Head to www.savemyexams.com for more awesome resources 2.1 Statistical Measures Question Paper Course Edexcel AS Maths Section 2. Data Presentation & Interpretation Topic 2.1 Statistical Measures Difficulty Hard Time Allowed 70 Score /54 Percentage /100 Page 1 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers Head to www.savemyexams.com for more awesome resources Question 1 a , b , c and d are 4 integers written in order of size, starting with the smallest. The sum of a , b and c is 70 The mean of a , b , c and d is 25 The range of the 4 integers is 14. Work out the median of a , b , c and d [4 marks] Question 2a The speeds (s), to the nearest mile per hour, of 80 vehicles passing a speed camera were recorded and are grouped in the table below. Speed, s (mph) 20 ≤ s <25 25 ≤ s <30 30 ≤ s <35 s ≥ 35 Number of vehicles 23 48 7 2 (i) Write down the modal class for this data. (ii) Write down the class group that contains the median. Page 2 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers [2 marks] Head to www.savemyexams.com for more awesome resources Question 2b (i) Assuming that ≥35 means ‘at least 35 mph but less than 40 mph’, calculate an estimate for the mean speed of the 80 vehicles. (ii) It is now discovered that ≥35 means ‘at least 35 mph but less than 60 mph’. Without further calculation, state with a reason whether this would cause an increase, a decrease or no change to the value of the estimated mean. [4 marks] Question 3a A veterinary nurse records the weight of puppies (in kg) at birth and again at their eight week check-up. The table below summarises the weight gain of 50 small breed puppies over their first eight weeks. Weight gain w (kg) 0.0 ≤ w < 0.5 0.5 ≤ w < 1.0 1.0 ≤ w < 1.5 1.5 ≤ w < 2.0 2.0 ≤ w < 2.5 Number of puppies f 1 8 19 18 4 Use linear interpolation to estimate the median and interquartile range of the weight gain of the 50 puppies. Page 3 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers [4 marks] Head to www.savemyexams.com for more awesome resources Question 3b Give a reason why it is not possible to determine the exact median for this data. [1 mark] Question 3c The veterinary nurse decides to monitor any puppies whose weight gain during their first 8 weeks was less than 0.8 kg. Estimate the number of puppies whose weight gain could be below 0.8 kg, and explain why the vet would need more information before determining for certain how many puppies would need to be monitored. [2 marks] Question 4a Workers at an elephant sanctuary measure the health of their elephants by weighing the amount of dung (d kg ) each one produces. The data for the mass of dung produced in one day by 18 elephants can be summarised as Σd = 895 and Σd 2= 45 810. Calculate the mean and variance of the amount of dung produced that day. [3 marks] Question 4b To calculate how much food (f kg ) to give each elephant, staff use the formula f= 3d – 25. Calculate the mean and variance of the amount of food the workers should give to the elephants each day. Page 4 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers [2 marks] Head to www.savemyexams.com for more awesome resources Question 5a A machine is set to fill sacks of potatoes to a target weight of 50 kg, although the actual weight of the sacks (w kg ) can vary from that target. To test the accuracy of the machine, a random sample of 20 sacks is taken and the values of y =(w -50) are recorded. The mean and standard deviation of y are found to be -1.8 and 3.1 respectively. Write down the mean and standard deviation of w . [2 marks] Question 5b Calculate the value of (i) Σw (ii) Σw 2 [3 marks] Question 5c Another 10 sacks of potatoes are sampled and the mean of these is found to be 51.2 kg. Calculate the mean of all 30 sacks of potatoes and comment on the accuracy of the machine. [3 marks] Page 5 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers Head to www.savemyexams.com for more awesome resources Question 6 Whilst in lockdown, 100 people were asked to record the length of time, rounded to the nearest minute, that they spent exercising on a particular day. The results are summarised in the table below: Frequency f 1 12 25 Time mins 0 ≤ t ≤10 10 < t ≤20 20 < t ≤30 30 < t ≤40 40 < t ≤50 50 < t ≤60 a b 14 Given that the estimate of the mean time spent exercising based on this table is 35.4 minutes, find the values of a and b . [4 marks] Question 7a The ages, x years, of 200 people attending a vaccination clinic in one day are summarised by the following: Σx = 7211 and Σx 2 = 275 360. Calculate the mean and standard deviation of the ages of the people attending the clinic that day. Page 6 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers [3 marks] Head to www.savemyexams.com for more awesome resources Question 7b One person chooses not to get the vaccine, so their data is discounted. The new mean is exactly 36. Calculate the age of the person who left and the standard deviation of the remaining people. [4 marks] Question 8a In January of 2021, the UK government announced a nationwide lockdown to control the spread of the coronavirus. The table below shows the means and standard deviations of the average amounts of time spent indoors per day by some people in London, UK and in Wellington, New Zealand, in January of 2021. London Wellington Number of people 25 15 Mean (hr) 20.9 15.1 Standard deviation 1.51 2.87 Suggest a reason, in the context of the question, for why (i) the mean in London is higher than the mean in Wellington (ii) the standard deviation in London is lower than the standard deviation in Wellington. Page 7 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers [2 marks] Head to www.savemyexams.com for more awesome resources Question 8b Based on the data in the table, do you think the government in New Zealand had imposed the same restrictions as those in the UK? Give a reason for your answer. [1 mark] Question 8c Calculate the overall mean for the average amounts of time spent indoors by all 40 people. [2 marks] Question 9a Data on the daily maximum gust in Camborne is gathered from the large data set. For the third week of October 1987, and the same week in 2015, the daily maximum gust in knots (kn) is shown in the table below: Daily maximum gust, kn Camborne 15th – 21st October 1987 53 59 55 54 36 14 29 Daily maximum gust, kn Camborne 15th – 21st October 2015 15 16 17 13 14 14 24 Using the data given above, find the mean and standard deviation of the daily maximum gust for Camborne for the third week of October 1987. [4 marks] Page 8 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers Head to www.savemyexams.com for more awesome resources Question 9b Without carrying out any calculations, state whether you think the mean and standard deviation for the 2015 data would be greater or less than your answers for part (a). Use your knowledge of the large data set to suggest a reason for each of your answers. [4 marks] Page 9 of 9 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers
