Exercise Set 1 - Questions PDF

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Exercise Set 1 1.

The weights (kg) of randomly selected cargo containers on an airline are as follows: 189 197 184

188 198 192

205 222 204

188 187 205

176 188 183

199 198

188 202

182 204

190 177

183 172

198 172

198 184

Perform the following tasks: (a) construct a frequency histogram and a relative frequency histogram (b) construct a cumulative relative frequency histogram (c) construct a stem-and-leaf plot (d) with the help of the plot from (c), identify the maximum, minimum, median and lower and upper quartiles of this dataset. Hence draw a boxplot for the data. (e) find the mean and standard deviation of the dataset; and also the corresponding 10% trimmed statistics (f) determine whether the data seems to be positively or negatively skewed, or symmetrical, using any of your answers from above (g) are there any outliers in the dataset? (h) describe how the stem-and-leaf plot found in (c) would change if the weights were recorded in hundreds of kg instead of kg. 2.

Recycled plastic at a recycling plant is contaminated with aluminium. The maximum acceptable level is 220ppm. The following data is the aluminium concentration for 26 plastic samples from the plant.

291 222 125 79 145 119 244 118 182 63 30 140 101 102 87 183 60 191 119 511 120 172 70 30 90 115 Summarise the data using both a stem and leaf plot and a boxplot. Describe the distribution of contamination levels and comment on the performance of the recycling plant in achieving the standard. 3. A company needs to replace light bulbs on a regular basis. A new brand claims to offer longer life and other benefits. The company compares its records of the life of 20 of its current bulbs (bulb 1) with 20 of the new brand (bulb 2). Make appropriate graphical and numerical summaries of the data and then make a recommendation on whether or not the company should change brands. bulb 1 1086 1280 911 1186

1139 1284

1358 1414

1090 1312

998 1176

935 1134

1009 1047

1449 1175

1148

1182

bulb 2 1235 1574 1208 1348

1590 1573

1492 1462

1642 1499

1517 1444

1399 1299

1317 1510

1440 1380

1466

1327

Faculty of Engineering and Industrial Sciences Second year Engineering: Applied Probability and Statistics

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