Tutorial Chapter 1

1. The following table gives the price of used-boats and the number of hours it has run.

No Hours Price (R1000) No Hours Price (R1000) No Hours Price (R1000)

1 1043 25 21 1256 29 41 1320 26
2 1269 30 22 1594 24 42 851 29
3 895 26 23 1402 31 43 917 29
4 986 29 24 852 28 44 1176 29
5 853 28 25 1282 23 45 1290 29
6 1285 31 26 1245 26 46 1216 25
7 1047 29 27 1323 26 47 1234 28
8 1625 30 28 712 29 48 1630 27
9 847 29 29 1515 29 49 1199 30
10 1063 27 30 926 29 50 951 28
11 1053 27 31 917 29 51 948 26
12 952 30 32 1019 27 52 1507 25
13 1149 28 33 1427 33 53 1540 26
14 1300 28 34 1451 26 54 1157 28
15 1000 28 35 1401 27 55 1177 27
16 1678 28 36 1358 27 56 1259 28
17 990 28 37 1442 26 57 1183 29
18 1165 24 38 1337 26 58 1118 27
19 874 31 39 1264 29 59 1610 28
20 960 26 40 1250 28 60 1661 26

1.1 Draw a random sample of size 10 from the list, read the random numbers from left to right, beginning at
Row 15, Column 20 on the THIRD page of Table A1 in Appendix A. List the sample of boats and the
hours it has run. (The sum of all the sample’s hours = 11 493)
1.2 Draw a systematic sample of size 10 from the list. Let the first randomly chosen element be number 5.
List the sample of boats and the price in R 1000. (The sum of the sample’s prices = R 278 000 )

2. The following table gives the ages of people applying for house loans:
Male Nr Age Nr Age Nr Age Nr Age Nr Age Nr Age
1 40 8 65 15 28 22 63 29 49 36 27
2 62 9 21 16 60 23 57 30 48 37 38
3 26 10 23 17 39 24 44 31 32 38 73
4 60 11 72 18 57 25 21 32 56 39 73
5 30 12 36 19 31 26 52 33 69 40 58
6 56 13 47 20 50 27 37 34 56 41 28
7 50 14 26 21 72 28 27 35 20 42 63

Female Nr Age Nr Age Nr Age Nr Age Nr Age Nr Age

1 51 6 72 11 74 16 43 21 60 26 56
2 26 7 45 12 37 17 53 22 26 27 48
3 59 8 22 13 47 18 39 23 33 28 21
4 34 9 45 14 33 19 42 24 32 29 45
5 54 10 37 15 46 20 68 25 50 30 60

Draw a stratified random sample of size 15 from the population.

For the stratum male, read vertically downwards and begin at Row 20, Column 8 on the first page of Table
A1 in Appendix A. (The sum of all the male sample’s ages = 362)
For the stratum female, read vertically downwards and begin at Row 10, Column 18 on the second page of
Table A1. (The sum of all the sample’s ages = 262)

APPENDIX_A_ STATISTICAL RANDOM NUMBER TABLES Page 2 - 4

Table 1: Random Numbers

Row
1 83 20 37 15 72 22 21 78 47 52 14 51 94 38 68 69 47 58 04 45 29 85 48 58 79
2 55 06 80 64 34 71 41 32 97 37 73 05 04 33 04 96 16 42 50 72 91 30 86 66 17
3 19 54 68 57 50 27 10 08 16 26 41 89 75 46 88 83 12 20 50 51 03 73 77 24 61
4 42 49 74 33 75 24 22 79 32 12 55 23 63 66 06 78 83 60 61 46 73 84 85 52 04
5 17 87 57 75 85 31 11 81 00 94 86 28 26 23 87 68 11 76 65 80 64 19 47 83 39

6 90 73 51 07 27 30 68 26 75 42 33 35 11 88 03 83 17 00 29 82 94 50 42 39 61
7 67 37 66 97 75 98 54 02 23 60 80 96 13 08 79 28 48 01 72 28 26 07 95 83 89
8 76 19 85 46 62 46 64 30 58 35 62 75 25 68 52 54 64 28 49 57 66 52 70 54 74
9 97 76 37 48 02 83 03 63 59 78 55 25 54 22 99 44 39 35 84 50 73 51 68 77 81
10 55 24 37 37 72 35 96 54 05 45 26 00 71 29 15 03 85 34 15 27 79 77 49 03 64

