Practice%20SAC%201-%20Sausages%20Solutions%202022

STUDENT NAME:________________________________________________________ Teacher Name:____________________________ Unit 3 Further Mathematics Practice SAC - Core Data Analysis Task on Sausages Reading time: 10 minutes Writing time: 1.5 hours QUESTION AND DATA BOOKLET Structure of Book Part Number of Marks 1 2 3 4 5 7 8 8 15 12 Directions to students Materials Question and Data booklet. Pens, pencils and a ruler are permitted. An approved CAS calculator may be used. One bound reference is permitted. Any loose sheets must be securely stapled or glued into the book. No white out liquid/tape is allowed. Instructions to Student Write your name in the space provided on this question and data booklet. Students must not communicate, interfere or cause a disturbance to other students. No food or drinks other than water (clear bottle with no label) are permitted during the SAC. Students must not write anything offensive on SAC materials. Attempt all questions and record your answers in the spaces provided. Any working out must be included as part of this document. Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the SAC room. Total Marks: 50

Sausages - Are they healthy? A recent study of the calorie content and sodium content in milligrams (mg) of sausages served by street vendors has been used in this Data Analysis Task. Your job will be to explore the given statistics and draw conclusions about the health benefits (or otherwise) of eating sausages. In the study, a number of different sausages were bought and analysed. The sausages were grouped as being mainly a beef-based sausage, a poultry-based sausage or other meat-based sausage. DATA SHEET The Sausage data is given in Table 1 below: Beef Sausages Poultry Sausages Other Meat Sausages Calories (calorie) Sodium(mg) Calories (calorie) Sodium(mg) Calories (calorie) Sodium(mg ) 186 495 129 430 173 458 181 477 132 375 191 506 176 425 102 396 182 473 149 322 106 383 190 545 184 482 94 387 172 496 190 587 102 542 147 360 158 370 87 359 146 387 139 322 99 357 139 386 175 479 107 528 175 507 148 375 113 513 136 393 152 330 135 426 179 405 111 300 142 513 153 372 141 386 86 358 107 144 153 401 143 581 195 511 190 645 152 588 135 405 157 440 146 522 140 428 131 317 144 545 138 339 149 319 135 298 132 253 Table 1

Part 1 - Analysis of the calories in beef based sausages. Q1 Calculate the following answers for the BEEF SAUSAGE: CALORIE data. Shape of Distribution: Approximately symmetrical Median (3 Significant Figures): 153 Mean (1 Decimal Place): 156.9 IQR: 38.5 Range: 79 Standard Deviation ( 3 significant Figures): 22.6 /6 Q2 The Median and Mean values for the calories in Beef sausages seem quite close together. In terms of the shape of the distribution, why has this occurred? Both the mean and median values for the calories in Beef sausages indicating the shape of the data is almost symmetrical. /1