Statistical sampling questions

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• Edexcel 9MA0 · June 2023 · Paper 31 · Q3 · 7 marks

  7 marks

  3

  
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  Examiner report

  Once again the large data set aspects of this question caused problems for some students but most scored some marks here. In part (a) a few responses simply quoted standard textbook answers about cleaning data by removing outliers and others were distracted by the class intervals for the data. Many though did realise that the “tr” values needed attention but a number didn’t seem to realise that trace entries had a value between 0 and 0.05 and therefore removing them would have a big effect on the calculations Ben wanted to carry out. Those that did appreciate the value of the “tr” usually suggested a suitable numerical value (usually 0) to replace them with and scored both marks. Part (b) was, unsurprisingly, answered very well with many scoring full marks. A few lost marks for truncating rather than rounding their answers for example 2.11 in (i) whilst others were convinced that the “tr” values should have been removed and had a denominator of 155 despite the question telling them that all 184 values were used. It is still surprising to see a small number of students using a denominator of 9 or 10 (the number of classes in the table) and a slightly larger proportion who couldn’t use the standard deviation formula, given in the formula booklet, correctly. It was encouraging to see a good number of students demonstrating some familiarity with the large data set and scoring some marks in part (c). In (i) we were simply looking for an awareness that because the large data set only had data for May to October this would not be representative of the whole population. Some demonstrated a lack of understanding of the principle of using a sample to make inferences by stating that 184 days was not a sufficiently large sample to represent the weather for the whole year. In this case the problem was not the sample size but the fact that the sample was not representative. In (ii) even some of those who had failed to mention May to October in (i) were able to score here by stating that because the missing months were in winter and they expected more rainfall then, the actual mean would be higher. The great storm of October 1987 featured in many incorrect answers to part (c).

  Text version

  Ben studies Daily Total Rainfall x mm in Leeming for 1987 using all the relevant large-data-set entries. His grouped table is: x = 0, 0.1-0.5, 0.6-1.0, 1.1-1.9, 2.0-4.0, 4.1-6.9, 7.0-12.0, 12.1-20.9, 21.0-32.0, tr; frequencies = 55, 18, 18, 21, 17, 9, 9, 6, 2, 29 respectively. Here tr denotes a trace amount. Using all 184 values, Ben estimates sum(x) = 390 and sum(x^2) = 4336.

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• Edexcel 9MA0 · October 2021 · Paper 31 · Q1 · 7 marks

  7 marks

  1

  
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  Examiner report

  In part (a) many scored the mark by referring to the possibility of bias being introduced by the interviewer or the lack of randomness when using quota sampling. The most common answers that did not score the mark referred to cost or time failing to appreciate that quota sampling is generally quicker and therefore cheaper to implement than simple random sampling. Some thought that quota sampling required a sampling frame which suggested they were confused about the different types of sampling. Part (b) was generally answered very well with most stating the distribution, and scoring the method mark, and then evaluating part (i) correctly on their calculator. Part (ii) met with less success as many could not deal with the inequality or were unsure how to use their calculator correctly. Some seemed to confuse significant figures with decimal places: the front of the exam paper instructs then to use 3 significant figures but some only gave an answer of 0.022 here and lost this mark. Part (c) was usually answered correctly and many went on to use the correct binomial distribution in part (d) though some found interpreting “fewer than 3” a problem and a common incorrect answer was 0.924 (from P( 3 X  ). Overall though this proved a good start to the paper and over 40% scored 6 or 7 marks here.

  Text version

  In a university, 8% of students are members of the university dance club. A random sample of 36 students is taken, and X is the number who are members of the dance club. Only 40% of dance club members can dance the tango.

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