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81 HISTOGRAM 35 Number of Students 30 25 20
15 10 5 0
20.5 30.5 40.5 50.5 60.5 70.5 80.5 Marks Example 12:
Draw a histogram for the following data.
Profits
Number of
(in lakhs)
Companies
010
4
1020
12
2030
24
3050
32
5080
18
8090
9
90100
3
Solution:
When the class intervals are unequal, a correction for unequal
class intervals must be made. The frequencies are adjusted as
follows: The frequency of the class 3050 shall be divided by two
since the class interval is in double. Similarly the class interval 5080 can be divided by 3. Then draw the histogram.
82 Now we rewrite the frequency table as follows.
Profits
(in lakhs)
010
1020
2030
3040
4050
5060
6070
7080
8090
90100 Number of
Companies
4
12
24
16
16
6
6
6
9
3 HISTOGRAM 30 No. of Companies 25
20
15
10
5
0
10 20 30 40
50
60
Profits (in Lakhs) 5.6.2 70 80 90 100 Frequency Polygon:
If we mark the midpoints of the top horizontal sides of the
rectangles in a histogram and join them by a straight line, the figure
so formed is called a Frequency Polygon. This is done under the
assumption that the frequencies in a class interval are evenly
distributed throughout the class. The area of the polygon is equal
to the area of the histogram, because the area left outside is just
equal to the area included in it.
83 Example 13:
Draw a frequency polygon for the following data.
Number of
Students
4
7
10
18
14
8
3 Weight (in kg)
3035
3540
4045
4550
5055
5560
6065 FREQUENCY POLYGON
20
18 Number of Students 16
14
12
10
8
6
4
2
0
30 35 40 45 50 55 60 65 Weight (in kgs) 5.6.3 Frequency Curve:
If the middle point of the upper boundaries of the rectangles
of a histogram is corrected by a smooth freehand curve, then that
diagram is called frequency curve. The curve should begin and end
at the base line.
84 Example 14:
Draw a frequency curve for the following data.
Monthly Wages
(in Rs.)
01000
10002000
20003000
30004000
40005000
50006000
60007000
70008000 No. of family
21
35
56
74
63
40
29
14 Solution:
FREQUENCY CURVE
80
70 No. of Family 60
50
40
30
20
10
0 1000 2000 3000...
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 Winter '08
 Moshiri
 Business

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