(a) Histogram
(b) Frequency Polygon
(c) Relative Frequency Histogram and Polygon
(d) Cumulative Frequency Polygon or Ogive
(e) Frequency Curves and Smoothed Ogive
(a) Histogram:
1. A
histogram consists of a set of adjacent rectangles having bases along
xaxis (marked off by class boundaries) and areas proportional to class
frequencies.
2. To
adjust the heights of rectangles in a frequency distribution with
unequal class interval sizes, each class frequency is divided by its
class interval size.
Class boundaries

Frequency

109.5119.5  1 
119.5129.5  4 
129.5139.5  17 
139.5149.5  28 
149.5159.5  25 
159.5169.5  18 
169.5179.5  13 
179.5189.5  6 
189.5199.5  5 
199.5209.5  2 
209.5219.5  1 
S f  120 
Class Interval

f

Class Boundaries

Size

Adjusted Frequency

1011

4

9.511.5

2

4 / 2 = 2

1214

12

11.514.5

3

12 / 3 = 4

1519

25

14.519.5

5

25 / 5 = 5

2029

60

19.529.5

10

6

3034

25

29.534.5

5

5

3539

15

34.539.5

5

3

4042

6

39.542.5

3

2

147

(b) Frequency Polygon:
1. It
is constructed by plotting the class frequencies against their
corresponding class marks (midpoints) and then joining the resulting
points by means of straight lines.
2. The
ends of the graph so drawn do not meet the ends of xaxis. A polygon
is a many sided closed figure. Therefore, extra classes are to be added
at both ends of the frequency distribution with zero frequencies.
3. The frequency polygon can also be obtained by joining the midpoints of the tops of rectangles of histogram.
(c) Relative Frequency Histogram and Polygon: Same as described above.
(d) Cumulative Frequency Polygon or Ogive:
1. The
graph showing the cumulative frequencies plotted against the upper
class boundaries is called a ‘cumulative frequency polygon’ or ‘ogive’.
2. The
graph corresponding to a less than or a more than cumulative frequency
distributions are called ‘lessthan’ and ‘morethan ogives’
respectively.
Class Boundaries

Frequency

Less than
Cumulative
Frequency

More than
Cumulative
Frequency

109.5119.5

1

1

119

119.5129.5

4

5

115

129.5139.5

17

22

98

139.5149.5

28

50

70

149.5159.5

25

75

45

159.5169.5

18

93

27

169.5179.5

13

106

14

179.5189.5

6

112

8

189.5199.5

5

117

3

199.5209.5

2

119

1

209.5219.5

1

120

0

S f

120

(e) Frequency Curves and Smoothed Ogives:
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