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Issue 3 February 2010 Specification Edexcel GCSE in Statistics (2ST01) Welcome to the Edexcel GCSE in Statistics Specification Issue 2 As a result of feedback from centres we have made changes. This version is Issue 2 and key changes are indicated by a sideline. This specification has been written to help all your students succeed. It has been designed in sections to help you find your way around the content. • The ‘specification at a glance’ pages give a clear and simple summary of the qualification, including the assessment arrangements, so you have all the important information in one handy place. • Section A features the unit content. Written by our team of teachers and examiners, it is presented in a style that allows you to quickly and easily see what you need to teach and students need to learn. • Section B provides clear and concise information about the assessment, including guidance about controlled assessment. You will also find all the practical information you need on making entries and assessing your students. • Section C includes information on the full range of support, services and training available to help you plan and deliver the course. You will find information on the range of teaching and learning material that will help you implement the course effectively, and a summary of all our services designed to support you every step of the way. However, that’s not all. The Edexcel GCSE in Statistics qualification will be supported better than ever before. Keep up to date with the latest news and services available by visiting our website: www.edexcel.com/gcse2009 Introduction The Edexcel GCSE in Statistics is designed for use in schools and colleges. It is part of a suite of *&6(TXDOL¿FDWLRQVRIIHUHGE\(GH[FHO About this specification 7KLVVSHFL¿FDWLRQ N complements the Edexcel GCSE in Mathematics N LVVXLWDEOHIRUHLWKHURQH\HDURUWZR\HDUVWXG\ N LVEDVHGRQJRRGSUDFWLFHLQVWDWLVWLFV N HPSKDVLVHVWKHWKHRUHWLFDOSUDFWLFDODQGDSSOLHGQDWXUHRIWKHVXEMHFW N LVVXLWDEOHIRUFURVVFXUULFXODUVWXGLHVDQGDFWLYLWLHV N SURYLGHVDEDFNJURXQGIRUWKHVWXG\RIVWDWLVWLFVEH\RQG*&6(OHYHO N LVVXSSRUWHGE\ { controlled assessment guidance and support { DFRXUVHWH[WERRNZULWWHQE\WKHVHQLRUH[DPLQLQJWHDP { SURIHVVLRQDOGHYHORSPHQWDQGWUDLQLQJHYHQWV { Edexcel ResultsPlus { Exam Wizard { DQHVSHF { data handling tool. )RUPRUHLQIRUPDWLRQSOHDVHVHHRXUZHEVLWHZZZHGH[FHOFRP Key subject aims 7KLVVSHFL¿FDWLRQ N DFWLYHO\HQJDJHVVWXGHQWVLQDQDFFHVVLEOHDQGUHOHYDQWGLVFLSOLQH N KHOSVVWXGHQWVDFTXLUHNQRZOHGJHDQGXQGHUVWDQGLQJRIVWDWLVWLFDOWHFKQLTXHVDQGFRQFHSWV N HQFRXUDJHVVWDWLVWLFDOSUREOHPVROYLQJ N GHYHORSVWXGHQWXQGHUVWDQGLQJRIWKHLPSRUWDQFHDQGOLPLWDWLRQVRIVWDWLVWLFV N supports students in their progression through statistics and other related disciplines. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 1 Contents A Specification at a glance 4 Qualification content 6 Knowledge and understanding 6 Skills 7 Specification content B 8 Foundation Tier 10 Higher Tier 25 Assessment 45 Assessment summary 45 Summary table of assessment 45 Assessment Objectives and weightings 46 Relationship of assessment Objectives to assessments 46 External assessment 47 Examination papers 1F and 1H 47 Calculators 48 Entering your students for assessment 48 Student entry 48 Forbidden combinations and Classification Code 49 Access arrangements and special requirements 49 Disability Discrimination Act (DDA) 49 Controlled assessment 2 50 Summary of conditions for controlled assessment 50 Internal standardisation 55 Authentication 55 Further information 55 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Contents Assessing your students 56 Awarding and reporting 56 Unit results 57 Qualification results 57 Resitting of units 57 Language of assessment 58 Quality of written communication 58 Stretch and challenge 58 Malpractice and plagiarism 58 Student recruitment 59 Progression 59 Previous knowledge 60 Grade descriptions 61 Resources, support and training 64 Edexcel resources 64 Edexcel publications 64 Endorsed resources 65 Edexcel support services 66 Training 67 D Appendices 68 C Appendix 1 Key skills 69 Appendix 2 Wider curriculum 70 Appendix 3 Codes 72 Appendix 4 Formulae sheets 73 Appendix 5 Controlled assessment 76 Appendix 6 Controlled assessment marking criteria 81 Appendix 7 Student Record Form 87 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 3 Specification at a glance 7KH(GH[FHO*&6(LQ6WDWLVWLFVLVDVVHVVHGWKURXJK • DZULWWHQSDSHU • DQLQWHUQDODVVHVVPHQWZLWKFRQWUROOHGFRQGLWLRQV Unit 1 *Unit codes: 5ST1F/5ST1H • ([WHUQDOO\DVVHVVHG 75% of the total GCSE • $YDLODELOLW\-XQHVHULHV • )LUVWDVVHVVPHQW-XQH Overview of content • Planning and data collection • 3URFHVVLQJUHSUHVHQWLQJDQGDQDO\VLQJGDWD • Reasoning, interpreting and discussing results • 3UREDELOLW\ Overview of assessment Foundation Tier (targeting grades G–C) • 2QHZULWWHQSDSHUODVWLQJKRXUPLQXWHV • PDUNVLQWRWDO • Consists of questions in familiar and unfamiliar contexts • &RQWDLQVVKRUWDQVZHUDQGORQJDQVZHUTXHVWLRQV • 4XHVWLRQVVHWRQVWDQGDUGVWDWLVWLFDOWHFKQLTXHVGLDJUDPVDQGSUREDELOLW\ • 4XHVWLRQVZKLFKJLYHWKHVWXGHQWWKHRSSRUWXQLW\WRDQDO\VHZULWWHQDQGVWDWLVWLFDOHYLGHQFH Higher Tier (targeting grades D–A*) • 2QHZULWWHQSDSHUODVWLQJKRXUV • PDUNVLQWRWDO • Consists of questions in familiar and unfamiliar contexts • &RQWDLQVVKRUWDQVZHUDQGORQJDQVZHUTXHVWLRQV • 4XHVWLRQVVHWRQVWDQGDUGVWDWLVWLFDOWHFKQLTXHVGLDJUDPVDQGSUREDELOLW\ • 4XHVWLRQVZKLFKJLYHWKHVWXGHQWWKHRSSRUWXQLW\WRDQDO\VHZULWWHQDQGVWDWLVWLFDOHYLGHQFH 4 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Specification at a glance Unit 2 Unit code: 5ST02 • Controlled conditions 25% of the total GCSE • $YDLODELOLW\-XQHVHULHV • )LUVWDVVHVVPHQW-XQH Overview of content • Planning and data collection • 3URFHVVLQJUHSUHVHQWLQJDQGDQDO\VLQJGDWD • Reasoning, interpreting and discussing results • 3UREDELOLW\ Overview of assessment • 1RWWLHUHGWDUJHWLQJJUDGH$–* • One controlled assessment • 7KUHHVHFWLRQV { planning { data collection and processing and representing data { LQWHUSUHWLQJDQGHYDOXDWLQJGDWD • 7DVNVSURYLGHGE\(GH[FHOHDFK\HDU • 6WXGHQWVDQGFHQWUHVDEOHWRSHUVRQDOLVHLQYHVWLJDWLRQZLWKLQWKHWDVN 6HH Appendix 3 IRUDGHVFULSWLRQRIWKLVFRGHDQGDOORWKHUFRGHVUHOHYDQWWRWKLVTXDOL¿FDWLRQ Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 5 A Qualification content Knowledge and understanding 7KH(GH[FHO*&6(LQ6WDWLVWLFVUHTXLUHVVWXGHQWVWRGHYHORSNQRZOHGJHDQGXQGHUVWDQGLQJLQWKH IROORZLQJDUHDV Planning and data collection • 3ODQQLQJDOLQHRIHQTXLU\RULQYHVWLJDWLRQ • 7\SHVRIGDWD • Census and sample data • Sampling techniques • &ROOHFWLQJRUREWDLQLQJGDWD Processing, representing and analysing data • 0HWKRGVRIWDEXODWLRQ • Diagrams and similar forms of representation • 0HDVXUHVRIFHQWUDOWHQGHQF\ • Measure of dispersion • 6XPPDU\VWDWLVWLFV • Scatter diagrams, correlation and regression • Time series • 4XDOLW\DVVXUDQFH • Estimation Reasoning, interpreting and discussing results • Inference and other reasoning • Predictions • Interpretation and conclusion Probability • 'H¿QLWLRQVDQGFDOFXODWLRQV • 'LVFUHWHSUREDELOLW\GLVWULEXWLRQV 6 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Qualification content A Skills 7KH(GH[FHO*&6(LQ6WDWLVWLFVSURYLGHVVWXGHQWVZLWKWKHRSSRUWXQLW\WRGHYHORSVNLOOVLQWKH IROORZLQJDUHDV • SODQQLQJDVWDWLVWLFDOHQTXLU\ • collecting data • SURFHVVLQJDQDO\VLQJDQGUHSUHVHQWLQJGDWD • LQWHUSUHWLQJDQGHYDOXDWLQJUHVXOWV • FRPPXQLFDWLQJSODQVUHVXOWVDQGFRQFOXVLRQVLQDYDULHW\RIIRUPV including using ICT. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 7 A Qualification content Specification content Foundation Tier 10 The collection of data 10 (a) Planning 10 (b) Types of data 11 (c) Population and sampling 12 (d) Collecting data 13 Processing, representing and analysing data 8 15 (b) Diagrams and representations 16 (c) Measures of central tendency 18 (e) Further summary statistics 19 (f) Scatter diagrams and correlation 20 (g) Time series 21 (h) Estimation 21 Reasoning, interpreting and discussing results 22 Probability 23 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Qualification content A Higher Tier 25 The collection of data 25 (a) Planning 25 (b) Types of data 26 (c) Population and sampling 27 (d) Collecting data 29 Processing, representing and analysing data 31 (a) Tabulation 31 (b) Diagrams and representations 32 (c) Measures of central tendency 34 (d) Measures of dispersion 35 (e) Further summary statistics 36 (f) Scatter diagrams and correlation 37 (g) Time series 38 (h) Quality assurance 39 (i) Estimation 39 Reasoning, interpreting and discussing results 40 Probability 42 Using the specification content 7KHVXEMHFWFRQWHQWIRU*&6(6WDWLVWLFVH[DPLQDWLRQSDSHUVLVSUHVHQWHG LQWZRWLHUV)RXQGDWLRQDQG+LJKHU ,QHDFKWLHUWKHFRQWHQWLVGLYLGHGLQWRWZRVHFWLRQV • the concise content description • italicisedVWDWHPHQWVJLYLQJIXUWKHUJXLGDQFHLQWKHIRUPRIH[DPSOHV or more detailed description. 0DWHULDOLQWURGXFHGLQWKH+LJKHU7LHUDQGQRWLQFOXGHGLQWKH)RXQGDWLRQ 7LHULVVKRZQLQbold. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 9 A Qualification content Foundation Tier Foundation Tier The collection of data (a) Planning Students should be taught to: specify a line of enquiry to be investigated; breaking it down into more manageable parts and sub-questions when necessary specify a hypothesis to be tested Terminology such as null hypothesis will not be required. A hypothesis such as ‘as motor cycles get older their value is likely to go down’ is expected. determine the data required for a line of enquiry, selecting an appropriate method of obtaining the data Use a questionnaire rather than an open-ended interview. Explain the rationale behind a sampling method. 