GCSE Statistics F: Foundation Tier Mark scheme F June Version: 1.0 Final

Transcription

1 GCSE Statistics 43101F: Foundation Tier Mark scheme 43101F June 2016 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 2016 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 of 27

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. Continental notation Accept a comma used instead of a decimal point (f example, in measurements currency), provided that it is clear to the examiner that the candidate intended it to be a decimal point. 4 of 27

5 Unlikely B3 f 4 crect 1 Evens Certain B4 B2 f 3 crect f 1 2 crect Impossible Likely 2(a) 12 2(b) ( ) 5 M1 Allow one err in the addition 11 A1 SC1 f Increases 2(c) Circled indicated Decreases 2(d) Circled indicated 5 of 27

6 3(a) Sight of one five bar gate Tallies 3, 10, 7 and 4 All 4 frequencies crect ft ft their tallies Heights of all 4 bars crect B2ft ft f 2 3 heights crect ft their frequency column, their tallies if their frequency column is blank ± 1 mm tolerance 3(b) All bars of equal width and gaps of equal width Mark intention, need not be ruled Condone no gap befe the first bar 4(a) 2 4(b) 6 6 of 27

7 6 4(c) M1 6 ( 100) 20 n ( 100) A1 n must be an integer and 1 n 19 Denominat 6, eg 20 6 (unless recovered) M0A0 7 of 27

8 (Crect key) 2 Crect alignment of circles ft Mark intention, ie approximate same size circles with Hatchback longer than Estate, and their rows lined up vertically ft their key unless 1 5 circles f Hatchback and 4(d) 1 1 circles f Saloon 2 and 1 circle f Spts 2 B2ft ft f any 1 2 crect rows ft their key unless 1 Half circles can be any ientation Allow open closed half circles Their circles must be consistent in size but do not have to be the same size as Estate Condone any shading, patterns etc Key = 1 is no marks 8 of 27

9 It s not numerical data It s qualitative data It s categical data 4(e) Igne any irrelevant, non-contradicty statements even if increct It s wds (not numbers) It s not the right type of data It s not the right type 5(a) Stem 10, 11, 12, 13 Leaves fully crect B2ft ft f 2 3 crect rows ft f crect undered leaves Accept Stem 13, 12, 11, 10 ft their stem if their stem is not in the crect der 9 of 27

10 5(b) 8.5 th 8 th and 9 th identified 117 and 119 identified 7 and 9 identified M1 118 A1 8 th and 9 th values may be identified on the diagram in an dered list 10 of 27

11 Alternative method 1 No and f 3 (are over 130) 3 (are over 130) B2 and (one quarter =) 4 (one quarter =) 4 Alternative method 2 5(c) No and 3 16 and 4 16 No and 0.18(75) and 0.25 B2 f 3 16 ( 1 4 =) (75) 18(.75)(%) No and 18(.75)(%) and 25(%) Accept 0.19 f , accept 19(%) f 18.75(%) Igne irrelevant statements, any relevant statements that are non-contradicty If a box is not ticked no equivalent can be in the text There are 16 children, only 3 of them are over 130 so if it was one quarter of the class there would only be 12 students B2 11 of 27

12 She is only asking people from one supermarket She is only asking people on one Monday mning Note, two different reasons can be in one statement Igne irrelevant increct statements unless contradicty 6(a) Only her local supermarket (implies only one supermarket) First Better to ask 20 people each day (implies only one day) Second Accept she is only asking people in a mning Accept she is only asking people on Monday Not everyone gs shopping then / at that time Not a variety of people as children would be at school then Second Second Second 20 isn t a large enough sample size 12 of 27

13 A suitable question with a time frame Allow per visit 3 me exhaustive boxes with no overlaps where at least 1 box accepts a range B2 f 3 me exhaustive boxes f 3 me boxes, no overlaps If inequality signs are used they must be crect f B2 f the response section, f condone po inequality notation, mark intention F the response section f B2, condone answer in just pounds, eg is wth B2 6(b) F the response section f B2 one of the boxes must accept a range, eg 1-5 Less than 5, me than 10, etc are not acceptable f the range box F the response section f B2, condone the use of wds such as less than me than, nothing, none F the response section f B2, condone a don t know box and a nothing box F the response section f B2, do not allow the use of the wd other Other cannot be used to fulfil the exhaustive mark 0 and don t know are not overlapping Allow 10+ to mean 10 me, me than 10, etc If no units are given assume in pounds 13 of 27

