EDEXCEL FUNCTIONAL SKILLS PILOT Maths Level 2 Test your skills Chapters 6 and 7 Investigating election statistics Applying skills in: handling data probability Answer all questions in this task. Write your answers in the spaces provided. Where you see this sign you must show how you get your answers as marks may be awarded for your working out. You may use a calculator. Pearson Education 2009 Functional Maths Level 2 Chapters 6 7 Test page 1 Draft for Pilot FS-Ma-L2test-Cha6-7.indd 1 8/5/09 11:50:47
Your task is to investigate how the electorate voted in the four different constituencies in Manchester in the 2005 General Election. 1 The column labelled Electorate 2005, lists the number of people who were eligible to vote in each constituency. The column labelled Result 2005, lists the party that won in each constituency. Constituency Manchester Blackley Manchester Central Manchester Gorton Manchester Withington Electorate Result Labour Conservative Liberal Democrat Large other 2005 2005 2005 2005 2005 2005 60 299 Labour 17 187 3690 5160 UK 1554 Independence 69 656 Labour 16 993 2504 7217 Green 1292 64 696 Labour 15 480 2848 9672 UK Independence 783 67 781 Liberal 15 205 3919 15 872 Green 1595 Democrat a) How many more people voted Labour than Conservative in Manchester Blackley? Number of people b) What was the range in the number of electorate in the different constituencies? Range c) What was the median number of people who voted Conservative? people Median d) What was the mean number of people who voted Liberal Democrat? people Mean e) What percentage of the electorate voted Labour in Manchester Gorton? people % Pearson Education 2009 Functional Maths Level 2 Chapters 6 7 Test page 2 Draft for Pilot FS-Ma-L2test-Cha6-7.indd 2 8/5/09 11:50:49
Investigating election statistics 6 7 f) Which constituency had the smallest percentage difference in votes between the parties that came first and second? Use the box below to show clearly how you get your answer. Constituency g) How many of the electorate did not vote in Manchester Central in the 2005 General Election? people 2 The table shows the results of the voting in Manchester Central. Political party Number of votes Rounded to the nearest 100 Labour 16 993 Conservative 2504 Liberal Democrat 7217 Green 1292 a) Complete the table for the numbers who voted for the major political parties, rounded to the nearest 100. b) Use your rounded figures to draw a bar chart to compare how the electorate voted in Manchester Central. 18000 Voting in Manchester Central in the 2005 General Election 16000 14000 12000 Number of votes 10000 8000 6000 4000 2000 0 Political party Pearson Education 2009 Functional Maths Level 2 Chapters 6 7 Test page 3 Draft for Pilot FS-Ma-L2test-Cha6-7.indd 3 8/5/09 11:50:50
3 A Mori poll before the election resulted in the following probabilities for how the electorate would vote in the General Election for 2005: Labour Conservative Liberal Democrat Others 37% 33% 22% a) What did the Mori poll find for the probability the electorate would vote for Others? Probability vote Others b) What was the probability that the voters would not vote Labour? % Probability not vote Labour c) Write as a decimal the probability that people would vote Liberal Democrat. % Probability vote Liberal Democrat 4 The total number of people who voted in the General Election in 2005 was 27 132 327. The Mori poll predicted that 37% would vote Labour. a) How many people did the Mori poll predict would vote Labour? Number of people The actual number that voted Labour in the 2005 General Election was 9 563 067. Percentage error = actual number of voters predicted numbers of voters actual number of voters 100 b) Calculate the percentage error in the number of people predicted to vote Labour by the Mori poll. Percentage error % Pearson Education 2009 Functional Maths Level 2 Chapters 6 7 Test page 4 Draft for Pilot FS-Ma-L2test-Cha6-7.indd 4 8/5/09 11:50:51
Investigating election statistics 6 7 5 The pie charts show the proportion of the vote in the General Elections in 2001 and 2005. Voting in the General Election 2001 Voting in the General Election 2005 Other Other Liberal Democrat Labour Liberal Democrat Labour Conservative Conservative Is it true to say that: The pie charts show that more people voted Labour in 2001 than in 2005? Give reasons for your answer. 6 A group of students conduct their own survey about how people will vote in the next local election. They surveyed people who were in the main shopping centre at 9 o clock one Monday morning. a) Give two reasons why this may not give an accurate representation of the way people will vote in the local election. 1.... 2.... b) What could the students do to work out a more accurate representation of the way people will vote in a general election? Pearson Education 2009 Functional Maths Level 2 Chapters 6 7 Test page 5 Draft for Pilot FS-Ma-L2test-Cha6-7.indd 5 8/5/09 11:50:52
