The document discusses various types of charts used in statistics, including pie charts, bar charts (simple, multiple, component, percentage), and scatter diagrams, highlighting their characteristics and applications in representing data visually. It explains the importance of visual comparison in understanding statistical information. Additionally, the document covers concepts of ungrouped and grouped data and mentions that examples are available in a separate MS Word file.

1. Probability & Statistics
(Lecture # 03)
Chapter # 02 (Part 02)
by
Muhammad Haroon
1
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com

2. Chart
A chart is a device used for representing a simple statistical data in a simple, clear and
effective manner. A chart has following characteristics;
 Chart gives a quick overall visual impression of the significant facts
 It shows result more clearly than the tables
 It shows the extent of differences between items
 It is useful for comparison
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
2

3. Pie Chart
It is a diagrammatic representation of data in circular form. In a pie chart, a circle is
divided into several sectors. The area of a sector of a circle is proportional to the angle
of the sector; the angle can be calculated as
Angel of sector =
𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑃𝑎𝑟𝑡
𝑇𝑜𝑡𝑎𝑙
× 360
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
3

4. Bar Chart
Bar charts enable magnitudes to be comparing visually. Bar may be horizontal or vertical.
They are of equal width, with their length or height proportional to the values they
represent. Vertical bar charts are used whenever time series are involved. Horizontal
bar charts are used to present data classified into different categories or divisions or
geographical areas. Vertical bars are more common in usage.
Types of Bar Charts:
Following are the types or bar charts or bar diagrams
 Simple bar chart
 Multiple bar chart
 Sub divided or component bar chart
 Percentage bar chart
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
4

5. 1.Simple Bar Chart
A bar chart representing a single item of data is called a simple bar chart e.g. Bar chart
showing total population of Pakistan in selected years. Bar chart showing number of
working in different industries of Pakistan in 1995, and so on. The bar charts are easy
to construct and interpret. The heights of the bars or their lengths represent the
magnitudes of the characteristics. Always remember to start with zero bases. Divide
the vertical (Y-axis) scale into a number of equal divisions and let each division
represent a certain magnitude of the data given. Equal vertical distances are taken to
represent the same.
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
5

6. 2.Multiple Bar Chart
In multiple bar charts, the component figures are shown as separate bars adjoining each
other. The height of the bar represents the actual value of the component, e.g. male
and female population of Pakistan in the census report of 1998 can be shown by
separate bars for male and female population placed adjacent to each other for each
of the years. This will help to compare male population with female population.
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
6

7. 3.Component Bar Chart
If a breakdown or distribution of an aggregate according to various classes or categories
is to be presented, subdividing the bars accordingly can do it. Such a chart is called a
component bar chart e.g. bar chart showing distribution of population according to age
groups, distribution of gross domestic product by industry of origin and so on.
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
7

8. 4.Presentage Bar Chart
The interest may sometimes be not on the increase or decrease in absolute values, but
on the change in the relative share of each part to the total. To present this, the bars
are divided in proportion to percentages the parts bear to the whole. All bars will be of
the same length or height equal to 100. This presentation is known as percentage
component bar chart
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
8

9. Scatter diagram
Scatter diagram is a set of points on a graph paper where one variable is taken on x-axis
and other is taken on y-axis, each point represents an observed pair of values.
A visual examination of a scatter diagram gives us some useful indications of the nature
and strength of the relationship between two variables and aids in choosing the
appropriate type of model for estimation. For example, if the points on the scatter
diagram tend to run from the lower left side to upper right side there said to be a direct
relationship between two variables. On the other hand, if points on the scatter diagram
tend to run from upper left to the lower right side, there is said to be inverse
relationship between two variables. If a straight line is used to describe the average
relationship between two variables, a linear relationship is said to exist. If the points on
the scatter diagram appear to lie along a curve, a curvilinear relationship is said to be
present.
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
9

10. Array
Arranging of data in ascending or descending order is called as an array. For example, if
we have the data: 4, 7, 6, and 1, then
Ascending Array: 1, 4. 6, 7
Descending array: 7, 6, 4, 1
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
10

11. Ungrouped Data
The fresh data (raw data) that have been collected for the first time and that have not
undergone any statistical treatment are called ungrouped data.
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
11

12. Grouped Data
When the ungrouped data are arranged according to classes or groups with their
respective frequencies are called grouped data.
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
12

13. Examples
Now, All Examples will be done on MS Word. Examples you can see MS Word file. File
Name “Lecture 03-Part 02-Examples.docx”
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com
13

14. End
14
Cell: +92300-7327761 Email: mr.harunahmad2014@gmail.com