Higher Engineering Mathematics

PRESENTATION OF STATISTICAL DATA 529

J

Figure 54.2

Problem 4. The number of issues of tools or

materials from a store in a factory is observed

for seven, one-hour periods in a day, and the

results of the survey are as follows:

Period 1 2 3 4 5 6 7

Number of

issues 34 179527136

Present these data on a vertical bar chart.

In a vertical bar chart, equally spaced vertical rectan-
gles of any width, but whose height is proportional
to the quantity being represented, are used. Thus the
height of the rectangle for period 1 is proportional to
34 units, and so on. The vertical bar chart depicting
these data is shown in Fig. 54.3.

Figure 54.3

Problem 5. The numbers of various types of

dwellings sold by a company annually over a

three-year period are as shown below. Draw per-

centage component bar charts to present these

data.

Year 1 Year 2 Year 3

4-roomed bungalows 24 17 7

5-roomed bungalows 38 71 118

4-roomed houses 44 50 53

5-roomed houses 64 82 147

6-roomed houses 30 30 25

A table of percentage relative frequency values,

correct to the nearest 1%, is the first requirement.

Since,

percentage relative frequency

=

frequency of member× 100

total frequency

then for 4-roomed bungalows in year 1:

percentage relative frequency

=

24 × 100

24 + 38 + 44 + 64 + 30

=12%

The percentage relative frequencies of the other

types of dwellings for each of the three years are

similarly calculated and the results are as shown in

the table below.

Year 1 Year 2 Year 3

(%) (%) (%)

4-roomed bungalows 12 7 2

5-roomed bungalows 19 28 34

4-roomed houses 22 20 15

5-roomed houses 32 33 42

6-roomed houses 15 12 7

The percentage component bar chart is produced by

constructing three equally spaced rectangles of any

width, corresponding to the three years. The heights

of the rectangles correspond to 100% relative fre-

quency, and are subdivided into the values in the

table of percentages shown above. A key is used (dif-

ferent types of shading or different colour schemes)

to indicate corresponding percentage values in the

rows of the table of percentages. The percentage

component bar chart is shown in Fig. 54.4.

Problem 6. The retail price of a product costing

£2 is made up as follows: materials 10 p, labour

20 p, research and development 40 p, overheads

70 p, profit 60 p. Present these data on a pie

diagram.

A circle of any radius is drawn, and the area of the

circle represents the whole, which in this case is £2.

The circle is subdivided into sectors so that the areas

of the sectors are proportional to the parts, i.e. the

parts which make up the total retail price. For the