Solutions 1a) 17 187 voted Labour and 3690 voted Conservative in Manchester Blackley. 17 187 3690 = 13 497 so 13 497 more people voted Labour than Conservative. 1b) The range is the highest value lowest value. The range in the number of electorate is: 69 656 60 299 = 9357 1c) To find the median number of people who voted Liberal Democrat, first write the number of voters in order of size: 2504, 2848, 3690, 3919. The median is the middle value. As there are an even number of values, the median is the mean of the middle two values. 2848 + 3690 Median = = 6538 2 2 = 3269 1d) To find the mean you need to add all the values together and divide by 4. 5160 + 7217 + 9672 + 15 872 39 926 Mean = = = 9981.5 4 4 The mean number of people should be a whole number, either 99 815 or 99 816 is acceptable. 1e) In Manchester Gorton 15 480 out of 64 696 voted Labour. As a percentage this is: 100 = 23.9 to one decimal place 15 480 64 696 1f) M/c Blackley, Labour won by 17 187 5160 = 12 027 votes M/c Central, Labour won by 16 993 7217 = 9776 votes M/c Gorton, Labour won by 15 480 9672 = 5808 votes M/c Withington, Liberal Democrat won by 15 872 15 205 = 667 votes As a percentage this is 667 100 = 0.98% to two decimal places 67781 1g) The number in the Other category was 69 656 (16 993 + 2504 + 7217 + 1292) 69 656 28 006 = 41 650 So 41 650 of the electorate in Manchester Central did not vote in the 2005 General Election. Answer 13 497 9357 3269 99 815 or 99 816 23.9% In Manchester Withington Liberal Democrats beat Labour by 0.98% 41 650 2a) Political party Number of votes Rounded to the nearest 100 17 000 2500 Labour 16 993 17 000 7200 Conservative 2504 2500 1300 Liberal Democrat 7217 7200 Green 1292 1300 Pearson Education 2009 Functional Maths Level 2 Chapters 6 7 Test page 6 Draft for Pilot FS-Ma-L2test-Cha6-7.indd 6 8/5/09 11:50:53
Investigating election statistics 6 7 2b) Voting in Manchester Central in the 2005 General Election Bars of equal width and gaps 18000 between the bars. Bars of 16000 correct height and correctly 14000 labelled. 12000 Number of votes 10000 8000 6000 4000 2000 3a) The sum of the probabilities of all possible outcomes = 1 or 100%. So, probability of Other = 100 (37 + 33 + 22) = 100 92 = 8%. 3b) prob(event happens) + prob(event doesn t happen) = 1 or 100% prob(vote Labour) = 37%, so prob(not vote Labour) = 100 37 = 63% 8% 63% 3c) prob(vote Liberal Democrat) = 22% = 0.22 0.22 4a) Mori poll predicted 37% would vote Labour. 37 100 = 27 132 327 = 10 038 960.99 = 10 038 961 to the 100 nearest whole number. This value could be taken to imply that not the number of Labour voters was less than 10 038 961 so 10 038 960 should be the correct answer. 4b) Using 10 038 960 10 038 960 9 563 067 % error = 100 9 563 067 100 = 4.98% to 3 sig figs 475 893 9 563 067 Using 10 038 961 10038961 9563067 % error = 100 9563067 100 = 4.98% to 3 sig figs 475894 9563067 0 Labour Conservative Polictical party Liberal Democrat Green 10 038 960 or 10 038 961 is acceptable Difference of 1 makes no difference to answer. 4.98% Note that when degree of accuracy is not given, you should work, in general, to 3 significant figures Pearson Education 2009 Functional Maths Level 2 Chapters 6 7 Test page 7 Draft for Pilot FS-Ma-L2test-Cha6-7.indd 7 8/5/09 11:50:54
5 No. Comparing the angles for the individual sectors, a larger angle represents the Labour vote in 2001 than 2005. It is tempting to say that this implies more people voted Labour in 2001 than in 2005. However, all you can say is that a larger proportion of the voters voted Labour in 2001. There could have been a larger number of voters in 2005 so that a smaller angle could still represent a larger number of people. 6a) Any two similar to: If they ask people who are in the main shopping centre at 9 o clock one Monday morning they will not include people who are at work at this time. Students who are of voting age are also unlikely to be included. Asking people at 9 o clock on Monday morning will not give a representative sample of people. Different times of the day/week should be included. The survey is also focused on one location and will not include people who use the local shops, rather than the main shopping centre. 6b) For example, could choose names at random from the local telephone books and telephone them to ask their opinion. Key points to highlight: pie charts represent the proportion of the whole and you cannot identify the numbers involved without being given more information. A larger angle does not imply a larger number of voters. Key points to focus on: location target audience time frame Any reasonable response based on relevant identification in 6a) is acceptable Pearson Education 2009 Functional Maths Level 2 Chapters 6 7 Test page 8 Draft for Pilot FS-Ma-L2test-Cha6-7.indd 8 8/5/09 11:50:54