Higher Engineering Mathematics, Sixth Edition

Presentation ofstatistical data 531

Problem 3. The distance in miles travelled by

four salesmen in a week are as shown below.

Salesmen P Q R S

Distance travelled miles 413 264 597 143

Use a horizontal bar chart to represent these data

diagrammatically.

Equally spaced horizontal rectangles of any width, but
whose length is proportional to the distance travelled,
are used. Thus, the length of the rectangle for salesman
Pis proportionalto 413miles, and so on. The horizontal
bar chart depicting these data is shown in Fig. 54.2.

0

P

Q

Salesmen

R

S

100 200 300

Distance travelled, miles

400 500 600

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 17 9 5 27 13 6

Present these data on a vertical bar chart.

In a vertical bar chart, equally spaced vertical rectangles
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.

1

10

20

Number of issues

30

40

23456

Periods

7

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

percentage 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 frequency,

and are subdivided into the values in the table of per-

centages shown above. A key is used (different types

of shading or different colour schemes) to indicate