534 STATISTICS AND PROBABILITY

Problem 10. The amount of money earned

weekly by 40 people working part-time in a fac-

tory, 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 are a much smaller number of extreme

values ranging from £30 to £170. If equal class inter-

vals are selected, the frequency distribution obtained

does not give as much information as one with

unequal class intervals. Since the majority of mem-

bers are between £80 and £100, the class intervals in

this range are selected to be smaller than those out-

side of this range. There is no unique solution and

one possible solution is shown in Table 54.2.

Problem 11. Draw a histogram for the data

given in Table 54.2

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
frequencies of the classes. The data given are shown

Table 54.3

1 2 3 4 5 6

Class Frequency Upper class boundary Lower class boundary Class range Height of rectangle

20–40 2 45 15 30

2

30

=

1

15

50–70 6 75 45 30

6

30

=

3

15

80–90 12 95 75 20

12

20

=

9

15

100–110 14 115 95 20

14

20

=

(^1012)
15
120–140 4 145 115 30
4
30

2
15
150–170 2 175 145 30
2
30

1
15
Table 54.2
Class Frequency
20–40 2
50–70 6
80–90 12
100–110 14
120–140 4
150–170 2
in columns 1 and 2 of Table 54.3. Columns 3 and 4
give the upper and lower class boundaries, respec-
tively. In column 5, the class ranges (i.e. upper class
boundary minus lower class boundary values) are
listed. The heights of the rectangles are proportional
to the ratio
frequency
class range
, as shown in column 6. The
histogram is shown in Fig. 54.8.
Problem 12. The masses of 50 ingots in kilo-
grams are measured correct to the nearest 0.1 kg
and the results are as shown below. Produce a
frequency distribution having about 7 classes for
these data and then present the grouped data as
(a) a frequency polygon and (b) a histogram.
8.0 8.6 8.2 7.5 8.0 9.1 8.5 7.6 8.2 7.8
8.3 7.1 8.1 8.3 8.7 7.8 8.7 8.5 8.4 8.5
7.7 8.4 7.9 8.8 7.2 8.1 7.8 8.2 7.7 7.5
8.1 7.4 8.8 8.0 8.4 8.5 8.1 7.3 9.0 8.6
7.4 8.2 8.4 7.7 8.3 8.2 7.9 8.5 7.9 8.0