532 STATISTICS AND PROBABILITY- The employees in a company can be split
into the following categories: managerial 3,
supervisory 9, craftsmen 21, semi-skilled 67,
others 44. Show these data on a pie diagram.
⎡
⎢
⎢
⎢
⎣A circle of any radius,
subdivided into sectors
having angles of 7^12◦
,22^12◦
,(^5212)
◦
, 167^12
◦
and110◦,
respectively.
⎤
⎥
⎥
⎥
⎦
- The way in which an apprentice spent his time
over a one-month period is as follows:
drawing office 44 hours, produc-
tion 64 hours, 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.⎤⎥
⎥
⎦- (a) With reference to Fig. 54.5, determine the
amount spent on labour and materials to
produce 1650 units of 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]- (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 the number of members in a set is small,
say ten or less, the data can be represented dia-
grammatically without further analysis, by means of
pictograms, bar charts, percentage components bar
charts or pie diagrams (as shown in Section 54.2).
For sets having more than ten members, those
members having similar values are grouped together
inclassesto form afrequency distribution.To
assist in accurately counting members in the vari-
ous classes, atally diagramis used (see Problems 8
and 12).
A frequency distribution is merely a table show-
ing classes and their corresponding frequencies (see
Problems 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 shown in Fig. 54.6(b) is 7.4 to 7.6 and the class
mid-point value is given by,
(
upper class
boundary value)
+(
lower class
boundary value)2and in Fig. 54.6 is7. 65 + 7. 35
2, i.e. 7.5.Figure 54.6One of the principal ways of presenting grouped
data diagrammatically is by using ahistogram,in
which theareasof vertical, adjacent rectangles are
made proportional to frequencies of the classes (see
Problem 9). When class intervals are equal, the
heights of the rectangles of a histogram are equal to
the frequencies of the classes. For histograms having
unequal class intervals, the area must be proportional
to the frequency. Hence, if the class interval of class
Ais twice the class interval of classB, then for equal
frequencies, the height of the rectangle representing