Business Statistics - Statistical Data and Its Presentation

 

Statistical Data and Its Presentation

 

Data

Data means a set of information, especially facts or numbers, collected to be examined and considered and used to help business enterprises, any non-profit organizations and Government Authorities making decisions in course of managing their affairs.

 

Statistical Data

Statistical data are the data that are collected and/or generated by statistics in process of statistical observations or statistical data processing.

 

What is meant by Presentation of Data?

After data is collected it needs to be presented in a meaningful, efficient and easily understandable manner to identify its main features at a glance using a suitable presentation method. Generally, the data in statistics can be presented in three different forms, such as textual presentation, tabular presentation and graphical presentation.

 

Tabular Presentation of Data

Data can be presented in tabular form in three different ways as follows:

1.       Simple Distribution,

2.       Simple Frequency Distribution, and

3.       Grouped Frequency Distribution

 

Simple Distribution

This is the method of distribution for presentation of data where the data is simply arranged either in ascending or descending order of the values of the observations without counting or considering the number of times each observation has been occurred in the data.

 

Example 1:

Consider the marks given below, which are obtained by 10 students in Mathematics: 36, 55, 73, 95, 42, 60, 78, 25, 62 and 75.

 

Find the range for the given data.

 

Solution:

Given Data: 36, 55, 73, 95, 42, 60, 78, 25, 62, and 75

 

The data given is called the raw data.

 

First, we have to arrange the data in the ascending order as follows: 25, 36, 42, 55, 60, 62, 73, 75, 78, and 95

 

Therefore, the lowest mark is 25 and the highest mark is 95.

 

We know that the range of the data is the difference between the highest and the lowest value in the data. Therefore,

Range = 95 − 25 = 70.

 

Note: Presentation of data in ascending or descending order can be time-consuming if we have a larger number of observations in an experiment. In other words, the method of simple distribution for presentation of data is suitable only for a data having small number of observations.

 

Simple Frequency Distribution

This is the method of distribution for presentation of data where the data is arranged in tabular form in terms of frequency (i.e. number of times of occurrences) of each identical value of the observations in the given data.

 

Example 2:

Consider the following marks obtained by 30 students in Mathematics (out of 100 marks):

 

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

 

Construct a Simple Frequency Distribution Table.

 

Solution:

In this example, the number of observations is larger compared to example 1. So, the presentation of data under the Simple Distribution Method is a bit time-consuming. Hence, we go for the Simple Frequency Distribution Method. In this method, we can arrange the data in tabular form in terms of frequency (i.e. number of times of occurrences) of each identical value of the observations in the given data.

 

For example, 3 students scored 50 marks. Hence, the frequency of 50 marks is 3. Now, let us construct the frequency distribution table for the given data.

 

Simple Frequency Distribution Table

Marks	Frequency
10	1
20	1
36	3
40	4
50	3
56	2
60	4
70	4
72	1
80	1
88	2
92	3
95	1
Total	30

 

 

Grouped Frequency Distribution

This is the method of distribution for presentation of data where the data is arranged in different groups along with their respective frequencies in a Grouped Frequency Distribution Table.

 

Example 3:

Consider the marks obtained by 100 students in a Mathematics subject (out of 100 marks)

 

95, 67, 28, 32, 65, 65, 69, 33, 98, 96,76, 42, 32, 38, 42, 40, 40, 69, 95, 92, 75, 83, 76, 83, 85, 62,

37, 65, 63, 42, 89, 65, 73, 81, 49, 52, 64, 76, 83, 92, 93, 68, 52, 79, 81, 83, 59, 82, 75, 82, 86, 90,

44, 62, 31, 36, 38, 42, 39, 83, 87, 56, 58, 23, 35, 76, 83, 85, 30, 68, 69, 83, 86, 43, 45, 39, 83, 75,

66, 83, 92, 75, 89, 66, 91, 27, 88, 89, 93, 42, 53, 69, 90, 55, 66, 49, 52, 83, 34, 36

 

Construct a Grouped Frequency Distribution Table.

Solution:

In this problem, we have 100 observations to present the data. In this case, we have more data than that in example 1 and example 2. So, these data should be arranged in the tabular form called the Grouped Frequency Distribution table. Hence, we group the given data like 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89 and 90-99 (As our data is from 23 to 98). The groups of data are called the “class intervals” or “classes”, and the size of a class is called “class-size” or “class-width”.

 

Class-width = Upper Class Boundary – Lower Class Boundary

 

For example, for the class interval 30-39 lower class limit is 30 and upper class limit is 39, whereas lower class boundary is (29 + 30)/2 = 29.5 and upper class boundary is (39 + 40)/2 = 39.5

 

Therefore, class-width of the class interval 30-39 = 39.5 – 29.5 = 10

 

Grouped Frequency Distribution Table

Class Interval (Marks)	Frequency
20 – 29	3
30 – 39	14
40 – 49	12
50 – 59	8
60 – 69	18
70 – 79	10
80 – 89	23
90 – 99	12
Total	100