IGCSE-Statistics 统计学03900390_s05_er

0390 Mathematics: Statistics (Half Credit) June 2005 1 CONTENTS FOREWORD ....................................................................................................................... 1 MATHEMATICS: STATISTICS (HALF CREDIT)................................................................ 2 Paper 0390/06 Paper 6 ................................................................................................................................. 2 FOREWORD This booklet contains reports written by Examiners on the work of candidates in certain papers. Its contents are primarily for the information of the subject teachers concerned. www.xtremepapers.net 0390 Mathematics: Statistics (Half Credit) June 2005 2 MATHEMATICS: STATISTICS (HALF CREDIT) Paper 0390/06 Paper 6 General comments This paper produced a wide range of marks. Whilst most candidates were able to attempt all the questions, there were some Centres who entered candidates who had clearly not covered the syllabus and who failed to reach the required standard. Most candidates answered questions to a suitable degree of accuracy, and it was pleasing to observe that only a few lost marks due to premature approximation. This occurred mainly in the use of normal tables. Candidates seemed to have sufficient time to answer all the questions, and only the weaker ones answered questions out of order. Comments on specific questions Question 1 This was well attempted by most of the candidates who had covered the syllabus. Nearly everyone recognised the normal approximation to the binomial and a pleasing number applied the continuity correction with almost all who did so getting it in the correct direction. As in previous years, many lost marks by finding the wrong area. Answer: 0.677. Question 2 This straightforward question on the mean and standard deviation of grouped frequencies produced many correct answers but some candidates provided answers which did not use the mid-point of the frequencies. The upper end, the lower end, the class width, and the semi-class width were all used. The mark scheme awarded method marks for trying something, so most candidates were able to score a few marks here. In part (ii) the correct mid-points had to be used to gain the method mark. A sizeable number of candidates worked backwards from the answer to show that f had to be 9 and then proceeded to verify it. This scored at most 2 marks out of the 4. Answer: (ii) 16.1. Question 3 Most candidates managed to obtained the given answer for part (i) but many failed to see any connection between this part and the next part, which was about completing the probability distribution table. The 4 decimal place requirement was not observed by everyone, some giving the answer as a fraction or to 3 significant figures, resulting in the loss of a mark. However, a mark was given for appreciating the values of X could be anything from 0 to 5 inclusive and many weaker candidates managed to pick up a mark here. Answer: (ii) 0, 0.2373; 1, 0.3955; 2, 0.2637; 3, 0.0879; 4, 0.0146; 5, 0.0010. www.xtremepapers.net 0390 Mathematics: Statistics (Half Credit) June 2005 3 Question 4 There are many useful features of a box-and-whisker plot, and comments such as ‘shows the distribution’, ‘none of the data are lost’, ‘easy to find the mode’ were all acceptable. Comments such as ‘quick and easy to understand’ were not deemed sufficient. There was generally good work at finding the medians and quartiles. A few failed to put in the decimal point, thus losing a mark. The graph was well done with most candidates knowing what a box-and-whisker plot was. The mark given for seeing the word ‘cholesterol’ somewhere on the graph was generally not obtained. Very few candidates gave a heading, or said that the axis represented cholesterol count. Answer: (ii) 5.4, 6.5, 8.3. Question 5 This question produced the greatest variety of answers. Candidates failed to appreciate that the results could be read off the table straight away, and used complicated tree diagram approaches. These did come up with the correct answer eventually if no mistakes were made. Part (iii) on independent events was poorly attempted, with many candidates using colloquial English rather than mathematics to argue their point, and others becoming muddled with independent events. Equivalent forms of the fractions were accepted. Answers: (i) 128 618 ; (ii) 1281 412 ; (iv) 564 358 . Question 6 There were some cases of premature approximation here, with candidates failing to use the normal tables properly, but generally part (i) was well done. Many candidates just ignored finding the probability that all 4 tyres had the required pressures, and just found the probability for one tyre. Very few got anywhere with part (ii). Probably about 10% found the z-value to be 1.282, and another 10% found 0.842, which though incorrect, allowed them to score 2 marks out of 3 if their answer was correctly worked out. The rest scored nothing. Answers: (i) 0.00429; (ii) 1.71 to 2.09. Question 7 This, the last question on the paper, was well attempted by many candidates, with almost everyone scoring well on part (ii) and a significant number doing well on both parts. Answers: (i) 15; (ii) 75; (iii) 90 720; (iv) 120. www.xtremepapers.net