STATISTICAL DESCRIPTION OF
DATA
(GRAPHICAL REPRESENTATION)
Introduction:
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Graphical representation is a way of analyzing
numerical data.
The visual display of statistical data in the form of
lines, points and other geometrical form and
symbols, is in the most general terms known as
Graphical Representation.
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Such visual representation can be divided into two
main groups:
Difference b/w Graphs and
Diagrams:
Diagrams
Graphs
•are use for categorical/ nominal data.
•use for quantitative data.
•can be drawn on an ordinary paper.
•always drawn on graph paper.
•Use only for comparisons.
•Use to study relationship between
variables.
•Data are represented by bars,
rectangles, circles or other geometrical
shapes.
•Data are represented by dots, straight
lines or curves.
•e.g: Bar chart.
•e.g: Histogram, Frequency Polygon
1. Bar Chart:
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It shows the frequency counts of values for the
different levels of categorical variable.
The bars show the level of variable and the height
of the bars show the counts of response for that
level.
Bar chart may be:
 Simple
Bar Chart
 Multiple Bar Chart
 Component Bar Chart
Simple Bar Chart:

A simple bar chart consists of horizontal or vertical
bars of equal widths and lengths proportional to
the value they represent.
Multiple Bar Chart:
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It shows two or more characteristics corresponding
to the values of common variable in the form of
grouped bars, whose lengths are proportional to
the values.
Component Bar Chart:
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also known as sub-divided bar chart.
is an effective technique in which each bar is
divided into two or more sections, proportional in
size to the component parts of a total being
displayed by each bar.
14
12
10
8
Series 3
Series 2
Series 1
6
4
2
0
Category 1
Category 2
Category 3
Category 4
How to construct Bar Graph?
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First, decide the title of the bar graph.
Draw the horizontal axis and vertical axis.
Label the horizontal axis.
Write the names/categories on the horizontal axis.
Label the vertical axis.
Finalize the scale range for the given data.
Finally, draw the bar graph that should represent
each category with their respective numbers.
Examples:

In a firm of 400 employees, the percentage of
monthly salary saved by each employee is given in
the following table. Represent it through a bar
graph.

A cosmetic company manufactures 4 different
shades of lipstick. The sale for 5 months is shown in
the table. Represent it using bar charts.
Month
Sales
Shade 1
Shade 2
Shade 3
Shade 4
January
45
60
44
45
February
70
54
56
54
March
39
89
97
77
April
55
76
90
89
May
32
78
43
78
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A school conducted a survey to know the favorite
sports of the students. The table below shows the
results of this survey:
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Following data gives the birth rates and death rates
per thousand of a few countries. Represent them by
multiple bar chart:
Country
Birth Rates
Death Rates
India
33
24
Japan
32
19
Germany
16
10
Egypt
44
24
Australia
20
9
New Zealand
18
8
France
21
16
2. Histogram:
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Histogram: a graphical display of data using bars
of different heights.
A histogram consists of a set of adjacent rectangles
whose bases are marked off by class boundaries on
the X-axis and whose height are proportional to the
frequencies associated with respective classes.
How do you make a histogram?
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To make a histogram, follow these steps:
On the vertical axis, place frequencies. Label this
axis "Frequency/ f".
On the horizontal axis, place the lower value of
each interval or class boundaries.
Draw a bar extending from the lower value of each
interval to the lower value of the next interval.
Examples:
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1: Construct a histogram for the following frequency
distribution of the heights of 100 male students at
college.
Height
60 -- 62
63 -- 65
66 -- 68
69 --71
72 –74
Num of
students
5
18
42
27
8
Difference b/w Bar Chart and
Histogram:
3. Frequency Polygon:
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Frequency polygons are a visually substantial
method of representing quantitative data and its
frequencies
A frequency polygon is a graph constructed by
using lines to join the midpoints of each interval, or
bin. The heights of the points represent the
frequencies.
Steps to Draw Frequency Polygon
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Mark the mid values/ class mark on the horizontal
axis.
Mark the frequency of the class on the vertical axis.
Corresponding to the frequency of each mid value,
mark a point at the height.
Connect these points using the line segment.
Example:
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Construct a frequency polygon for the following
data:
Classes
20--24 25-29
30--39 40--44
45--49
50--54
55—64
f
1
26
20
15
14
2
22