11 12 29 63 58 84 75 61 53 11 09 69 69 11 16 62 31 48 83 73 21 82 10 70 87 56
12 40 74 32 02 30 93 56 33 50 94 36 37 34 26 28 23 36 31 73 73 57 55 92 43 03
13 28 23 78 80 23 98 97 16 99 86 94 69 93 93 70 67 68 53 11 04 04 18 05 22 91
14 18 11 67 73 29 59 78 37 66 62 66 71 08 77 20 98 80 13 08 21 44 68 66 60 15
15 79 36 14 75 23 41 74 46 91 00 12 78 89 97 21 01 40 08 31 96 92 75 06 64 08

16 89 02 33 69 91 95 70 70 22 65 40 85 89 96 54 05 45 44 72 34 23 32 60 43 08
17 52 83 17 02 17 85 35 75 34 75 21 38 18 83 18 48 55 27 66 63 36 33 91 01 87
18 49 93 37 01 71 80 38 09 76 30 64 04 23 28 33 86 43 28 39 29 56 35 60 91 47
19 19 82 36 96 12 53 94 00 21 77 81 03 36 83 31 69 07 01 27 71 54 01 27 38 83
20 01 02 33 71 85 69 39 89 92 42 93 08 86 45 99 19 59 56 11 01 70 16 66 07 28

21 70 23 28 73 71 33 44 28 15 69 24 45 62 11 68 35 63 23 13 06 61 52 45 61 74
22 02 99 40 01 23 37 36 41 82 55 72 42 91 06 35 69 09 32 23 23 40 18 58 78 76
23 36 61 46 37 95 73 89 20 50 77 44 60 30 83 47 72 26 84 00 82 34 15 26 26 23
24 28 68 39 42 28 36 85 39 29 10 22 62 75 29 58 30 14 78 99 99 28 14 27 45 51
25 23 95 60 71 84 24 49 90 38 42 10 95 81 95 19 17 39 68 45 90 46 20 03 25 83

26 92 14 05 83 10 38 71 74 92 04 26 93 75 07 29 01 10 21 74 86 91 04 51 76 40
27 37 15 22 86 98 54 72 10 96 29 99 51 81 60 27 46 36 30 30 68 67 92 26 05 84
28 96 84 03 37 18 07 76 06 69 67 36 43 65 98 31 48 18 96 00 13 91 25 37 69 66
29 13 07 59 57 60 30 63 65 80 63 25 46 71 86 92 19 84 71 89 49 00 56 09 07 08
30 95 63 25 05 08 32 08 71 92 17 51 10 02 06 62 77 76 07 75 85 30 33 85 11 73

31 29 81 10 89 59 20 66 52 04 19 60 65 90 57 89 40 42 15 92 94 43 04 47 16 07
32 49 81 91 00 08 95 58 17 46 79 68 56 12 26 69 28 94 09 74 70 57 51 01 51 69
33 33 78 85 24 00 90 71 75 17 58 49 31 96 04 71 66 42 32 15 05 93 06 36 23 89
34 77 02 91 18 09 69 40 05 06 76 73 50 39 11 92 04 70 93 51 96 57 16 13 13 07
35 36 76 64 09 38 54 65 02 33 62 07 07 22 24 98 05 87 00 48 05 21 25 43 52 66

36 83 31 69 00 66 14 88 09 89 21 36 64 73 10 78 78 82 56 77 58 58 60 63 57 64
37 04 89 25 40 49 78 97 34 31 91 83 93 41 68 46 07 00 40 14 09 14 39 40 44 25
38 28 92 55 43 44 85 74 38 94 96 28 65 23 49 79 93 56 92 43 65 64 20 46 67 47
39 04 18 42 87 45 19 49 65 57 43 08 00 06 04 44 68 52 16 27 07 21 38 20 43 30
40 79 50 22 49 76 10 60 08 60 67 69 73 22 86 61 36 06 98 69 32 91 39 05 85 49

41 11 18 15 65 05 34 63 70 70 99 78 69 49 66 85 87 91 24 05 89 23 83 01 74 02
42 04 73 57 27 95 44 38 34 04 11 69 09 53 20 59 59 49 70 88 26 23 70 99 48 19
43 55 15 18 85 46 80 76 11 89 87 19 58 44 72 19 90 31 43 06 67 70 10 72 35 83
44 25 62 90 52 56 08 32 91 29 46 04 39 00 90 65 74 77 63 92 58 11 67 27 96 32
45 91 44 73 08 52 43 46 56 36 20 70 11 96 34 27 45 52 74 59 07 15 53 91 65 16

46 07 14 89 71 48 60 16 23 00 97 32 78 87 68 27 87 93 49 82 01 69 84 89 10 37
47 68 42 19 79 42 25 65 38 58 01 61 57 89 77 82 13 13 87 18 99 01 94 97 92 75
48 59 12 53 02 04 36 97 09 34 01 46 86 83 20 41 75 04 96 47 48 73 15 11 46 71
49 61 77 16 15 83 14 34 15 11 54 77 26 69 48 11 55 13 74 16 87 78 15 49 37 08
50 19 35 98 88 38 08 81 59 64 20 71 76 63 30 51 61 39 26 29 84 15 66 57 43 94
Table 1: Random Numbers - continued

Row
1 05 82 59 43 12 46 05 83 00 85 31 59 83 40 40 20 27 58 13 91 39 01 04 61 89
2 62 89 27 39 36 49 72 84 41 25 64 69 20 44 22 99 90 74 18 17 64 30 85 20 64
3 09 20 65 80 20 90 84 91 45 69 92 54 80 47 93 87 98 13 94 47 62 32 02 11 20
4 91 50 44 01 00 09 11 08 98 30 94 68 49 55 54 74 36 36 43 88 21 32 98 18 57
5 27 01 13 98 92 88 18 80 23 43 86 98 53 43 91 85 05 77 34 64 15 49 69 54 06

6 02 16 81 03 59 25 25 77 39 88 98 50 67 68 47 81 97 85 13 93 76 88 76 63 05
7 83 21 22 96 41 80 45 98 74 25 68 69 29 03 67 89 82 00 41 47 63 78 76 17 71
8 08 83 00 46 50 55 71 29 31 32 03 86 90 85 48 35 18 59 04 67 90 72 45 45 54
9 69 70 08 40 80 21 53 75 59 23 92 39 62 58 01 60 58 45 14 50 34 61 28 01 61
10 17 86 72 30 28 32 96 54 39 17 86 92 10 38 39 57 44 49 53 28 88 30 68 40 68

11 53 54 76 59 01 75 95 16 18 30 87 65 01 56 86 09 73 43 34 10 14 86 05 05 94
12 49 60 82 05 43 45 22 01 80 04 78 53 61 66 36 14 87 34 77 89 99 29 02 59 33
13 56 21 68 81 78 88 39 20 22 59 65 54 82 48 16 87 51 96 85 82 07 40 42 31 23
14 45 90 64 19 54 55 11 20 98 69 46 72 79 81 77 17 17 33 33 24 41 02 38 84 31
15 31 47 37 44 12 34 88 15 76 06 21 37 55 73 20 36 43 64 41 01 69 86 70 53 63

16 50 15 29 95 78 75 04 04 20 67 08 96 36 94 09 28 66 36 54 11 40 39 14 66 27
17 59 31 67 76 61 25 33 17 42 75 99 46 87 02 11 61 37 22 81 81 21 59 04 05 94
18 18 03 59 78 22 66 86 27 11 99 67 53 08 64 80 23 16 58 11 80 20 90 07 05 69
19 14 47 55 76 56 70 00 15 83 37 28 71 63 20 78 04 96 33 31 41 36 56 09 13 28
20 26 13 41 73 86 13 78 11 31 86 40 92 84 08 98 99 26 17 14 08 03 59 11 86 20

