stat chapter 1

7/29/2019 Stat Chapter 1

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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

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