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GRAPHIC REPRESENTATION
Frequency distribution
Histogram
Pie chart
Polygon
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GRAPHIC REPRESENTATION
There are many forms of representing datagraphically. They are
(i) Bar graphs
(ii) Histograms
(iii) Frequency polygons
(iv) Ogive
(v) Pictographs
(vi) Pie charts
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HISTOGRAMS
A histogram is a graphical representation of a continuousfrequency distribution i.e. grouped frequency distributions.
It is a graph, including vertical rectangles, with no space betweenthe rectangles.
The class-intervals are taken along the horizontal axis and therespective class frequencies on the vertical axis using suitablescales on each axis.
For each class, a rectangle is drawn with base as width of theclass and height as the class frequency. The area of the
rectangles must be proportional to the frequencies of therespective classes.
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EXAMPLE
The following is the frequency distribution of
weights of 30 students of class IX of a
school. Draw a histogram to represent the
data.
Classes 45-50 50-55 55-60 60-65 65-70 Total
Frequenc
y
3 7 12 5 3 30
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SOLUTION
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FREQUENCY POLYGON
A frequency polygon is the join of the mid-
points of the tops of the adjoining rectangles
in histogram.
The mid-points of the first and the last
classes are joined to the mid-points of the
classes preceding and succeeding
respectively at zero frequency to completethe polygon.
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EXAMPLE ON FREQUENCY POLYGON
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SOLUTION
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FREQUENCY CURVE
This can be obtained by drawing a smooth free
hand curve through the vertices of frequency
polygon.
Example:Draw frequency polygon and frequency curve for the
following distribution.Marks
obtained
20-24 25-29 30-34 35-39 40-44 45-49
No. of
student
s
5 12 20 15 8 5
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OGIVE AND CUMULATIVE FREQUENCY CURVE
This is a graphic representation of the
cumulative frequency distribution of
continous variable.
There are two ways of constructing an ogive
or cumulative frequency curve.
Less than Ogive
More than ogive
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OGIVE CURVES
LESS THAN OGIVE CURVE MORE THAN OGIVE CURVE
This is obtained by plotting
the less than cumulative
frequencies (on Y Axis)
against the upper classlimits (along X axis) .The
points are joined by a
smooth free hand curve.
It is an upward sloping
curve.
This is obtained by plotting
the more than cumulative
frequencies ( on Y axis.)
against the lower classlimits ( along X axis). The
points are joined by a
smooth free hand curve.
It is a downward sloping
curve.
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Draw a 'less than' ogive and more than
ogive curve for the following data:
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Upper limits of classes
Less
than
c.
f.
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EXAMPLE
Using the data given below, construct a
'more than' cumulative frequency table and
draw the Ogive.
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SOLUTION
Classes Exclusive/continuous
classes
frequency More than c.f
1-10 0.5 - 10.5 3 60
11-20 10.5 - 20.5 8 57
21-30 20.5 - 30.5 12 49
31-40 30.5 - 40.5 14 37
41-50 40.5 - 50.5 10 23
51-60 50.5 - 60.5 6 13
61-70 60.5 - 70.5 5 7
71-80 70.5 - 80.5 2 2
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PROBLEM NO. 12 PAGE 1.30
Construct frequency table for following data regarding the annual profits
in thousands of rupees in 50 firms , taking 25-34, 35-44 etc as the
intervals.
28, 35, 61, 29, 36, 48, 57, 67, 69, 50, 48, 40, 47, 42,
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Classes Continuous
classes
frequency Less than
c.f
25-34 24.5-34.5 5 5
35-44 34.5-44.5 19 24
45-54 44.5-54.5 13 37
55-64 54.5-64.5 11 48
65-74 64.5-74.5 2 50
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GROUP A
24.5 34.5 44.5 54.5 64.5 74.5
0
10
20
30
40
50
Scale
On x Axis 1cm=10
units
On Y axis 1cm= 10
units
Answer 1
Profit in (000)
No.
Offirms
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The number of firms having profit between
Rs.37000 and Rs.58000
No. of firms having profit below 37000 are 9
No. of firms having profit below 58000 are 39
So,
Total number of firm having profit betweenRs.37000 and Rs.58000 is (39-9)=30
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Group A
24.5 34.5 44.5 54.5 64.5 74.5
0
10
20
30
40
50
No.
Offirms
Profit in (000)
Answer 2 Scale
On x Axis 1cm=10
units
On Y axis 1cm= 10
units
Profit is Rs. 62000
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Group A
24.5 34.5 44.5 54.5 64.5 74.5
0
10
20
30
40
50
No.
Offirms
Profit in (000)
Answer 3 Scale
On x Axis 1cm=10
units
On Y axis 1cm= 10
units
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MIDDLE 50 % PROFIT GROUP
Middle 50 % group is 25 firms at mid of
distribution.
So , middle 25 firms are 12.5 to 37.5 on Y
axis.
By graph,
Profit of middle group is Rs. 39000 to
Rs.55000
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PIE CHART
A pie chart (or a circle graph) is circular chart divided
into sectors, illustrating proportion. Angle at centre: x/Total * 360
55%30%
10%
3% 2%
Market share
Colgate Close Up Pepsident
Babool other
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EXAMPLE
The following table gives the distribution of
outlay in five year plan India of under the
major heads of development expenditure:
Heads Expenditure ( in Rs. Cr.)
a) Agriculture 8000
b) Irrigation 4000
c) Industry 7000
d) Transport 5500
e) Miscellaneous 2500
Total 27000
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SOLUTION
Heads Expenditure
( in Rs. Cr.)
(x)
Angle at the Centre =x/27000 * 360
a) Agriculture 8000
8000/27000 * 360= 10667 107
b) Irrigation 4000 4000/27000 * 360= 5333 53
c) Industry 7000 7000/27000 * 360= 9333 93
d) Transport 5500 5500/27000 * 360= 7333 73
e) Miscellaneous 2500 2500/27000 * 360= 3334 34
Total 27000 360
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30%
15%
26%
20%
9%
Expenditure
a) Agriculture
b) Irrigation
c) Industry
d) Transport
e) Miscellaneous
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The following table gives the distribution of
out lay of the budget of a state under major
head of development expenditure:
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EXAMPLE
Heads Expenditure
(in Rs.Cr.)
a) Agriculture and community
development
10000
b) Irrigation and Power 4000
c) Industry and mining 8000
d) Transport and communication 6000
e) Miscellaneous 2000
The following table gives the distribution of out lay ofthe budget of a state under major head of
development expenditure: Represent the information
by a suitable diagram or chart
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TABULATION OF DATA Tabulation refers to systematic arrangement of data
using rows and columns which makes it easy tocompare and use for further analysis.
A standard statistical table should have the followingparts:
1. Table number2. Title
3. Head note
4. Captions
5. Body6. Footnote
7. source
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EXAMPLE
Present the following information in a suitabletabular form , supplying the figures not directlygiven:
In 1995 out of total 2000 worker in factory ,
1550 were members of trade union. The numberof women workers employed was 250, out ofwhich 200 did not belong to any trade union.
In 2000, the number of union workers was 1725
of which 1600 were men. The number of nonunion workers was 380, among which 155 werewomen.
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TABLE FORMATE
Year
Type
1995 2000
Men Women Total Men Women Total
Members
Non
Members
Total