21 15 48 08 82 78 86 96 10 30 68 39 56 83 40 20 87 78 70 72 04 50 99 29 85 10
22 34 48 72 72 73 86 33 65 83 07 58 10 88 59 26 37 66 41 68 81 62 66 28 92 43
23 65 69 29 69 92 82 14 52 33 06 55 34 34 39 63 15 49 35 96 50 96 26 46 08 40
24 80 57 63 54 67 88 74 91 46 19 76 72 31 48 54 06 50 77 23 54 84 31 47 43 70
25 05 19 50 15 10 46 57 33 35 43 32 26 28 69 87 42 56 19 84 74 66 30 97 88 57

26 46 82 58 38 69 60 45 30 87 20 99 49 54 37 62 39 85 28 20 42 19 85 31 71 67
27 37 56 45 19 41 81 01 64 56 36 33 98 74 39 86 04 53 89 97 08 75 06 01 59 92
28 61 87 51 22 82 64 80 59 68 96 17 21 16 06 54 01 76 42 26 71 68 61 37 44 30
29 43 09 34 04 22 74 50 40 59 38 48 42 90 07 82 26 67 56 28 30 86 10 18 80 60
30 08 61 37 97 92 99 04 86 18 13 87 49 03 66 49 21 05 95 57 49 00 99 29 97 93

31 64 34 51 15 75 50 96 34 18 62 57 71 76 60 73 67 07 58 27 86 93 09 51 45 85
32 03 80 28 68 55 12 40 15 33 71 83 99 47 57 53 11 16 29 84 66 83 14 44 87 86
33 07 56 93 41 79 03 53 88 96 74 55 26 12 82 54 73 03 75 76 67 86 71 66 42 14
34 19 56 34 12 33 15 53 20 73 71 47 44 72 28 30 70 00 06 74 95 30 00 19 91 22
35 61 31 26 88 76 04 58 26 18 93 98 86 34 23 49 89 18 11 86 27 53 00 53 13 33

36 86 46 76 51 40 15 84 80 00 65 17 87 05 61 12 04 51 40 63 38 72 56 64 23 22
37 79 29 04 49 48 03 68 07 73 14 83 76 97 12 80 32 03 58 32 44 12 69 41 40 93
38 39 91 64 66 27 53 09 68 69 55 69 06 15 07 00 16 38 61 36 59 41 94 23 00 08
39 18 69 34 50 24 86 13 87 38 80 17 52 20 44 72 90 07 93 70 90 93 01 23 50 41
40 72 31 56 06 13 40 42 30 91 20 97 74 22 82 57 27 11 52 63 48 05 84 87 88 06

41 95 71 75 06 78 52 62 30 12 88 32 03 71 57 22 22 17 84 75 21 45 19 43 86 86
42 94 75 80 44 52 98 54 85 87 95 50 68 06 43 47 14 13 29 73 77 30 50 43 30 49
43 61 64 25 07 29 13 08 66 61 71 95 46 85 75 02 71 00 81 62 64 18 97 54 68 88
44 31 22 03 05 10 37 37 72 46 14 24 97 43 37 52 42 27 93 21 25 52 36 36 60 67
45 88 36 06 14 67 38 48 55 20 41 78 75 77 58 53 11 18 10 09 48 62 82 62 38 76

46 81 17 66 58 06 41 94 78 33 99 07 35 10 72 73 06 82 67 54 23 33 51 18 80 38
47 31 70 02 98 29 45 04 23 94 16 73 76 69 77 59 85 40 22 36 08 09 61 30 87 92
48 84 80 17 22 82 60 79 58 38 97 61 98 54 66 24 66 43 05 83 56 27 52 56 85 25
49 38 42 84 95 76 65 27 05 47 49 77 63 74 80 28 30 36 35 97 85 52 55 42 29 94
50 43 93 58 45 07 35 16 87 78 15 52 43 73 77 23 59 65 40 54 52 60 07 12 91 50
Table 1: Random Numbers - continued

