Grouped Frequency Distribution Table

Height of Students (in cm.) Number of students(Frequency)
130-139 19
140-149 42
150-159 35
160-169 78
170-189 26
Total 200

The first column of the table represents the class interval with a class width of 10. In each class the lowest number denotes the lower class limit and the higher number indicates the upper class limit. For the class 150-159, the lower class limit is 150 and the upper class limit is 159. This is known as grouped frequency distribution.