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TYPES OF CHARTS AND
GRAPH IN STATISTICS
Advantages:
∙ a picture is worth a thousand words
∙ make data simple and intelligible
∙ great memorizing effects
∙ universal utility
∙ save time and labour
∙ make comparison easy
∙ attractive and impressive
Disadvantages:
- numeric detail offered by a table is lost
- additional relationships within the data is not known
- formatting charts needs more time than tabulation
Why graph and charts?
Definition of Bar Graph
❑ A Bar Graph is a chart that
uses either horizontal or vertical
bars to show comparisons
between categories
Classification of Bar Charts
Bar Charts
Single (vertical)
Multiple
Stacked
Y –
Axis
Represents
individually
separate and
distinct values.
X-
Axis Shows the
specific
categories being
compared.
Advantages of Bar chart
- show each data category in a frequency
distribution
- display relative numbers or proportions of
multiple categories
- summarize a large data set in visual form
- estimate key values at a glance
- be easily understood due to widespread use in
business and the media
Disadvantages of Bar graph
- require additional explanation
- be easily manipulated to yield false
impressions
- fail to reveal key assumptions, causes, effects,
or patterns
Years 1989 1990 1991 1992 1993
Profit
(million
$$)
10 12 18 25 42
EXAMPLE
EXAMPLE
EXPENSE OF FAMILY A B
FOOD 2000 1700
CLOTHING 2400 2800
PETROL 1000 1100
TOTAL 5400 5600
GRAPH
REPRESENTATION
1000 1100
2400 2800
2000 1700
100
%
80
%
60
%
40
%
20
%
0
%
A B
Chart
Title
FOO
D
CLOTHI
NG
PETR
OL
HISTOGR
AM
HISTOGRAM
Ans :- Histogram is a graphical representation
that is helpful to organise and display the data
in more user-friendly format.
- It helps in comparing process within
specified limits.
- It summarizes large data.
- It assists in decision making.
EXAMPLE
CLASS IINTERVAL
PRICE RANGE OF
PENS)
20 - 30 30 - 40 40 - 50 50 - 60
FREQUENCY(NUMBE
R OF PENS)
15 20 30 25
GRAPH
35
30
25
20
15
10
5
0
20 -
30
30 -
40
40 -
50
50 -
60
FREQUENC
Y
20 - 30 30 - 40
40 - 50
50 -
60
EXAMPLE
- Let us take a large set of numbers :-
24, 17, 14, 22, 25, 26, 38, 42, 47, 24,
12, 28,
19, 32, 21, 46, 35, 28, 21, 31, 18, 19. INTERVAL TALLY FREQUENCY
15 - 20 |||| 4
20 - 25 |||| 5
25 - 30 |||| 4
30 - 35 || 2
35 - 40 || 2
40 - 45 | 1
45 - 50 || 2
GRAPH
5
4 4
2 2 2
1
6 5 4 3 2 1 0
15 -
20
20 -
25
25 -
30
30 -
35
35 -
40
40 -
45
45 -
50
Series
1
15 -
20
20 -
25
25 -
30
30 -
35
35 -
40
40 -
45
45 -
50
Constructing Statistical Graphs-
General Procedures
- Draw and label the x and y-axes
- Choose a suitable scale for the
frequencies or cumulative frequencies,
and label it on the y- axis.
- Represent the class boundaries for the
histogram or ogive, or the midpoint for
the frequency polygon, on the x-axis.
- Plot the points and then draw the
bars or lines.
Example
The following data consists of weights, in kilograms, of 20 people:
50, 65, 75, 80, 85, 85, 86, 86, 87, 87, 87, 90, 92, 98, 105.
Placing this data into a stem and leaf plot helps us organise and analyse and
group our data better. This is not a necessary step.
Step 1: Group your data into the table.
Tally Frequency
Cumulativ
e
Frequenc
y
40<weights<
50<weights<
60<weights<
70<weights<
80<weights<
90<weights<
100<weights<
Step 5: Draw your graph
- The first coordinate in the plot always starts at a
- value of 0
- The second coordinate is at the end of the first interval.
- The third coordinate is at the end of the second interval and
so on
Definition of Pie-Chart
- A pie chart (also called a Pie Graph or
Circle Graph) makes use of sectors in
a circle. The angle of a sector is
proportional to the frequency of the
data.
- A pie chart is a good way of displaying
data when you want to show how
something is shared or divided.
The formula to determine the angle
of
a sector in a circle graph is:
ANGLE OF SECTOR = FREQUENCY OF
THE DATA
TOTAL FREQUENCY
X
3
60
EXAMPLE
- In a school, there are 750
students in Year1, 420 students
in Year 2 and 630 students in
Year 3. Draw a circle graph to
represent the numbers of
students in these groups.
SOLUTION
- Total number of students = 750 + 420 + 630 =
Year 1 size of
angle =
X
=
150
o
Year 2 size of
angle =
Year 3 size of
angle =
42
0180
0
630
1800
750
1800
X
=
X360 =
8
4
o
126
o
42%
23%
35%
No. of
students
Year
1
Year
2
Year
3
150 X
= 42%
360
36
0
84 X
= 23%
36
0
So, In
percentage =
So, In
percentage =
So, In percentage =
126
X100 =
35%
Advantages
- Size of the circle can be made proportional
to the total quantity it represents
- Summarize a large data set in visual form
- Be visually simpler than other types of
graphs
- Permit a visual check of the
reasonableness or accuracy of
calculations
- Require minimal additional explanation
- Be easily understood due to widespread
use in business and the media
Advantages
appealing.
Disadvantages
- They are difficult to draw
- Icons must be of consistent
size.
- Best for only 2-6 categories.
- Very simplistic
box plot
- Box plots (also called box-and-whisker plots or box-
whisker plots ) give a good graphical image of the
concentration of the data.
- They also show how far the extreme values are from most
of the data.
- A box plot is constructed from five values: the minimum
value, the first quartile, the median, the third quartile, and
the maximum value.
- We use these values to compare how close other data
values are to them.
Step 1 – Order Numbers
- Order the set of numbers from least to
greatest
- Find the median. The median is the middle number. If
the data has two middle numbers, find the mean of
the two numbers. What is the median?
Step 2 – Find the Median
- Find the lower and upper medians or quartiles.
These are the middle numbers on each side of the
median. What are they?
Step 3 – Upper & Lower Quartiles
Now you are ready to construct the actual box & whisker
graph. First you will need to draw an ordinary number
line that extends far enough in both directions to include
all the numbers in your data:
Step 4 – Draw a Number
Line
Locate the main median 12 using a vertical
line just above your number line:
Step 5 – Draw the
Parts • Next, draw a box using the lower and upper
median lines as endpoints:
Step 5 – Draw the
Parts
CARTOGRAM
CARTOGRAM
