Provide Information Regarding Statistics & Econometrics : Visual Representation of Data Lecture 03

Visual Representation of Data

Lecture 03

Visual representation means diagrammatic and graphic representation of statistical data. Although classification and frequency distribution transform the data into summarized form, visual representation is improving the scenario. The visual representation is used to compare two or more complex data sets in the simplest way, which is helpful in insight development.

Following are common visual representations of data used in statistics.

Histogram

A histogram is a diagrammatic device that is used to represent frequency distribution by adjacent rectangles. It is obtained by plotting class boundaries along the x axis and the class frequency along the y axis. The width of the rectangle is meaningless, but the height represents the class frequency of a class. In the case of an unequal class interval, the proportional frequency is used on the y axis. The proportional frequency is obtained by dividing the class frequency by their respective class interval.

Example

Construct a histogram of the following frequency distribution.

Class	13 – 20	21 – 28	29 – 36	37 – 44	45- 52	53 – 60
Frequency	2	7	19	12	9	1

Solution:

First, convert the class limits into class boundaries.

Class	f	Class Boundary	f
13 – 20	2	12.5 – 20.5	2
21 – 28	7	20.5 – 28.5	7
29 – 36	19	28.5 – 36.5	19
37 – 44	12	36.5 – 44.5	12
45 – 52	9	44.5 – 52.5	9
53 – 60	1	52.5 – 60.5	1

Example

Construct a histogram of the following frequency distribution.

Class	10 – 20	20 – 25	25- 40	40 – 50	50 – 55	55 – 65
Frequency	20	15	75	60	40	30

Solution

Class	f	h	f / h
10 – 20	20	10	2.00
20 – 25	15	5	3.00
25 – 40	75	15	5.00
40 – 50	60	10	6.00
50 – 55	40	5	8.00
55 – 65	30	10	3.00

Frequency Polygon

A frequency polygon is a graphic device used to represent the frequency distribution. The frequency distribution is obtained by plotting the points the class marks on the x axis and the class frequencies on the y axis and joining by dotted line segments. The frequency polygon is used to compare two or more data points in a single graph.

Example: Construct a frequency polygon for the following frequency distribution.

Age	00 – 05	05 - 10	10 – 15	15 - 20	20 - 25	25 - 30	30 – 35
No. of person	125	80	78	120	150	165	97

35 – 40	40 – 45	45 – 50	50 - 55	55-60
88	99	50	43	36

Solution:

Age	Class Marks	f
00 – 05	2.5	125
05 – 10	7.5	80
10 – 15	12.5	78
15 – 20	17.5	120
20 – 25	22.5	150
25 – 30	27.5	165
30 – 35	32.5	97
35 – 40	37.5	88
40 - 45	42.5	99
45 – 50	47.5	50
50 - 55	52.5	43
55 - 60	57.5	36

Bar Diagram

A bar diagram is a visual representation of data in which bars of uniform width are drawn with equal spacing between them. The height of each bar is proportional to the value of the category or class they represent.

Types of Bar Diagram

1. Simple Bar Diagram

A simple bar diagram consists of horizontal and vertical rectangles of equal width and height that are proportional to the values they represent. The vertical bars are used to represent qualitative variables, whereas the horizontal rectangles are used to represent geographical or spatial distributions.

The temperature of various cities is given below:

City	A	B	C	D	E
Temperature	32	35	30	25	21

2. Multiple Bar Diagram

The multiple bar diagram to compare two or more features corresponding to the values of the common variable. Each rectangle is used to represent the frequency of a variable and is considered a good tool for comparison of two or more kinds of information.

The maximum and minimum temperature of various cities is given below:

City	A	B	C	D	E
Max. Temperature	32	35	30	25	21
Min. Temperature	29	26	25	21	18

3. Component Bar Diagram

A component bar diagram is used to represent in which the total value is divided into two or more components. The length of each component is proportional to the individual value of the total magnitude.

The number of enrolled students in a local school in various academic years is given below:

Year	2015	2016	2017	2018	2019	2020
Male Students	210	321	410	500	590	700
Female Students	80	170	205	230	270	320
Total	290	491	615	730	860	1020

4. Pie Chart

A pie chart is a circular diagram suitable for visual representation for categorical data. In a pie chart, the angle of the circle is divided into various components as: