GCSE STATISTICS 43101F. Unit 1. Mark scheme June Version: 1.0 Final

Transcription

1 GCSE STATISTICS 43101F Unit 1 Mark scheme June 2017 Version: 1.0 Final

2 Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation events which all associates participate in and is the scheme which was used by them in this examination. The standardisation process ensures that the mark scheme covers the students responses to questions and that every associate understands and applies it in the same crect way. As preparation f standardisation each associate analyses a number of students scripts. Alternative answers not already covered by the mark scheme are discussed and legislated f. If, after the standardisation process, associates encounter unusual answers which have not been raised they are required to refer these to the Lead Assessment Writer. It must be stressed that a mark scheme is a wking document, in many cases further developed and expanded on the basis of students reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this mark scheme are available from aqa.g.uk Copyright 2017 AQA and its licenss. All rights reserved. AQA retains the copyright on all its publications. However, registered schools/colleges f AQA are permitted to copy material from this booklet f their own internal use, with the following imptant exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even f internal use within the centre.

3 Glossary f Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus, f GCSE Mathematics papers, marks are awarded under various categies. If a student uses a method which is not explicitly covered by the mark scheme the same principles of marking should be applied. Credit should be given to any valid methods. Examiners should seek advice from their seni examiner if in any doubt. M M dep A B B dep E ft SC [a, b] Method marks are awarded f a crect method which could lead to a crect answer. A method mark dependent on a previous method mark being awarded. Accuracy marks are awarded when following on from a crect method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. A mark that can only be awarded if a previous independent mark has been awarded. Explain marks are awarded f a full and detailed explanation Follow through marks. Marks awarded following a mistake in an earlier step. Special case. Marks awarded within the scheme f a common misinterpretation which has some mathematical wth. Or equivalent. Accept answers that are equivalent. eg, accept 0.5 as well as Accept values between a and b inclusive Accept answers which begin 3.14 eg 3.14, 3.142, Use of brackets It is not necessary to see the bracketed wk to award the marks. 3

4 Examiners should consistently apply the following principles Diagrams Diagrams that have wking on them should be treated like nmal responses. If a diagram has been written on but the crect response is within the answer space, the wk within the answer space should be marked. Wking on diagrams that contradicts wk within the answer space is not to be considered as choice but as wking, and is not, therefe, penalised. Responses which appear to come from increct methods Whenever there is doubt as to whether a candidate has used an increct method to obtain an answer, as a general principle, the benefit of doubt must be given to the candidate. In cases where there is no doubt that the answer has come from increct wking then the candidate should be penalised. Questions which ask candidates to show wking Instructions on marking will be given but usually marks are not awarded to candidates who show no wking. Questions which do not ask candidates to show wking As a general principle, a crect response is awarded full marks. Misread miscopy Candidates often copy values from a question increctly. If the examiner thinks that the candidate has made a genuine misread, then only the accuracy marks (A B marks), up to a maximum of 2 marks are penalised. The method marks can still be awarded. Further wk Once the crect answer has been seen, further wking may be igned unless it gs on to contradict the crect answer. Choice When a choice of answers and/ methods is given, mark each attempt. If both methods are valid then M marks can be awarded but any increct answer method would result in marks being lost. Wk not replaced Erased crossed out wk that is still legible should be marked. Wk replaced Erased crossed out wk that has been replaced is not awarded marks. Premature approximation Rounding off too early can lead to inaccuracy in the final answer. This should be penalised by 1 mark unless instructed otherwise. 4

5 11 1(a) Accept eleven 1(b) 4½ symbols f hse and 2 symbols f rabbit Mark intention B2 f 4½ symbols f hse 2 symbols f rabbit Dog ft ft their pictogram 1(c) Do not accept 14 without Dog Categical 1(d) 5

6 50 2(a) Accept fifty ( o ) = 60 (students) 90( o ) = 30 (students) 135( o ) = 45 (students) 3( o ) = 1 (student) M1 May be on diagram 2(b) 15 A1 SC1 f 105 Check the diagram but answer line takes precedence 45( o ) = 15 (students) M1A1 15 in Go home sect with blank answer line M1A = 8, 120 8, answer 15 M1A = 8, M = 8 on its own M0 6

