Higher Engineering Mathematics, Sixth Edition

534 Higher Engineering Mathematics

8. A company has five distribution centres and
   the mass of goods in tonnes sent toeach
   centre during four, one-week periods, is as
   shown.

Week 1 2 3 4

Centre A 147 160 174 158

Centre B 54 63 77 69

Centre C 283 251 237 211

Centre D 97 104 117 144

Centre E 224 218 203 194

Use a percentage component bar chart to

present these data and comment on any

trends.

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

Four rectangles of equal

heights, subdivided as follows:

week 1: 18%, 7%, 35%, 12%,

28% week 2: 20%, 8%, 32%,

13%, 27% week 3: 22%, 10%,

29%, 14%, 25% week 4: 20%,

9%, 27%, 19%, 25%. Little

change in centresAandB,a

reduction of about 8% inC,an

increase of about 7% inDand a

reduction of about 3% inE.

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

9. The employees in a company can be split
   into the following categories: managerial 3,
   supervisory9, craftsmen 21, semi-skilled67,
   others 44. Show these data on a pie diagram.
   ⎡ ⎢ ⎢ ⎢ ⎢ ⎣
   A circle of any radius,
   subdivided into sectors
   having angles of 7^12

◦

, (^2212)
◦
,
(^5212)
◦
, (^16712)
◦
and110◦,
respectively.
⎤ ⎥ ⎥ ⎥ ⎥ ⎦

10. The way in which an apprentice spent his
    time over a one-month period is as follows:
    drawingoffice44hours,production64hours,
    training 12 hours, at college 28 hours.
    Use a pie diagram to depict this information.
    ⎡ ⎢ ⎢ ⎢ ⎢ ⎣
    A circle of any radius,
    subdivided into sectors
    having angles of 107◦,
    156 ◦, 29 ◦and 68◦,
    respectively.

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

11. (a) With reference to Fig. 54.5, determine
    the amount spent on labour and materi-
    als toproduce 1650unitsof the product.
    (b) If in year 2 of Fig. 54.4, 1% corresponds
    to 2.5 dwellings, how many bungalows
    are sold in that year. [(a) £ 495, (b) 88]


12. (a) If the company sell 23500 units per
    annum of the product depicted in
    Fig. 54.5, determine the cost of their
    overheads per annum.
    (b) If 1% of the dwellings represented in
    year 1 of Fig. 54.4 corresponds to
    2 dwellings, find the total number of
    houses sold in that year.
    [(a)£ 16450,(b)138]

54.3 Presentation of grouped data

When thenumber of members in aset is small,say ten or

less, the datacan be represented diagrammatically with-

out further analysis, by means of pictograms, bar charts,

percentage components bar charts or pie diagrams (as

showninSection54.2).

For sets having more than ten members, those members

having similar values are grouped together inclasses

to form afrequency distribution. To assist in accu-

rately counting members in the various classes, atally

diagramis used (see Problems 8 and 12).

A frequency distribution is merely a table showing

classes and their corresponding frequencies (see Prob-

lems 8 and 12).

The new set of values obtained by forming a frequency

distribution is calledgrouped data.

The terms used in connection with grouped data are

shown in Fig. 54.6(a). The size or range of a class

is given by theupper class boundary valueminus

thelower class boundary value, and in Fig. 54.6 is

7. 65 − 7 .35, i.e. 0.30. Theclass intervalfor the class

showninFig.54.6(b)is7.4to7.6andtheclassmid-point

value is given by,

(

upper class

boundary value

)

+

(

lower class

boundary value

)

2

andinFig.54.6is

7. 65 + 7. 35

2

, i.e. 7.5.