Presentation of statistical data 295

Table 31.3

1 2 3 4 5 6

Class Frequency Upper class Lower class Class range Height of

boundary boundary 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
frequencies of the classes. The data given are shown
in columns 1 and 2 of Table 31.3. Columns 3 and 4
give the upper and lower class boundaries, respectively.
In column 5, the class ranges (i.e. upper class bound-
ary 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 Figure 31.8.
30
4/15
2/15
6/15
Frequency per unit
class range
10/15
8/15
12/15
60 85
Class mid-point values
105 130 160
Figure 31.8
Problem 12. The masses of 50 ingots in
kilograms are measured correct to the nearest 0.1kg
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
frequency polygon and 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
Therangeof the data is the member having the largest
value minus the member having the smallest value.
Inspection of the set of data shows thatrange= 9. 1 −
7. 1 = 2. 0.
The size of each class is given approximately by
range
number of classes
Since about seven classes are required, the size ofeach
class is 2. 0 ÷7,i.e.approximately0.3,andthustheclass
limitsare selected as 7.1 to 7.3, 7.4 to 7.6, 7.7 to 7.9,
and so on. Theclass mid-pointfor the7.1 to7.3 class is
7. 35 + 7. 05
2
i.e. 7. 2
the class midpoint for the 7.4 to 7.6 class is
7. 65 + 7. 35
2
i.e. 7. 5
and so on.