7 The angle is three times as big 3 45 = = 3 2(c) Packed lunch = 45 (students) and 15 (students) 3 = 45 (students) 45 degrees is one third of 135 degrees Beware of students using the wding from the question, eg Packed lunch is bigger and Go home would fit in to Packed lunch 3 times Height 45 f walk and height 10 f cycle ± 1 mm tolerance Height 30 f car height 35 f bus ft ± 1 mm tolerance ft their height f car Height 30 f car and 2(d) height 35 f bus and ± 1 mm tolerance bars of equal width and gaps between the bars of equal width ft their height f bus = 65 their height f car Igne gap befe the first bar and gap after the last bar 7

8 Car 3(a) 0 3(b) Accept zero, nought, etc Do not accept impossible, no chance, nothing etc Answer of 0, it s impossible M A1 Accept percentage fraction equivalents Do not igne further wking f the A mark 3(c) Igne probability wds with 0.37 unless contradicty , 0.37 and unlikely on the answer line M1A , 0.37 and likely on the answer line M1A out of 1 37 in 100 M1A x 200 M1 6 A1 3(d) 6 out of 200 M1A1 6 Answer 200 M1A0 Beware of , answer 6 M0A0 8

9 It would be quicker f the conduct to collect questionnaires from a sample of passengers Igne irrelevant non-contradicty statements Students do not need to make reference to a sample as it is inferred by the question, however, f points about the census, it must be clear that they are referring to a census 4(a) It s quicker (referring to a sample) It s easier as it takes less time (referring to a sample) There s too many people to give them to everyone It takes a lot of time to give out 240 questionnaires 240 is too many people (implies it would take too long to do) A census would give too much data (only 240 passengers) It takes too long (not clear that that they are referring to a census) It s easier It s cheaper A census is expensive 9

10 You would only have asked passengers in first class Do not allow there might not be 25 passengers in first class 4(b) Only asking one type of person There are people who are not in first class and they re not being asked Needs to ask all classes (not just first class) He s only asking (the first 25) people in first class He s asking people in first class Needs to ask some poer people There are people who do not use first class Any reference to doing a census is, eg They should ask everybody It s not representative of the whole train 10

11 Give each passenger a number from 1 to 240 Give each passenger a different / unique number Use seat numbers to select passengers Use a random number generat (to select 25 passengers) Any reference to a list of everybody a register 4(c) Students cannot just mention random numbers f the second Do not accept the name of a website f the second, students must mention that the website will generate random numbers Give each passenger a number from 1 to 240 and put all of the numbers in a hat and pull out 25 Put the names of all of the passengers in a hat and pick out 25 Put names in a hat and pull out 25 Give each passenger a number 3 5(a) Accept three Section B 5(b) 11

12 5(c) (Section C =) 3 (Section D =) 7 The values 3 and 7 must be given in the crect der Accept three and seven in the crect der Any suitable hypothesis relating high blood pressure and the number of fizzy drinks consumed eg The me fizzy drinks you consume, the higher your blood pressure 6(a) Do not allow questions Students cannot just restate the question, eg There is a link between high blood pressure and how many fizzy drinks a person drinks is A person s blood pressure increases by how many fizzy drinks they drink (not stating me less fizzy drinks) Fizzy drinks cause higher blood pressure A suitable question with a time frame 3 me non-overlapping boxes 3 me exhaustive boxes 6(b) Allow 6+ to mean me than 6 6 me etc Students cannot sce full marks if increct inequalities are used but mark intention f up to B2 Igne boxes labelled as other, me, less, don t know 47 6(c) Accept fty seven 12

13 45 to 54 6(d) Any crect similarity eg The percentage of men and women with high blood pressure in the 65 and over categy is the same The 25 to 34 categy has the lowest percentage f both men and women 65 and older are the same percentage 6(e) As men and women get older a higher percentage get high blood pressure 65 and older are the same number 65 and older are the same As men and women get older me get high blood pressure (do not know exact numbers) They are all the same age groups Blood pressure increases with age (not necessarily) As you get older your blood pressure increases (not necessarily) 13

14 7(a) Easier to control (extraneous) variables Easier to control the running speed Easier to measure (the speed / heart rate) The weather may affect them / the experiment / perfmance / heart rate / running speed / the track / Jane s equipment To control the experiment / the conditions / the variables Athletes can be monited me easily There are less facts that interrupt her experiment Recd me accurately / be me accurate Might be other people on the track Easier to do in the gym (me infmation is needed) Positive 7(b) [139, 141] 7(c) 14

15 Fourth task: Any reference made to making calculations drawing diagrams Last task: Any reference made to a conclusion 7(d) Any reference to measures of location measures of spread, graphs charts is the first Any reference to making interpretations, interpreting graphs, analysing evaluating results, checking if the hypothesis is crect is the second Allow the fourth task to be a conclusion if the last task is blank / irrelevant eg Fourth task: Write a conclusion Last task: Check answers Allow the last task to be a reference to making calculations drawing diagrams if the fourth task is blank / irrelevant eg Fourth task: Check the data Last task: Calculate averages Fourth task: Plot data Last task: Compare results Fourth task: Plot data Last task: Compare Students cannot sce if the tasks are the wrong way round: eg Fourth task: Analyse the results Last task: Calculate some averages 15

16 (2) 8(a)(i) 52(.2)% Igne further wking when changing fmat simplifying the fraction, eg changing fraction to decimal etc; but not ratio Igne wds such as likely, evens etc % 17.6% 8(a)(ii) Igne further wking when changing fmat simplifying the fraction, eg changing fraction to decimal etc; but not ratio Igne wds such as likely, evens etc Accept % with crect wking, eg = % (with no wking) 16

17 Alternative method (.) 0.2(0) 2350 M1 Accept equivalent fractions and percentages (03 ) 1650 Ticks No and 0.199(.) 0.2(0) and 0.27(03 ) A1 Accept equivalent percentages Accept equivalent fractions expressed with the same denominat. 8(b) Alternative method ( 1650) ( 2350) 1650 Ticks No and [328.35, 330] [634.5, ] M1 A1 Accept equivalent fractions, decimals and percentages If both boxes are blank, no can be implied by a crect statement in wds F the A mark students must be able to make a comparison (ie both answers must be decimals, both answers must be percentages, both fractions must have the same denominat) 9(a) (0)68, 408, 163, 584, 538, (0)53, 436, (0)11 B3 Values can be written in any der 6 7 crect values B2 4 5 crect values 17

18 The sample (of 8 pupils) may not have a very good mix of ages/ gender/ethnicity etc The pupils chosen may not want to be on the poster The pupils chosen may not be suitable f appearing on the poster 9(b) Condone will not within a statement Igne irrelevant non-contradicty statements The head teacher should choose sensible pupils She should choose a mix of pupils One of the students may be absent They may not be comftable with it It may not be representative / It will not produce a good range Some of the numbers are bigger than 600 They may choose the same person twice Butter 10(a) 18

19 Ticks yes and states that all of the index numbers are above 100 Accept any indication, including a cross, in place of a tick If both boxes are blank, yes can be implied by a crect reason 10(b) Condone Yes, none are less than 100 Yes, they all went up by 30% me Yes, the lowest (index) number is 130 which is above 100 Yes, the base number of 100 is lower (than all of the items) Yes, the base number is lower (than all of the items) Yes, the lowest (index) number is 130 Yes, the base number is 100 Yes, they all went up No, (any comment) M (c) A1 Crect money notation Condone 0.52p 0.52 M1A0 19

20 20 t < 30 11(a) Condone 20 < t < < t t to (b) (23, 54, 90,) 96, 100 All 5 cumulative frequencies plotted at crect heights All 5 cumulative frequencies plotted at upper class boundary All 5 cumulative frequency plots joined with curve lines ft ft ± 1 square tolerance ft their part (b) provided that cumulative frequency values are increasing 11(c) If their cumulative frequency graph is not increasing then The graph ds not need to be drawn down to the hizontal axis, ie the point (0, 0) ds not need to be plotted Crect heights can be anywhere within the group f the first Igne graph befe t = 10 and after t = 50 Bars drawn as well as crect graph 20

21 Reads across from M1 ± ½ square tolerance 11(d) [18.7, 19.0] A1ft ft their increasing graph Igne bars, ft their increasing curve polygon Alternative method 1 (½ 36) M1 28 A1 Alternative method 2 11(e) Reads up from 25 minutes and deducts this value from 100 M1 ± ½ square tolerance 28 A1ft ft their increasing graph Igne bars, ft their increasing curve polygon 21

22 15 12(a) Accept fifteen th piece of data M1 45 A1 12(b) Beware, the range is 45 eg 65 20, answer 45 M0A0 Attempt at identifying the 12 th piece of data on the diagram ( from a crectly dered list) eg crossing out the first 11 crossing out the last 11 crossing out the first and last 11 Circling of the 5 on the fties row (allow any indication) Answer 5 with no wking M1 M1 M0 22

23 th piece of data M1 18 th piece of data 12(c) (Lower quartile =) 32 (Upper quartile =) 53 A1 A1 If students have not used the answer lines then their answers must be clearly labelled in the wking to gain full marks Attempt at finding the 6 th piece of data the 18 th piece of data on the diagram ( from a crectly dered list) is M1 Lower quartile = 53 Upper quartile = 32 Circling of the 2 on the thirties row Circling of the 3 on the fifties row (allow any indication) M1A1A0 M1 23

24 Median at 45 ft ± ½ square tolerance ft their median from part (b) Lower quartile at 32 and upper quartile at 53 ft ± ½ square tolerance ft their lower quartile and their upper quartile from part (c) 12(d) Minimum at 20 and maximum at 65 and box and whiskers drawn with median between the quartiles ± ½ square tolerance 1 me hizontal lines missing is maximum B2 Condone hizontal line drawn through the box 24

25 Class 11A had higher marks on average Class 11B had a wider variety of marks ft ft ft their box plot from part (d) ft their box plot from part (d) 12(e) Students must identify which is which The context of the question must be mentioned, eg mark, sces, results, etc Allow they to mean the results, eg They were better on average f Class 11A Class 11A has a higher average mark/sce/result (than Class 11B) Class 11A has a higher median mark/sce/result (than Class 11B) Class 11A has a higher median/average (than Class 11B) Class 11B has a wider range of marks/sces/results (than Class 11A) Class 11A s marks were me consistent (than Class 11B) Class 11A was me consistent (than Class 11B) Class 11B has a bigger range (than Class 11A) The range of Class 11A is 45, the range of Class 11B is 55 25

26 Fully crect tree diagram, ie B2 Accept decimals, percentages equivalent fractions f crect probabilities in any pair of branches 13(a) eg P(Ball 1 Red) = their 10 3 their M1 A1ft their P(Red 1) their P(Red 2) ft their probabilities from part (a) providing they are (0, 1) Check diagram f wking 13(b) Igne further wking when changing fmat simplifying their fraction, eg changing fraction to decimal etc; but not ratio 9 eg = 0.9 M1A = = 9 : 100 M1A = 9 : 100 M1A = 100 (not a change of fmat) M1A0 26

27 Alternative method their M1 their 10 3 their 10 7 their 10 3 their their 10 3 M1dep 21 eg their (c) A1ft ft their probabilities from part (a) providing they are (0, 1) Alternative method their M their their M1dep A1ft ft their probabilities from (a) and (b) provided all probabilities are in the range (0, 1) Check diagram f wking Igne further wking when changing fmat simplifying their fraction, eg changing fraction to decimal etc; but not ratio 27

28 (All) people living in the village 14(a) The people in the town People in the village near the facty (BOD) The population of the village (The) villagers Adults in the village People living near the facty (The) village 28

29 Less time consuming f Vanda / quick to send out (Me) convenient to fill in / send out People can fill in the questionnaire without influence from the interviewer Less embarrassing (f the person completing the questionnaire) People may be me truthful (on a postal questionnaire) 14(b) It s cheap / less expensive needs a reason to suppt the statement to gain The questionnaires can easily be sent to lots of people You can do it in your own time It s easy to do because you can send lots out at the same time Easier to collect / collate / process It s easy/easier (me infmation is needed) Less biased (me infmation is needed) Me accurate (me infmation is needed) It s quick/quicker (me infmation is needed) 29

30 It is a leading question There is no disagree option eg The question tries to suggest a particular answer eg The response boxes do not cover all the possible responses 14(c) Condone reasons written in reverse der in one statement Igne irrelevant non-contradicty statements Criticism of question: It s a biased question needs a reason to suppt the statement to gain Questions should not begin Don t you agree that Accept a rewded question that is not leading People feel they must agree They are using emotive wds like beautiful/disgraceful It s fceful It s not neutral (needs clarification) The question is too demanding (ambiguous) The question makes you feel uncomftable Criticism of response section: It s not exhaustive Not enough response boxes 30