To print higher resolution math symbols, click the Hi Res Fonts for Printing button on the jsmath control panel. If the math symbols print as black boxes, turn off image alpha channels using the Options pane of the jsmath control panel. Whitby Community College Your account expires on 8 Nov, 2015 Summarising and Representing Data Exam questions Syllabus Edexcel A Level Questions 10 Time 1 hour 23 minutes Total Marks 69 This paper contains a set of questions followed by the corresponding mark schemes. The time you should spend on each question together with its worth in marks is also given. The content of this paper is based on material from a wide selection of national and international examination boards and organisations. You are advised to have a set of geometrical equipment, pen, HB pencil, eraser. Check if you are allowed a calculator. Some examinations, but not all, allow calculators, including graphical models. NOTES The following browsers have been tested with this facility Mozilla Firefox, Microsoft Internet Explorer and Google Chrome. Microsoft Internet Explorer (IE) was tested on versions 7 to 10 IE6 is no longer officially supported by www.mathsnetalevel.com. See the website for the small font problem with IE7 upwards, and IE8 was tested in IE7 compatibility mode. The latest versions of Google Chrome have a customised print preview which allows you to easily adjust the margins and whether or not headings are printed. Best results are when the background printing of images and colours is enabled (not available in Chrome). There are known printing format issues with the Opera web browser and we do not recommend using this browser. Many of the questions use the jsmath applet. This requires special fonts to be installed for successful printing. These fonts can be downloaded from http//www.math.union.edu/~dpvc/jsmath/. Use the Download the TeX fonts option. Full instructions for their use can be found at http//pubpages.unh.edu/~jsh3/jsmath/ http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20da 1/10
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2015 MathsNet A Level. Licensed to Whitby Community College. Page 2 Summarising and Representing Data Exam questions Questions 10 Time 1 hour 23 minutes Total Marks 69 Q1 ID 5483 In a shopping survey a random sample of 110 teenagers were asked how many hours, to the nearest hour, they spent shopping in the last month. The results are summarised in the table below. hours frequency 0 6 20 7 10 19 11 14 20 15 19 28 20 26 14 27 55 9 A histogram was drawn and the group (11 14) hours was represented by a rectangle that was 2 cm wide and 2.5 cm high. Calculate the width and height of the rectangle representing the group (20 26) hours. Use linear interpolation to estimate the median and interquartile range. [8 marks, 10 minutes] Q2 ID 5481 In a study of how students use their mobile telephones, the phone usage of a random sample of 11 students was examined for a particular week. The total length of calls, in minutes, for the 11 students were 47 54 54 55 45 69 47 27 49 98 61 Find the median and quartiles for these data. A value that is greater than Q3 + 1 5 ( Q3 Q1) or smaller than Q1 1 5 ( Q3 Q1) is defined as an outlier. Show that 98 is the only outlier. (c) Draw a box plot for these data indicating clearly the position of the outlier. [8 marks, 10 minutes] Q3 ID 6192 The pulse rates, in beats per minute, of a random sample of 15 small animals are shown in the following table. 139 160 148 128 157 140 113 142 129 154 100 156 136 131 151 Draw a stem and leaf diagram to represent the data. Find the median and the quartiles. (c) Draw a box plot to represent these data. [9 marks, 11 minutes] http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20da 3/10
2015 MathsNet A Level. Licensed to Whitby Community College. Page 3 Q4 ID 6096 [5 marks, 6 minutes] Year 12 students taken a General studies examination. The results are illustrated in the box and whisker plots. One student commented that the plots show there were more males than females. Comment on this statement. Give two comparisons between the overall performance of the males and females. (c) Give one advantage and one disadvantage of using box and whisker plots rather than histograms to display the results. Q5 ID 6074 Complete the following table of values for the height and weight of seven students. Standard Values Mode Median Mean deviation Height(cm) 149 159 166 164 181 146 166 161 6 10 9 Weight(kg) 45 51 49 181 41 172 181 181 51 The ages (in months) of seven students are 208, 198, 214, 194, 203, 193, 213 Represent these values in an ordered stem and leaf diagram. [6 marks, 7 minutes] Q6 ID 352 Each of the 41 students on a computer course recorded the number of minutes, x, to the nearest minute, spent surfing the internet during a given day. The results are summarised below Find x 2009 x 2 99667 for these data. [2 marks, 2 minutes] http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20da 4/10
2015 MathsNet A Level. Licensed to Whitby Community College. Page 4 Q7 ID 7112 The birth weights, in kg, of 1462 babies are summarised in the table below. Weight (kg) 0 0 1 0 1 0 2 0 2 0 2 5 2 5 3 0 3 0 3 5 3 5 4 0 4 0 5 0 5 0 6 0 Midpoint x, (kg) 0 5 1 5 2 25 3 25 3 75 4 5 Frequency f 2 5 64 310 780 290 8 3 [You may use f x 4680 and fx 2 15249 75] Write down the missing midpoints in the table above. Calculate an estimate of the mean birth weight. (c) Calculate an estimate of the standard deviation of the birth weight. (d) Use interpolation to estimate the median birth weight. (e) Describe the skewness of the distribution. Give a reason for your answer. [11 marks, 13 minutes] Q8 ID 6188 Rachel measured the lengths in millimetres of some of the leaves on a tree. Her results are recorded below. 41 35 47 49 45 46 31 40 47 38 Find the mean and standard deviation of the lengths of these leaves. [3 marks, 4 minutes] http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20da 5/10
2015 MathsNet A Level. Licensed to Whitby Community College. Page 5 Q9 ID 5770 [11 marks, 13 minutes] The maximum temperatures x degrees Celsius recorded during each month of 2005 in Cambridge are given in the table below Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 9 1 7 1 10 4 14 2 16 6 21 9 20 2 22 8 21 1 17 4 10 2 7 5 These data are summarised by n 12 x 178 5 x 2 3034 33 Calculate the mean and standard deviation of the data. Determine whether there are any outliers. (c) The formula y 1 8x + 32 is used to convert degrees Celsius top degrees Fahrenheit. Find the mean and standard deviation of 2005 maximum temperatures in degrees Fahrenheit. (d) In New York the monthly maximum temperatures are recorded in degrees Fahrenheit. In 2005 the mean was 67 and the standard deviation was 14. Briefly compare the maximum monthly temperatures in Cambridge and New York in 2005. Q10 ID 5454 In a survey a sample of 46 fields is taken. Their areas are summarised in the grouped frequency table. Area 0 x 3 3 x 6 6 x 11 11 x 16 16 x 27 frequency 4 7 13 18 4 Calculate an estimate of the sample mean and sample standard deviation. Decide whether there could be any outliers at the upper end of the distribution. [6 marks, 7 minutes] http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20da 6/10
2015 MathsNet A Level. Licensed to Whitby Community College. Page 6 Summarising and Representing Data Exam questions Mark Scheme ID 5483 [8 marks, 10 minutes] (11 14) width (20 26) width (11 14) height (20 26) height Median, Q 2 Q1 Q3 IQR 4 represented by 2 cm 7 represented by 3 5 cm freq. density 20 4 5 represented by 2 5 cm freq. density 14 7 2 represented by 1 cm 55 39 10 5 + 4 13 7 20 27 5 20 6 5 + 4 8 1 19 82 5 59 14 5 + 5 18 7 28 18 7 8 1 10 6 A2 ID 5481 [8 marks, 10 minutes] (c) data sorted Median Q1 Q3 limits See below 27, 45, 47, 47, 49, 54, 54, 55, 61, 69, 98 54 47 61 26 and 82 98 is only outlier M1A2 http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20da 7/10
2015 MathsNet A Level. Licensed to Whitby Community College. Page 7 A3 ID 6192 [9 marks, 11 minutes] (c) stem and leaf diagram median LQ box plot See diagram 140 129 UQ 154 See diagram B3 B2 B3 A4 ID 6096 (c) comment any two comments IQR average skew for Females skew for Males advantage disadvantage not true; box plots do not show frequencies Females has the largest range Females has the largest IQR Males has the highest average positive positive box plot shows key values (quartiles etc) box plot does not show mode or frequencies B2 [5 marks, 6 minutes] A5 ID 6074 [6 marks, 7 minutes] mode height median height mean weight sd weight see below 166 164 102 9 65 2 16 1 represents 161 http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20da 8/10
2015 MathsNet A Level. Licensed to Whitby Community College. Page 8 A6 ID 352 x n 2009 4 9 41 [2 marks, 2 minutes] A7 ID 7112 [11 marks, 13 minutes] missing midpoints mean 2 75 5 5 fx 201 1462 4680 3 1462 B2 (c) standard deviation fx 2 1462 fx 1462 2 (d) (e) median m skew 15249 75 2 3 201 0 429 1462 731th value m 3 0 731 3 81 3 5 3 0 1161 381 m 3 224 negative because mean < median M1A2 A8 ID 6188 [3 marks, 4 minutes] mean x 2 x 10 41 + 35 + 47 + 49 + 45 + 46 + 31 + 40 + 47 + 38 41 9 10 41 2 + 35 2 + 47 2 + 49 2 + 45 2 + 46 2 + 31 2 + 40 2 + 47 2 + 38 2 17871 standard deviation x 2 10 5 6116 x 2 10 17871 2 41 9 10 http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20da 9/10
2015 MathsNet A Level. Licensed to Whitby Community College. Page 9 A9 ID 5770 [11 marks, 13 minutes] x 178 5 1 4 875 12 (c) (d) s x + 2s x 2s y s 67 58 78 14 10 12 3034 33 178 5 2 5 12 12 26 12 3 64 no outliers 1 8(x) + 32 58 78 1 8 5 62 10 12 New York has higher mean New York has higher spread 62 M1 M1 0 ID 5454 [6 marks, 7 minutes] sample mean fx 2 fx f 4 1 5 + 7 4 5 + 13 8 5 + 18 13 5 + 4 21 5 10 37 46 4 2 25 + 7 20 25 + 13 72 25 + 18 182 25 + 4 462 25 6219 5 standard deviation x + 2s 6219 5 1 0 37 2 46 5 26 10 37 + 10 52 20 89 there could be outliers M1 http//www.mathsnetalevel.com/examprint.php?q5454,5770,6188,7112,352,6074,6096,6192,5481,5483&tsummarising%20and%20representing%20d 10/10