10 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Foundation Tier (b) Qualification content A Types of data Students should be taught to: recognise that data can be obtained from primary or secondary sources Primary sources could include raw data, surveys, questionnaires which may have more than two categories, investigations and experiments, whilst secondary sources could include databases, published statistics, newspapers, internet pages. recognise the difference between quantitative and qualitative variables Number of pets is quantitative, favourite name is qualitative. recognise the difference between discrete and continuous data Number of people is discrete, whilst height is continuous. recognise, understand and use scales of measurement — categorical, rank Categorical: hair colour, rank: exam grades. FDWHJRULVHGDWDWKURXJKWKHXVHRIZHOOGH¿QHGSUHFLVHGH¿QLWLRQVLQWHUYDOVRU class boundaries 7KHXVHRIFODVVERXQGDULHVVXFKDVDDQGWHUPVVXFKDVFODVVZLGWK and class interval is expected. understand the meaning of bivariate data which may be discrete, continuous, grouped or ungrouped Plotting and interpreting points in a 2D framework is expected. XQGHUVWDQGXVHDQGGH¿QHVLWXDWLRQVIRUJURXSHGDQGXQJURXSHGGDWD The construction and use of two-way tables, obtained from surveys and questionnaires. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 11 A Qualification content (c) Foundation Tier Population and sampling Students should be taught to: understand the meaning of the term population 7KHGH¿QLWLRQRIµSRSXODWLRQ¶FDQYDU\²IRUH[DPSOHLWFRXOGEHDFODVVJURXS or the cars in a car park. XQGHUVWDQGWKHZRUGFHQVXVHVSHFLDOO\ZLWKUHJDUGWRZHOOGH¿QHGVPDOOVFDOH and large populations, for example national census A census obtains information about every member of a population. understand the reasons for sampling and that sample data is used to estimate values in the population 5HDVRQVWRLQFOXGHWLPHDQGHI¿FLHQF\DQGLPSRVVLELOLW\RIUHDFKLQJWKHZKROH population in many circumstances. understand the terms random, randomness and random sample The relation between ‘random’ and ‘equally likely’ may be tested. generate and use random numbers Using a calculator, or a computer (including the use of a spreadsheet) or by experiment. understand, design and use a sampling frame Designing a sampling frame is expected. EHDEOHWRVHOHFWDVLPSOHUDQGRPVDPSOHRUDVWUDWL¿HGVDPSOHE\RQHFDWHJRU\ as a method of investigating a population An appreciation of an appropriate sample size is expected, as is the ability to make a random selection or sample from a population using calculators or computers. Examples of one category might include male/female or KS2/KS3/KS4. have a basic idea of the concept of bias, how it might occur in a sampling procedure and how it might be minimised Possible bias in sources of secondary data, for example vested interests. 12 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Foundation Tier (d) Qualification content A Collecting data Students should be taught to: collect or obtain data by observation, surveys, experiments (including controlled experiments), counting, data logging, questionnaires and measurement Writing improved or good questions for a questionnaire is expected. obtain primary data by questionnaires or experiment understand the effects of accuracy on measurements Knowing that measured data such as length or time is subject to some error. For example, that every measurement is taken to a given level of accuracy. understand the advantages and disadvantages of using interviews versus questionnaires Deciding which technique might be more appropriate, and why, is expected. GHVLJQDQGXVHHI¿FLHQWDQGHIIHFWLYHGDWDFDSWXUHVKHHWVDQGPHWKRGVRI recording data understand the role and use of pilot studies and pre-testing The rationale behind pilots for questionnaires and pre-tests for experiments is expected. understand and account for the problems of design, ambiguity of wording, OHDGLQJDQGELDVHGTXHVWLRQVGH¿QLWLRQVDQGREWDLQLQJWUXWKIXOUHVSRQVHV The minimisation of ambiguity and bias is expected. understand the advantages and disadvantages of open and closed questions As used in questionnaires. be aware of, and understand, the problems related to identifying the appropriate population, the distribution and collection of questionnaires, errors in recorded answers, non-responses and missing data Dealing with problems such as non-response and rogue values is expected. identify appropriate sources of secondary data 1HZVSDSHUV2I¿FHRI1DWLRQDO6WDWLVWLFVWKHLQWHUQHWDQGRWKHUV Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 13 A Qualification