Row
1 38 53 42 52 77 97 74 90 36 41 22 96 35 88 47 56 15 31 10 96 96 91 11 66 23
2 14 88 27 32 18 21 07 08 75 64 07 42 20 23 09 35 63 35 09 43 63 73 42 62 82
3 33 63 17 37 35 75 59 24 30 32 82 37 88 02 39 89 71 69 98 69 46 99 39 37 06
4 76 85 31 10 40 41 80 52 29 11 81 16 77 32 95 97 83 76 66 26 67 10 87 72 09
5 88 01 30 82 14 46 86 66 01 57 93 61 47 52 34 17 44 69 10 01 27 88 99 72 10

6 14 00 83 19 69 27 50 66 40 88 90 23 36 99 19 57 07 02 26 54 08 58 99 65 40
7 54 54 47 23 42 33 26 04 30 85 28 31 70 21 78 53 57 53 47 52 13 81 88 31 84
8 85 52 76 66 33 63 39 10 18 74 99 33 70 17 18 03 80 97 63 06 40 42 32 83 38
9 64 32 83 92 95 63 56 09 14 71 98 23 69 61 25 39 40 02 17 78 10 33 68 33 16
10 90 70 12 77 15 40 12 73 88 30 10 23 37 18 56 93 98 99 24 29 30 88 64 59 91

11 95 95 61 10 17 01 66 60 72 87 02 32 87 37 13 34 42 81 56 92 44 56 21 16 83
12 56 32 31 30 66 15 24 56 17 40 29 94 00 12 33 73 64 18 25 57 24 29 10 63 56
13 90 93 22 32 34 01 85 87 87 63 66 14 63 79 57 38 92 05 07 74 46 03 08 34 77
14 22 68 40 08 23 41 52 62 62 32 86 83 94 22 83 68 53 92 91 02 26 27 52 95 83
15 01 47 89 99 92 81 42 74 55 12 39 56 07 18 42 44 99 03 84 21 09 58 19 51 91

16 73 96 84 59 04 62 00 32 58 39 21 40 58 31 03 87 17 49 20 42 69 37 50 72 90
17 11 02 17 48 69 10 45 17 64 03 71 52 28 69 85 47 21 09 62 99 95 18 16 02 74
18 63 63 03 06 86 79 22 60 58 49 68 40 33 71 80 77 60 66 96 73 64 36 59 83 14
19 81 89 60 01 39 12 53 76 96 61 30 75 95 76 03 06 36 58 06 32 54 67 18 69 21
20 98 47 18 94 90 05 60 90 70 89 56 32 50 50 83 20 87 19 21 75 11 00 20 66 27

21 77 60 77 58 53 03 38 51 17 32 98 11 08 95 82 06 65 20 41 96 06 59 05 78 94
22 04 21 59 29 44 30 44 71 60 74 98 19 10 00 89 55 81 74 67 96 85 61 22 66 92
23 89 40 97 47 05 75 10 15 16 93 37 88 52 40 09 07 17 51 75 84 93 19 60 47 16
24 64 23 21 50 59 30 63 62 38 97 70 29 11 80 96 95 00 50 67 67 35 03 91 19 20
25 47 09 35 19 65 71 61 31 30 73 67 66 40 93 85 46 50 23 36 20 70 72 22 49 80

26 58 70 04 80 52 12 54 35 26 68 33 16 90 06 61 48 80 98 92 13 66 47 31 07 87
27 88 25 67 75 85 86 06 35 76 40 48 92 54 04 97 89 73 43 19 18 39 34 16 84 60
28 70 04 01 40 91 43 94 04 42 52 89 25 54 34 48 57 43 89 49 62 86 52 34 97 99
29 35 69 24 36 56 42 04 66 74 70 41 84 28 74 51 94 96 55 74 30 80 00 60 44 46
30 85 21 62 70 72 13 82 04 33 07 95 02 24 97 61 06 00 86 06 76 97 32 28 66 23

31 60 69 86 93 29 13 90 58 54 91 11 81 56 50 53 46 37 07 09 97 86 94 96 68 58
32 79 12 40 58 92 38 30 17 40 20 47 35 72 79 54 43 83 40 41 16 90 95 32 05 95
33 94 97 08 82 62 37 09 94 81 95 51 51 88 54 68 07 61 18 98 71 95 84 47 21 99
34 03 14 30 66 77 01 07 23 58 32 56 29 05 25 60 83 29 12 94 60 43 90 09 06 57
35 47 76 39 25 81 16 72 79 63 29 14 47 30 85 24 34 65 63 62 07 01 19 63 42 74

