a Your answer will depend on the random number you select as the starting point for your systematic sample. However, the process you followed to select your sample is likely to be similar to that outlined. As a 10 per cent sample has been requested, the sampling fraction is 1/10. Your starting point is selected using a random number between 0 and 9, in this case 2. Once the firm numbered 2 has been selected, every tenth firm is selected:

2 12 22 32 42 52 62 72 82 92 These are shaded in brown on the sampling frame and will result in a regular pattern whatever the starting point:

b The average (mean) annual output of fi rms for your sample will depend upon where you started your systematic sample. For the sample selected above it is £757,000.
c Systematic sampling has provided a poor estimate of the annual output because there is an underlying pattern in the data, which has resulted in fi rms with similar levels of output being selected.

0 1163 20 1072 40 1257 60 1300 80 1034 1 10 21 7 41 29 61 39 81 55 2 57 22 92 42 84 62 73 82 66 3 149 23 105 43 97 63 161 83 165 4 205 24 157 44 265 64 275 84 301 5 163 25 214 45 187 65 170 85 161 6 1359 26 1440 46 1872 66 1598 86 1341 7 330 27 390 47 454 67 378 87 431 8 2097 28 1935 48 1822 68 1634 88 1756 9 1059 29 998 49 1091 69 1101 89 907 10 1037 30 1298 50 1251 70 1070 90 1158 11 59 31 10 51 9 71 37 91 27 12 68 32 70 52 93 72 88 92 66 13 166 33 159 53 103 73 102 93 147 14 302 34 276 54 264 74 157 94 203 15 161 35 215 55 189 75 168 95 163 16 1298 36 1450 56 1862 76 1602 96 1339 17 329 37 387 57 449 77 381 97 429 18 2103 38 1934 58 1799 78 1598 98 1760 19 1061 39 1000 59 1089 79 1099 99 898