content Foundation Tier Students should be taught to: extract data from secondary sources, including those based on ICT 7KHVDPSOLQJRIVHFRQGDU\GDWDIURPVRXUFHVVXFKDVWKH2I¿FHRI1DWLRQDO Statistics is expected or data on subjects of students’ own interests, including that extracted from the internet. understand the aspects of accuracy, reliability, relevance and bias as related to secondary data Questioning the reliability of secondary sources and data is expected. Examples of secondary data include the internet, Retail Price Index (RPI) or Consumer Price Index (CPI), Key Data and Abstract of Statistics, GCSE results. design simple statistical experiments to obtain data Students will be expected to comment on the design of experiments, for example using controls and random allocation. understand the meaning of explanatory and response variables 7KHLGHQWL¿FDWLRQRIH[SODQDWRU\LQGHSHQGHQWDQGUHVSRQVHGHSHQGHQW variables is expected. XQGHUVWDQGWKHQHHGIRULGHQWL¿FDWLRQRIWKHYDULDEOHVWREHLQYHVWLJDWHG Knowledge of redundant variables is expected. understand surveys Examples from other school subjects (including science) and everyday life. 14 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Foundation Tier Qualification content A Processing, representing and analysing data Students should be taught to: construct frequency tables by tallying raw data where appropriate 7KHXVHDQGLQWHUSUHWDWLRQRIWKHVWDQGDUG¿YHSRLQWWDOO\LQDWDOO\FKDUWLV H[SHFWHGLHWDOO\LQJDIUHTXHQF\RIZLWKIRXUYHUWLFDOEDUVDQGRQHGLDJRQDO bar across them. tabulate using class intervals as appropriate For continuous or discrete data. tabulate using various forms of grouping the data Could include qualitative or quantitative categories. combine categories to simplify tables with an understanding of the problems of RYHUVLPSOL¿FDWLRQWKHHIIHFWVRQUHDGDELOLW\WKHLGHQWL¿FDWLRQRUPDVNLQJRI trends and the loss of detail Students will be expected to comment on aspects such as loss of detail or masking of trends. read and interpret data presented in tabular or graphical form Tables of data drawn from media and from government and other statistical sources may be used, for example social trends. design suitable tables, including summary tables; design and use appropriate two-way tables Systematically listing outcomes from single or two successive events. convert raw data to summary statistics, design, construct and present summary tables Understanding of the difference between raw data and summary statistics is expected. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 15 A Qualification content (b) Foundation Tier Diagrams and representations Students should be taught, as appropriate, to construct, draw, use and understand: correct and precise labelling of all forms of diagrams The labelling and scaling of axes is expected. pictograms, bar charts, multiple or composite bar charts and pie charts for qualitative, quantitative and discrete data The reasons for choosing one form of representation are expected. vertical line (stick) graphs for discrete data Comparative line graphs are expected. for continuous data: pie charts, histograms with equal class intervals, frequency diagrams, cumulative frequency diagrams, population pyramids No distinction will be made between cumulative frequency polygons and curves, whilst frequency polygons could be open or closed. stem and leaf diagrams for discrete and continuous data 6WXGHQWVPD\QHHGWRGH¿QHWKHVWHPIRUWKHPVHOYHV A key is expected. scatter diagrams for bivariate data 6WXGHQWVPD\EHUHTXLUHGWRGH¿QHWKHLURZQVFDOHV line graphs and time series Trend lines by eye and seasonal variation are expected. choropleth maps (shading) For example, showing temperature across Europe by shading regions. simple properties of the shape of distributions of data including symmetry, positive and negative skew the distinction between well-presented and poorly presented data Poorly presented data can be misleading. 16 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Foundation Tier Qualification content A Students should be taught, as appropriate, to construct, draw, use and understand: the shape and simple properties of frequency distributions; symmetrical positive and negative skew the potential for visual misuse, by omission or misrepresentation Knowledge of causes such as unrepresentative scales is expected. the transformation from one presentation to another Bar chart to pie chart, etc. KRZWRGLVFRYHUHUURUVLQGDWDDQGUHFRJQLVHGDWDWKDWGRHVQRW¿WDJHQHUDO trend or pattern $QDO\WLFDOGH¿QLWLRQRIDQRXWOLHUZLOOQRWEHUHTXLUHG Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 17 A Qualification content (c) Foundation Tier Measures of central tendency Students should be taught to: work out and use the mean, mode and median of raw data presented as a list No more than 30 numbers in the list will be examined. work out the mean, mode and median for discrete data presented as a frequency distribution Graphical and other methods for the median are expected. 