Higher Engineering Mathematics, Sixth Edition

Measures of central tendency and dispersion 547

25

Cumulative frequency 10

40

30

20

50

30 35 Q 140 Q 245 Q 3

Upper class boundary values (hours)

50 55 60

Figure 55.2

The set is ranked, giving:

71415171719202121222223

24 26 27 28 29 30 32 37

(a) There are 20 numbers in the set, hence the first

10% will be the two numbers 7 and 14, the sec-

ond 10% will be 15 and 17, and so on. Thus the

41st to 50th percentile group will be the numbers

21 and 22.

(b) The first decile group is obtained by splitting the

ranked set into 10 equal groups and selecting the

first group, i.e. the numbers 7 and 14. The second

decile groupare the numbers 15 and 17, and so on.

Thus the 8th decile group contains the numbers

27 and 28.

Now try the following exercise

Exercise 210 Further problemson

quartiles, deciles and percentiles

1. The number of working days lost due to
   accidents for each of 12 one-monthly periods

are as shown. Determine the median and first

and third quartile values for this data.

27 37 40 28 23 30 35 24 30 32 31 2

[30, 25.5, 33.5days]

2. The number of faults occurring on a produc-
   tion line in a nine-week period are as shown
   below. Determine the median and quartile
   values for the data.

30 27 25 24 27 37 31 27 35

[27, 26, 33faults]

3. Determine the quartile values and semi-
   interquartile range for the frequency distri-
   bution given in Problem 1 of Exercise 208,
   page 544.
   [
   Q 1 = 164 .5cm,Q 2 = 172 .5cm,
   Q 3 =179cm, 7 .25cm

]

4. Determine the numbers contained in the 5th
   decile group and in the 61st to 70th percentile
   groups for the set of numbers:

40 46 28 32 37 42 50 31 48 45

32 38 27 33 40 35 25 42 38 41

[37 and 38; 40 and 41]

5. Determine the numbers in the 6thdecile group
   and in the 81st to 90th percentile group for the
   set of numbers:

43 47 30 25 15 51 17 21

36 44 33 17 35 58 51 35

37 33 44 56 40 49 22

44 40 31 41 55 50 16

[40, 40, 41; 50, 51, 51]