36 55 27 45 90 71 55 39 16 51 60 71 48 97 14 86 01 62 30 09 73 27 88 76 82 78
37 79 34 98 20 16 98 48 91 03 76 84 21 97 94 22 56 53 85 80 16 15 78 97 78 21
38 31 38 71 89 90 19 49 79 27 55 91 25 30 20 43 69 70 93 40 14 68 68 32 04 17
39 50 49 64 74 87 31 51 14 67 16 17 71 61 58 31 43 41 51 15 47 72 66 94 81 15
40 41 37 41 68 77 81 54 93 70 81 93 59 88 83 80 88 15 96 42 07 17 66 33 05 16

41 13 92 62 98 41 56 65 74 39 46 93 55 86 17 82 55 10 16 91 31 71 92 03 72 10
42 01 91 50 71 64 56 35 82 51 11 31 72 72 35 78 77 56 33 59 42 20 19 68 76 37
43 96 06 41 93 42 74 73 62 26 66 49 63 48 43 00 11 77 34 47 21 96 41 75 26 72
44 98 40 95 36 27 86 92 38 97 80 95 49 82 35 80 79 16 51 81 02 84 53 38 54 39
45 38 28 14 50 16 00 72 79 63 48 23 65 62 94 25 45 28 16 28 92 77 94 38 62 98

46 53 58 26 11 17 63 64 61 39 13 70 01 03 75 43 79 55 43 57 08 95 62 64 98 38
47 79 87 44 92 78 04 43 87 70 03 22 77 39 91 59 33 63 54 13 00 09 87 33 39 52
48 35 89 85 45 93 09 74 73 42 74 64 39 13 98 94 04 03 24 49 53 49 49 04 10 01
49 11 62 82 96 22 17 84 39 48 15 74 51 80 42 27 97 67 92 97 13 11 00 01 45 70
50 92 78 73 32 88 03 31 01 80 44 02 15 98 94 37 89 87 36 56 98 72 55 60 22 85
3. The members of a class are numbered 1 to 85. Use the following random numbers to create a random
sample of 6 students. Work from top to bottom. Write down the 6 students’ names. (The selected random
numbers add up to 191)
1 7 2 5 8 9 4 0 4 6 3 8 7 0 3 3 2 1 2 7 4 3 7 9
7 9 9 6 6 0 1 7 3 5 4 9 3 1 4 9 2 4 0 9 3 5 4 7
5 3 2 2 8 1 5 3 2 1 9 2 1 9 3 3 6 2 5 2 7 3 5 1

4. The houses in a street are numbered from 1 to 550. Use the random numbers in question 3, working
from left to right along the top row, to select a random sample of 5 houses. (The selected random
numbers add up to 1550)

5. A biologist plants 190 seeds in pots numbered from 1 to 190. List the numbers of the pots you would
include in a systematic sample of size 10. Let the first number you select be 7.

6. A company places each of its employees on one of 5 salary scales: A, B, C, D and E. The number of
employees on each scale is listed below:
A 130 B 275 C 415 D 260 E 90
How many people from each scale should be included in a sample of size 60?

An old test
1. A campus planner at a local university working on bikeways needs information about bicycle commuters.
She designed a questionnaire. One of the questions asks how many minutes it takes the rider to pedal from
home to campus. Information on 24 bicycle commuters (numbered from 1 to 24) yielded the following times:

No TIME No TIME No TIME No TIME No TIME No TIME

1. 22 2. 29 3. 27 4. 30 5. 12 6. 22
7. 22 8. 13 9. 19 10. 23 11. 17 12. 10
13. 9 14. 20 15. 18 16. 13 17. 22 18. 38
19. 13 20. 14 21. 17 22. 10 23. 15 24. 31

Use systematic sampling method to select required sample of 4 bicycle commuters. Let the first element of
the sample be 2. (3)