3 notation is expected. identify the modal class interval for grouped frequency distributions for discrete or continuous data Frequency distributions with equal class intervals only. work out and use estimates for the mean and median of grouped frequency distributions for discrete or continuous data Graphical and other methods for the median are expected. The use of sigma notation is expected. understand the appropriateness, advantages and disadvantages of each of the three measures of central tendency Explanation of why certain measures are inappropriate is expected. be able to make a reasoned choice of a measure of central tendency appropriate to a particular line of enquiry 18 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Foundation Tier (d) Qualification content A Measures of dispersion work out and use the range for data presented in a list or frequency distribution The possible effect of an outlier on range is expected. work out the quartiles, percentiles and interquartile range for discrete and continuous data presented either as a list, frequency table or grouped frequency table Graphical and other methods are expected. construct, interpret and use box plots The use of box plots includes comparisons. understand the advantages and disadvantages of each of the measures of dispersion range, quartiles, interquartile range, percentiles use an appropriate measure of central tendency, together with range, quartiles, interquartile range and percentiles to compare distributions of data An awareness that a full comparison needs at least both a measure of central tendency and a measure of dispersion is expected. Extra measures are included. (e) Further summary statistics Students should be taught to: simple index numbers Price relative = (Price ÷ Price in base year) × 100 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 19 A Qualification content (f) Foundation Tier Scatter diagrams and correlation Students should be taught to: plot data as points on a scatter diagram The labelling and scaling of axes is expected. recognise positive, negative and zero linear correlation by inspection Terms such as strong or weak are expected. understand the distinction between correlation, causality and a non-linear relationship The points lying on the circumference of a circle are related but show zero correlation. ¿WDOLQHRIEHVW¿WSDVVLQJWKURXJK ( x , y ) to the points on a scatter diagram, by eye may be required Questions will state when ( x , y ) is required. to use interpolation and extrapolation and understand the pitfalls Particularly the problem of extrapolating beyond the range. interpret data presented in the form of a scatter diagram 20 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Foundation Tier (g) Qualification content A Time series Students should be taught to: plot points as a time series; draw a trend line by eye and use it to make a prediction No more than 20 points are expected. calculate and use appropriate moving averages 8SWRDQGLQFOXGLQJDSRLQWPRYLQJDYHUDJH LGHQWLI\DQGGLVFXVVWKHVLJQL¿FDQFHRIVHDVRQDOYDULDWLRQE\LQVSHFWLQJWLPH series graphs (h) Estimation Students should be taught to: estimate population means from samples estimate population proportions from samples with application in opinion polls and elsewhere understand the effect of sample size on estimates and the variability of estimates Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 21 A Qualification content Foundation Tier Reasoning, interpreting and discussing results Students should be taught, in the context of real data, to: apply statistical reasoning, explain and justify inferences, deductions, arguments and solutions &DVHVFOHDUO\UHVWULFWHGWRWKHFRQWHQWRIWKHVSHFL¿FDWLRQDWWKHDSSURSULDWH level. explore connections and look for and examine relationships between variables For example, height and weight, age and depreciation of a car, GNP and mortality in infants. consider the limitations of any assumptions Simple cases only, for example honest replies to questionnaires, equally likely outcomes in probabilities, representativeness of sample of population, reliability of secondary data. relate summarised data to any initial questions or observations The relevance of measures of central tendency. interpret all forms of statistical tables, diagrams and graphs To include real published tables and graphs. compare distributions of data and make comparisons using measures of central tendency, measures of dispersion and percentiles The shapes of distributions and graphs may be used. Formula for variance and standard deviation to be given. check results for reasonableness and modify their approaches if necessary For example, the mean must lie between the maximum and minimum, ‘the average bicycle speed was 130 km per hour’ is not reasonable. interpret correlation as a measure of the strength of the association between two variables The use of words such as ‘weak’ or ‘strong’ are expected. 