Basic Engineering Mathematics, Fifth Edition

290 Basic Engineering Mathematics

Problem 3. The distance in miles travelled by

four salesmen in a week are as shown below.

Salesman P Q R S

Distance travelled (miles) 413 264597143

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 sales-

manPis proportional to 413 miles, and so on. The

horizontal bar chart depicting these data is shown in

Figure 31.2.

0

P

Q

Salesmen

R

S

100 200 300

Distance travelled, miles

400 500 600

Figure 31.2

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 34 5 6 7

Number of issues 34179527136

Present these data on a vertical bar chart

1

10

20

Number of issues

30

40

23456

Periods

7

Figure 31.3

In a vertical bar chart, equally spaced vertical rect-

angles 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 proportionalto 34

units, and so on. The vertical bar chart depicting these

data is shown in Figure 31.3.

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

calculatedandtheresultsareasshowninthetablebelow.

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%

Thepercentagecomponentbarchartisproducedbycon-

structing three equally spaced rectangles of any width,

correspondingtothe three years. The heightsof the rect-

angles correspond to 100% relative frequency and are