Higher Engineering Mathematics

544 STATISTICS AND PROBABILITY

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 group are the numbers 15 and 17,

and so on. Thus the 8th decile group contains

the numbers27 and 28.

Now try the following exercise.

Exercise 211 Further problems on quar-

tiles, deciles and percentiles

1. The number of working days lost due to acci-
   dents 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, 33.5 days]


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, 33 faults]

3. Determine the quartile values and semi-
   interquartile range for the frequency distri-
   bution given in Problem 1 of Exercise 209,
   page 540.
   [
   Q 1 = 164 .5 cm,Q 2 = 172 .5 cm,
   Q 3 =179 cm, 7.25 cm

]

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 6th decile
   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]