22 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Foundation Tier Qualification content A Probability Students should be taught to: understand the meaning of the words event and outcome Tossing a coin is an event with outcomes landing heads or tails. understand words such as: impossible, certain, highly likely, likely, unlikely, possible, evens, and present them on a likelihood scale Interpretation of real-life situations will be expected, for example ‘the probability that the horse will win the next race is 0.3’; ‘the probability that I will get a grade C or better in my GCSE Statistics is 3 ’ 4 put outcomes in order in terms of probability 8VHRILVH[SHFWHG put probabilities in order on a probability scale Labelling of the scale will be expected. understand the terms ‘random’ and ‘equally likely’ understand and use measures of probability from a theoretical perspective and from a limiting frequency or experimental approach )RUPDOGH¿QLWLRQDQGQRWDWLRQRIDOLPLWZLOOQRWEHUHTXLUHGEXWWHUPLQRORJ\ such as ‘as the number of trials increases’ is expected. understand that in some cases the measure of probability based on limiting frequency is the only viable measure The probability of a sports team winning can only be measured from a limiting frequency perspective. For example, medical statistics for the assessment of health risks. compare expected frequencies and actual frequencies; use probability to assess risk Examples may be taken from insurance scenarios. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 23 A Qualification content Foundation Tier Students should be taught to: produce, understand and use a sample space Listing all outcomes of single events and two successive events, in a systematic way. understand the terms mutually exclusive and exhaustive and understand the addition law P(A or B) = P(A) + P(B) for two mutually exclusive events P(A or B) = P(A) + P(B); ‘Mutually exclusive’ means that the occurrence of one outcome prevents another, 3p = 1 when summed over all mutually exclusive outcomes. know, for mutually exclusive outcomes, that the sum of the probabilities is 1 and in particular the probability of something not happening is 1 minus the probability of it happening If P(A) = p then P(not A) = 1 – p draw and use tree diagrams and probability tree diagrams for independent events Listing all possible joint or compound outcomes. understand, use and apply the addition law for mutually exclusive events and the multiplication law for independent events To correctly apply P(A and B) = P(A) u P(B), P(A or B) = P(A) + P(B). 24 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier Qualification content A Higher Tier The collection of data (a) Planning Students should be taught to: specify a line of enquiry to be investigated; breaking it down into more manageable parts and sub-questions when necessary; specify a hypothesis to be tested Terminology such as null hypothesis will not be required. A hypothesis such as ‘as motor cycles get older their value is likely to go down’ is expected. determine the data required for a line of enquiry, selecting an appropriate method of obtaining the data and justifying the choice of method by comparing it with possible alternatives Use a questionnaire rather than an open-ended interview. Explain the rationale behind a sampling method, in relation to size or type of sample. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 25 A Qualification content (b) Higher Tier Types of data Students should be taught to: recognise that data can be obtained from primary or secondary sources Primary sources could include raw data, surveys, questionnaires which may have more than two categories, investigations and experiments, whilst secondary sources could include databases, published statistics, newspapers, internet pages, etc. recognise the difference between quantitative and qualitative variables Number of pets is quantitative, favourite name is qualitative. recognise the difference between discrete and continuous data Number of people is discrete, whilst height is continuous. recognise, understand and use scales of measurement – categorical, rank Categorical: hair colour, rank: exam grades. FDWHJRULVHGDWDWKURXJKWKHXVHRIZHOOGH¿QHGSUHFLVHGH¿QLWLRQVLQWHUYDOVRU class boundaries 7KHXVHRIFODVVERXQGDULHVVXFKDVDDQGWHUPVVXFKDVFODVVZLGWK and class interval is expected appreciate the implications of grouping for loss of accuracy in both calculations and presentations understand the meaning of bivariate data which may be discrete, continuous, grouped or ungrouped Plotting and interpreting points in a 2D framework is expected. XQGHUVWDQGXVHDQGGH¿QHVLWXDWLRQVIRUJURXSHGDQGXQJURXSHGGDWD The construction and use of two-way tables obtained from surveys and questionnaires. 