14 Any suitable fact 6(c) Any reference to family size, number of people you are buying f, etc Any reference to the number of times somebody gs shopping the number of items purchased Any reference to budget income payday Any reference to deals/offers/discounts Any reference to how expensive the supermarket is Any reference to shopping in non-supermarkets, eg if people buy from the local butcher, the local baker, the fish stall on the market, etc Any reference to transpt arrangements, eg if they have a car Any reference to one-off purchases / buying something unusual Distance to supermarket How old somebody is (unless qualified) Price 7(a) (Boys) Keyboard and (Girls) Recder 14 of 27

15 Any crect different comparison, eg A higher proption of boys played Drum kit than girls The proption of girls playing Violin is about twice the proption of boys The least popular f boys is flute, the least popular f girls is drums Me boys played Electric guitar than Violin, but it was the other way round f girls Do not accept statements that simply state percentages without giving a comparison It must be clear which instrument(s) the candidate is referring to 7(b) Overall, a greater proption of girls played instruments than boys Given that the numbers of boys and girls should be approximately equal, condone comparisons such as Me girls play the piano than boys (Over) twice the number of girls play flute than boys Girls tend to play me instruments than boys A similar percentage of boys and girls play keyboard / piano / classical guitar Condone statements such as Boys play the drums a lot me than girls Only 8% of boys play violin but 15% of girls play violin comparison here) ( only implies a 8% of boys play violin, 15% of girls play violin 15 of 27

16 7(c) Ticks No and gives a suitable reason, eg The categies are not mutually exclusive Some children play me than one instrument Someone who plays the piano may also play the keyboard No, the column dsn t add up to 100 No, the actual percentage is 61/ = 38% 16 of 27

17 7(d) Bars drawn up to 100% f each age group bars should have equal widths and should be separated ± ½ square tolerance One bar accurately divided ± ½ square tolerance Second bar accurately divided and both bars shaded ± ½ square tolerance Accept equivalent labelling of parts SC1 f an accurate and crectly shaded multiple bar chart drawn with equal width bars provided there is a gap separating the bars f ages 5-7 from those f 8-13 F the third allow inconsistent der of shading so long as the proptions are crect and the shading matches the key 17 of 27

18 (a) B2 f 9 10 entries filled in crectly B2ft f denominat 25 ft f numerat 7 ft from part (a) f their numerat only 8(b) 7 F B2 igne fw after unless the answer is no longer a probability, eg 25 7 = 0.16 is B = 3.57 is 25 7 F B2 igne wds with unless contradicty of 27

19 60 total Small 30 total Cola All 9 remaining values crect B3ft B2ft 5-8 remaining values crect ft 2-4 remaining values crect 8(c) Fruit juice Cola Lemonade Total Small Large Total Additional Guidance ft their 60 f total Small and their 30 f total Cola, do not allow negative decimal answers million 9(a) Do not allow m 6.7 mil million 9(b) Do not allow 6 6 m 6 mil 9(c) Due to rounding 19 of 27

20 Manufacturing 9(d) Condone po spelling 12 (million) (e) M (million) A1 SC1 f digits 252 Digits 252 means , 2520, 0.252, etc f 21 and no other value from the Type of job table used, so = 35 is f example 15 5 sight of 5 1 M1 10(a) 3 A1 Likely equivalents of 5 1 include 10 2, 15 3, % 6, 6, 3 3, 6, 6 6, 3, 6 12, 3 6 : 6 : 3 etc M1 20 of 27

21 10(b) L S S L B L L L S S S S L L S B2 f 12 additional simulated values filled in crectly. 10(c) (S) 7 (L) 7 (B) 1 ft Follow through from their part (b) In this part you must follow through from part (b) Do not accept tallies unless the total is given Fewer baskets (than expected) Me small/ large trolleys (than expected) ft Igne any numbers saying how many fewer baskets there were than expected etc Follow through from previous parts 10(d) The number of people choosing a small trolley is not twice the number choosing a basket Only 1 B (should be 3) He had 1 B Fewer people choose baskets than (small/large) trolleys ft totals tallies from their part (c), if part (c) is blank ft their part (b) 21 of 27

22 There are equal numbers of small trolleys and large trolleys ft Follow through from previous parts Additional Guidance 10(e) Fewer people choose baskets than (small/large) trolleys If part (c) contains an err, follow through can be given from part (c) if statements are true f their results eg 6S, 8L, 1B There are similar numbers of small trolleys and large trolleys There are 6 small trolleys which is as expected Number of people asked is 15 ft totals tallies from their part (c), if part (c) is blank ft their part (b) ft ft If part c is increct, eg 6 small trolleys and 8 large trolleys, if a mark has been given in part (d) f noting a difference in those numbers, do not allow a mark in part (e) f noting they are similar 11(a) 30 11(b) M1 60 A1 SC (c) Convenience Opptunity 22 of 27

23 Alternative method (25) 40.1(25%) 2.492( ) 2.5 M1 11(d) Alt their 0.401(25) their 2.492( ) M1dep 16 A1 SC2 f SC1 f Alternative method M (d) Alt 2 of their their M1dep 16 A1 SC2 f SC1 f from no clearly increct wking M1M1A1 23 of 27

24 12(a) B To see the range of answers people give To see if the questionnaire wks/ questions are clear To see if there are any errs/ problems To see how many people respond To test the questions To see if it is effective (it refers to the questionnaire) 12(b) To make sure that the questions give him the infmation/data/answers that he wants To see if his questionnaire would give the right answers To see how big the sample size needs to be To test the data collection method To see if it is wthwhile to carry out the (full) study To see if the answers are right It s a test run (attempt at a definition, not a reason) To check results will be accurate/reliable (not specific enough) To see if questions are biased To get better results (detail lacking as to why results will be better) To see if he should open the stall 24 of 27

25 A closed question has response boxes/ a choice of answers An open question ds not have response boxes 12(c)(i) Any crect difference mentioned is unless accompanied by a clearly increct contradicty statement, eg An open question allows you to write in your own wds, a closed question is yes/no (crect statement about open questions) A closed question has response boxes, an open question allows you to give an opinion (crect statement about closed questions) A closed question is multiple choice, an open question is yes/no (crect statement about closed questions, but statement about open questions is clearly increct) Closed questions have pre-chosen answers such as Yes/No Closed questions are multiple choice / have set answers Closed questions have a response section (unless qualified) Closed questions have only one sht answer / a specific answer Closed questions are answered either Yes/No A closed question is one where there are only a few answers 25 of 27

26 Two different reasons: Ease at answering/collecting Easier to answer / collect the data / carry out a survey Quicker to answer / collect the data Response options can help clarify meaning of questions 12(c)(ii) Ease of Analysis Makes analysis of data simpler/quicker/ cheaper Limits possible answers / people stick to the point Problems due to po handwriting lessened Easier to make comparisons Easier to graph B2 f each advantage Advantages should come from different categies Response Rate Improves response rate Less likely to miss out questions Additional Guidance Note, two different reasons can be in one statement Igne irrelevant increct statements unless contradicty People are me willing to tell you infmation Smaller amount of data to wk with (lacks detail) It s quicker / easier (unless they explain why) Answers to the questionnaire are me accurate/reliable is given explaining why) (unless me detail 26 of 27

27 12(d) Include a pre-paid envelope / collect questionnaires in person Give an incentive to answer (eg prize draw, donation to charity) Interview people (face-to-face, by telephone) Make the questionnaire shter Allow people to answer online Sending a reminder Additional Guidance Give a deadline f returning the questionnaire Interview people in the market Give it out to people using the market 27 of 27