Basic Engineering Mathematics, Fifth Edition

294 Basic Engineering Mathematics

Table 31.1(a)

Class Tally

70–72 1

73–75 11

76–78 1111 11

79–81 1111 1111 11

82–84 1111 1111

85–87 1111 1

88–90 111

Table 31.1(b)

Class Class mid-point Frequency

70–72 71 1

73–75 74 2

76–78 77 7

79–81 80 12

82–84 83 9

85–87 86 6

88–90 89 3

Problem 9. Construct a histogram for the data

given in Table 31.1(b)

The histogram is shown in Figure 31.7. The width of

the rectangles corresponds to the upper class boundary

values minus the lower class boundary values and the

heightsoftherectanglescorrespondtotheclassfrequen-

cies. The easiest way to draw a histogram is to mark the

71

4

2

Frequency^6

10

8

12

14

16

74 77 80 83

Class mid-point values

86 89

Figure 31.7

class mid-point values on the horizontal scale and draw

the rectangles symmetrically aboutthe appropriateclass

mid-point values and touching one another.

Problem 10. The amount of money earned

weekly by 40 people working part-time in a factory,

correct to the nearest £10, is shown below. Form a

frequency distribution having 6 classes for these

data

80 90 70 110 90 160 110 80

140 30 90 50 100 110 60 100

80 90 110 80 100 90 120 70

130 170 80 120 100 110 40 110

50 100 110 90 100 70 110 80

Inspection of the set given shows that the majority of

the members of the set lie between £80 and £110 and

that there is a much smaller number of extreme val-

ues ranging from £30 to £170. If equal class intervals

are selected, the frequency distribution obtained does

not give as much information as one with unequal class

intervals.Sincethemajorityof themembers liebetween

£80 and £100, the class intervals in this range are

selected to be smaller than those outside of this range.

There is no unique solution and one possible solution is

shown in Table 31.2.

Table 31.2

Class Frequency

20–40 2

50–70 6

80–90 12

100–110 14

120–140 4

150–170 2

Problem 11. Draw a histogram for the data given

in Table 31.2

When dealing with unequal class intervals, the his-

togram must be drawn so that the areas (and not

the heights) of the rectangles are proportional to the