2. Answer the following as true or false: (indicate the correct option with X) (5)

True False
2.1 A parameter is a statistical measure computed from the entire universe
2.2 A variable is a statistical measure computed from a subset taken from
the universe
2.3 A population is always only a collection of people
2.4 When we investigate the whole population it is called a census
2.5 Inferential statistics condenses large volumes of data into few summary
measures.
3. There are 3210 students in 4 different departments K; L; M and N of a faculty in a particular university. A
stratified random sample size of 125 must be drawn from the population. Calculate the number of students
chosen from each department using stratified random sampling method. (4)

Department Number of students Sample

K 700
L 555
M 1200
N 755

4. Suppose there are 192 people on the electoral roll in a retirement village. Select a random sample of 4
people from the village using the table of random numbers given below. Start at the top left corner and read
the random numbers vertically from top to bottom. (4)

Row

1 83 20 37 15 22 21 78 47 14 51 94 38 69 47 58 04 29 85 48 58
2 55 06 80 64 71 41 32 97 73 05 04 33 96 16 42 50 91 30 86 66
3 19 54 68 57 27 10 08 16 41 89 75 46 83 12 20 50 03 73 77 24
4 42 49 74 33 24 22 79 32 55 23 63 66 78 83 60 61 73 84 85 52
5 17 87 57 75 31 11 81 00 86 28 26 23 68 11 76 65 64 19 47 83

Questions from 2016 exam papers:

1.1 A politician who is running for the office of mayor of a city with 25 000 registered voters’ commissions
a survey. In the survey, 48% of the 200 registered voters interviewed say they plan to vote for her.
1.1.1 What is the population of interest? (2)
1.1.2 What is the sample? (2)
1.2.1 The owner of a large fleet of 350 taxis in Johannesburg is trying to estimate his costs for the next
year’s operations. He needs to select a sample of 20, what sampling method should he use? (2)
A: Simple B: Random C: Stratified D: Snowball E: Quota
random sampling random sampling
sampling sampling

1.2.2 Determine the scale of measurement for the following: the total annual fuel costs of each of the 20
taxis. (2)
A: Nominal B: Ordinal C: Interval D: Ratio E: None

Indicate if the following are true or false:

2.1 The number of defective items manufactured, is an example of qualitative data. (1)
2.2 A population is a subset of a sample on which observations are made. (1)
2.3 Data which is captured at the point where it is generated is called primary data. (1)
2.4 Collecting of data, analysis of the data and drawing meaningful conclusions are the three basic
statistical processes that lead to good decision making. (1)
2.5 The questionnaire is the only method to collect qualitative data. (1)
2.6 The number of white cars passing through a tunnel in one hour is an example of quantitative data. (1)

Questions from 2017 exam papers:

1.1 In order to check public transport busses for roadworthiness, a sample of 35 is required from the
population of 1260 registered busses. If you need to draw a systematic sample and the first vehicle you
select is bus number 15, what is the number of the next two busses you must check? (2)
A: 51 and 87 B: 35 and 70 C: 50 and 85 D: 36 and 72 E: None

1.2 A big shop has got a fresh produce, clothing and cosmetic department. The manager plans to send
12 of the consultants on a marketing course. He decides to take a stratified random sample. How many
consultants from each department should he select? (3)
Department Consultants Number of consultants
selected for course
Fresh Produce 25

Clothing 12

Cosmetic 20

2. A group of students is numbered 1 to 250. Use the random number table below and select a sample of 5
students, starting from row 3 column 11 read the numbers vertically downwards. Write the number of the
sampled students in the cells provided. (5)
Row
1 90 73 51 07 27 30 68 26 75 42 33 35 11 88 03 83 17 00 29 82 94 50 42 39 61
2 67 37 66 97 75 98 54 02 23 60 80 96 13 08 79 28 48 01 72 28 26 07 95 83 89
3 76 19 85 46 62 46 64 30 58 35 62 75 25 68 52 54 64 28 49 57 66 52 70 54 74
4 97 76 37 48 02 83 03 63 59 78 55 25 54 22 99 44 39 35 84 50 73 51 68 77 81
5 55 24 37 37 72 35 96 54 05 45 26 00 71 29 15 03 85 34 15 27 79 77 49 03 64

A: B: C: D: E: