Practice Questions Level 3 Mathematical Studies 1350 Analysis of Data April 2018 F 2 1 The World Health Organisation (WHO) collects data and predicts the average life expectancy for someone born at a particular time in a particular country. The data below are for 193 countries and refer to the year 2009. The data have been organised into a grouped frequency table as shown below. Life expectancy at birth (L) Number of countries 45 ≤ L < 50 12 50 ≤ L < 60 24 60 ≤ L < 70 44 70 ≤ L < 75 53 75 ≤ L < 80 32 80 ≤ L < 85 28 (a) (i) On the grid below, draw a histogram for these data. L 40 50 60 70 80 90 Life expectancy at birth in 2009 (years) [4 marks] Version 1.0 1350/1 3 (ii) Using your histogram, or otherwise, estimate how many of these countries have a life expectancy at birth greater than 77 years. [2 marks] (b) (i) From the data given in the table above, estimate a value for the median life expectancy. [3 marks] (ii) For these data, the WHO gives the mean life expectancy for someone born in 2009 as 68 years. Explain why this differs from your median value found in part (b)(i). [1 mark] Version 0.4 1350/1 4 2 The table shows the winner and the length of the winning jump for the Olympic long jump between 1948 and 2012 Year Winner (Male) Country Length Winner (Female) Country Length (metres) (metres) 1948 Willie Steele USA 7.825 Olga Gyarmati HUN 5.695 1952 Jerome Biffle USA 7.57 Yvette Williams NZL 6.24 1956 Greg Bell USA 7.83 Elzbieta Krzeszinska POL 6.35 1960 Ralph Boston USA 8.12 Vera Krepkina URS 6.37 1964 Lynn Davies GBR 8.07 Mary Rand GBR 6.76 1968 Bob Beamon USA 8.90 Viorica Viscopoleanu ROM 6.82 1972 Randy Williams USA 8.24 Heide Rosendahl FRG 6.78 1976 Ami Robinson USA 8.35 Angela Voigt GDR 6.72 1980 Lutz Dombrowski GDR 8.54 Tatyana Kolpakova URS 7.06 1984 Carl Lewis USA 8.54 Anisoara Stanciu-Cusmir ROM 6.96 1988 Carl Lewis USA 8.72 Jackie Joyner-Kersee USA 7.40 1992 Carl Lewis USA 8.67 Heike Drechsier GER 7.14 1996 Carl Lewis USA 8.50 Chioma Ajunwa NGR 7.12 2000 Ivan Pedroso CUB 8.55 Heike Drechsier GER 6.99 2004 Dwight Phillips USA 8.59 Tatyana Lebedeva RUS 7.07 2008 Irving Saladino PAN 8.34 Maurren Maggi BRA 7.04 2012 Greg Rutherford GBR 8.31 Brittney Reese USA 7.12 (a) (i) Calculate the mean distance jumped for the men’s long jump winners from 1948 to 2012 [1 mark] (a) (ii) Calculate the standard deviation of the distances jumped for the men’s long jump winners from 1948 to 2012 [2 marks] Version 0.4 1350/1 5 (a)(iii) An outlier is any value more than two standard deviations from the mean. Using the data relating to the men’s long jump winners from 1948 to 2012, identify any outliers, showing calculations to support your reasoning. [3 marks] (b) In the men’s long jump, the shortest winning jump was by Ellery Clark in 1896. The longest winning jump was in 1968 by Bob Beamon, who jumped 40.2% further than Ellery Clark. How far did Ellery Clark jump? [3 marks] (c) The mean distance jumped for the women’s long jump winners from 1948 to 2012 is 6.80 metres and the standard deviation for this period is 0.411 Use these values and your answers from part (a) to compare the winning distances jumped by men and women in the long jump competition since 1948. [2 marks] Version 0.4 1350/1 6 3 The grouped frequency table below and the histogram opposite show some of the details for the finishing times of the top 50 runners in the 2013 London Marathon. (a) (i) Use the information given to complete the table below. Finishing time Number of runners Frequency density (hours : mins) 2:06 ≤ t < 2:07 300 2:07 ≤ t < 2:10 7 2:10 ≤ t < 2:20 7 70 2:20 ≤ t < 2:25 8 160 2:25 ≤ t < 2:28 10 2:28 ≤ t < 2:30 Total 50 [5 marks] (ii) Complete the histogram opposite [2 marks] (b) (i) Calculate an estimate for the man finishing time of these 50 runners. [3 marks] Version 0.4 1350/1 7 Frequency density 0:00 2:05 2:10 2:15 2:20 2:25 2:30 Time taken (hours and minutes) (b) (ii) The mean finishing time for all the runners in the London Marathon was 4:32 Estimate how many of these 50 runners finished in less than half the mean finishing time. [3 marks] Version 0.4 1350/1 8 4 The Great North Run is a half marathon that takes place in the North East of England every year. The table shows the times taken, to complete the 2010 race, by the 120 members of the ‘all GNR’ club. These are the runners who have taken part every year since the race began. Time, t minutes Number of runners 0 ≤ t < 80 80 ≤ t < 100 100 ≤ t < 120 120 ≤ t < 140 140 ≤ t < 160 160 ≤ t < 180 180 ≤ t < 200 200 ≤ t < 280 280 ≤ t (a) Draw a cumulative frequency diagram on the grid on the opposite page to show the data. You may use the spare column in the table above for any calculation required. [4 marks] (b) Use your cumulative frequency diagram to find: (i) the median; [1 mark] (ii) the lower quartile; [1 mark] (iii) the upper quartile. [1 mark] Version 0.4 1350/1 9 Cumulative frequency Cumulative Time, minutes t Version 0.4 1350/1 10 (c) The times of the ‘all-GNR’ club runners were also recorded in 2005. The data are shown as a box and whisker diagram below. To the graph below, add another box and whisker diagram representing the data for 2010. [3 marks] (d) Use the box and whisker diagrams to compare the performances of the ‘all-GNR’ club runners in 2005 and 2010. You should make two different comments. [2 marks] Comment 1 Comment 2 Version 0.4 1350/1 11 5 The table shows the average life expectancy for people born in 2011 in 11 European countries and 11 African countries. Average life expectancy European countries African countries Country Age Country Age Belarus 71 Angola 39 France 81 Egypt 73 Germany 80 Kenya 59 Italy 82 Niger 53 Latvia 73 Nigeria 48 Moldova 71 South Africa 49 Poland 76 Tanzania 53 Russia 66 Togo 63 Spain 81 Tunisia 75 Sweden 81 Uganda 53 United Kingdom 80 Zimbabwe 50 (a) Show the data on an ordered back-to-back stem and leaf diagram. [5 marks] Average life expectancy European countries African countries Version 0.4 1350/1 12 (b) Use one measure of location and one measure of spread to compare average life expectancy in these European and African countries. Comment on your results. [3 marks] Version 0.4 1350/1 13 6 Freshly cut wood is full of moisture and needs to dry out. George cuts some silver birch logs and weighs one over a period of drying. The table gives the mass of the log whilst drying in the garage. Number of days since being cut 0 3 7 10 14 17 21 Mass (g) 1925 1775 1710 1640 1570 1525 1480 Source: George (a) What was the mass of the log on the day it was cut? [1 mark] Answer ................................................................... g (b) What type of data has George collected? Circle the two correct answers. [2 marks] Primary Secondary Discrete Continuous Qualitative Version 0.4 1350/1 14 7 A flight from Heathrow to Sydney has 400 passengers. Seats on the plane are numbered 01 – 10 for first class 11 – 70 for business class and 71 – 400 for economy class passengers. The airline needs to conduct an in-flight survey to find out what passengers think about the food served on the plane. Interviews will be carried out when all seats are occupied and it is planned to conduct 80 interviews in total. Two alternative sampling methods have been suggested. Method A Select at random 2 passengers from first class 12 passengers from business class 66 passengers from economy class. Method B Choose a simple random sample of 80 different passengers from those on the plane. (a) For Method A. (i) Name the sampling method suggested [1 mark] Answer (ii) Show how the numbers 2, 12 and 66 were calculated for the sample sizes in this case. [2 marks] (b) For Method B, describe how random numbers could be used to select the sample. [3 marks] Version 0.4 1350/1 15 8 The world athletics championships takes place every two years. The men’s 100 metres race is thought by many to be one of the track highlights. In 2009, Usain Bolt of Jamaica set the men’s 100 metres race world record at 9.58 seconds. The table below gives the winning times of the men’s 100 metres race at the world athletics championships since 1991. Year Runner Nationality Time (seconds) 1991 Carl Lewis USA 9.86 1993 Linford Christie Great Britain 9.87 1995 Donovan Bailey Canada 9.97 1997 Maurice Greene USA 9.86 1999 Maurice Greene USA 9.80 2001 Maurice Greene USA 9.82 2003 Kim Collins Saint Kitts and Nevis 10.07 2005 Justin Gatlin USA 9.88 2007 Tyson Gay USA 9.85 2009 Usain Bolt Jamaica 9.58 2011 Yohan Blake Jamaica 9.92 (a) Use the data to calculate: (i) the mean time for the 100 metres race winners; [1 mark] (ii) the standard deviation of the time for the 100 metres race winners.