26 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier (c) Qualification content A Population and sampling Students should be taught to: understand the meaning of the term population 7KHGH¿QLWLRQRIµSRSXODWLRQ¶FDQYDU\²IRUH[DPSOHLWFRXOGEHDFODVVJURXS or the cars in a car park. XQGHUVWDQGWKHZRUGFHQVXVHVSHFLDOO\ZLWKUHJDUGWRZHOOGH¿QHGVPDOOVFDOH and large populations, eg National census A census obtains information about every member of a population. The types of questions used for a census and how the collected data is used. understand the reasons for sampling and that sample data is used to estimate values in the population 5HDVRQVWRLQFOXGHWLPHDQGHI¿FLHQF\DQGWKHLPSRVVLELOLW\RIUHDFKLQJWKH whole population in many circumstances. understand the terms random, randomness and random sample The relation between ‘random’ and ‘equally likely’ may be tested. understand the use of random numbers using a random number table, calculator or computer (including the use of a spreadsheet); understand, design and use a sampling frame Designing a sampling frame is expected. EHDEOHWRVHOHFWDVLPSOHUDQGRPVDPSOHRUDVWUDWL¿HGVDPSOHE\more than one category as a method of investigating a population An appreciation of an appropriate sample size is expected, as is the ability to make a random selection or sample from a population using calculators or computers. Examples of one category might include male/female or KS2/KS3/KS4. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 27 A Qualification content Higher Tier Students should be taught to: understand and use systematic, quota and cluster sampling With particular reference to large-scale lines of enquiry such as quality control or opinion polls. Quota sampling: for example, market research, using a quota of subjects of VSHFL¿HGW\SH Cluster sampling: for example, grouping subjects by area. have a basic idea of the concept of bias, how it might occur in a sampling procedure and how it might be minimised Possible bias in sources of secondary data, for example vested interests. understand the strengths and weaknesses of various sampling methods, LQFOXGLQJELDVLQÀXHQFHVDQGFRQYHQLHQFH $QDZDUHQHVVRILQÀXHQFHVVXFKDVJHQGHUVRFLDOEDFNJURXQGRU geographical area is expected. 28 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier (d) Qualification content A Collecting data Students should be taught to: collect or obtain data by observation, surveys, experiments (including controlled experiments), counting, data logging, convenience sampling, questionnaires and measurement Writing improved or good questions for a questionnaire is expected. obtain primary data by questionnaires, experiments or simulations Simulations such as the rolling of a die can be obtained using a calculator or a spreadsheet. understand the effects of accuracy on measurements Knowing that measured data such as length or time is subject to some error. For example, recognise that every measurement is taken to a given level of accuracy and that measurements given to the nearest whole unit may be inaccurate by up to p 1 unit. 2 understand the advantages and disadvantages of using interviews versus questionnaires Deciding which technique might be more appropriate, and why, is expected. GHVLJQDQGXVHHI¿FLHQWDQGHIIHFWLYHGDWDFDSWXUHVKHHWVDQGPHWKRGVRI recording data understand the role and use of pilot studies and pre-testing The rationale behind pilots for questionnaires and pre-tests for experiments is expected. understand and account for the problems of design, ambiguity of wording, OHDGLQJDQGELDVHGTXHVWLRQVGH¿QLWLRQVDQGREWDLQLQJWUXWKIXOUHVSRQVHVwith simplest form of random response in sensitive cases The minimisation of ambiguity and bias is expected. ([DPSOHRIDVHQVLWLYHFDVHZKHQHPRWLRQV¿QDQFHSROLWLFVRUFULPLQDO activity are involved. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 29 A Qualification content Higher Tier Students should be taught to: understand the advantages and disadvantages of open and closed questions As used in questionnaires. be aware of, and understand, the problems related to identifying the appropriate population, the distribution and collection of questionnaires and surveys, errors in recorded answers, non-responses and missing data Dealing with problems such as non-response and rogue values is expected. identify appropriate sources of secondary data 1HZVSDSHUV2I¿FHRI1DWLRQDO6WDWLVWLFVWKHLQWHUQHWDQGRWKHUV extract data from secondary sources, including those based on ICT 7KHVDPSOLQJRIVHFRQGDU\GDWDIURPVRXUFHVVXFKDV2I¿FHRI1DWLRQDO Statistics is expected or data on subjects of students’ own interests, including that extracted from the internet. understand the aspects of accuracy, reliability, relevance and bias as related to secondary data Questioning the reliability of secondary sources and data will be expected. Examples of secondary data include the internet, Retail Price Index (RPI), Consumer Price Index (CPI), Key Data and Abstract of Statistics, GCSE results. design simple statistical experiments to obtain data Students will be expected to comment on the design of experiments, eg using controls and random allocation including replication, randomisation and matched pairs. understand the meaning of explanatory and response variables 7KHLGHQWL¿FDWLRQRIH[SODQDWRU\LQGHSHQGHQWDQGUHVSRQVHGHSHQGHQW variables is expected. XQGHUVWDQGWKHQHHGIRULGHQWL¿FDWLRQRIWKHYDULDEOHVWREHLQYHVWLJDWHG Knowledge of redundant variables will be expected. understand surveys; the appropriateness of the conditions Examples from other subjects (including science) and everyday life. 30 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier Qualification content A Processing, representing and analysing data (a) Tabulation Students should be taught to: construct frequency tables by tallying raw data where appropriate 7KHXVHDQGLQWHUSUHWDWLRQRIWKHVWDQGDUG¿YHSRLQWWDOO\LQDWDOO\FKDUWLV H[SHFWHGLHWDOO\LQJDIUHTXHQF\RIZLWKIRXUYHUWLFDOEDUVDQGRQHGLDJRQDO bar across them. tabulate using class intervals as appropriate, including open-ended classes and classes of varying width For continuous or discrete data. tabulate using various forms of grouping the data Could include qualitative or quantitative categories. combine categories to simplify tables with an understanding of the problems of RYHUVLPSOL¿FDWLRQWKHHIIHFWVRQUHDGDELOLW\WKHLGHQWL¿FDWLRQRUPDVNLQJRI trends and the loss of detail Students will be expected to comment on aspects such as loss of detail or masking of trends. SUREOHPVDVVRFLDWHGZLWKXQGHUDQGRYHUVLPSOL¿FDWLRQWKURXJK LQDSSURSULDWHQXPEHURIVLJQL¿FDQW¿JXUHVRUDQXQVXLWDEOHJURXSVL]H An awareness of problems associated with creating categories that are too broad, too narrow or redundant. read and interpret data presented in tabular or graphical form Tables of data drawn from media and government and other statistical sources may be used, for example social trends. design suitable tables, including summary tables; design and use appropriate two-way tables Systematically listing outcomes from single or two successive events. convert raw data to summary statistics, design, construct and present summary tables Understanding the difference between raw data and summary statistics is expected. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 31 A Qualification content (b) Higher Tier Diagrams and representations Students should be taught, as appropriate, to construct, draw, use and understand: correct and precise labelling of all forms of diagrams The labelling and scaling of axes is expected. pictograms, bar charts, multiple or composite bar charts and pie charts for qualitative, quantitative and discrete data and comparative pie charts with area proportional to frequency The reasons for choosing one form of representation are expected. vertical line (stick) graphs for discrete data and cumulative frequency step polygons Comparative line graphs are expected, as are comparative step polygons. for continuous data: pie charts, histograms with equal class intervals, frequency diagrams, cumulative frequency diagrams, population pyramids, histograms with unequal class intervals and the concept of frequency density No distinction will be made between cumulative frequency polygons (other than step polygons) and curves, whilst frequency polygons could be open or closed. Changes over time, for example population pyramids. Practical consequences applied to all forms of representation. stem and leaf diagrams for discrete and continuous data 6WXGHQWVVKRXOGEHDEOHWRGH¿QHWKHVWHPIRUWKHPVHOYHV A key is expected. scatter diagrams for bivariate data 6WXGHQWVVKRXOGEHDEOHWRGH¿QHWKHLURZQVFDOHV line graphs and time series Trend lines by eye and seasonal variation are expected. 32 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier Qualification content A Students should be taught, as appropriate, to construct, draw, use and understand: choropleth maps (shading) For example, showing temperature across Europe by shading regions. simple properties of the shape of distributions of data including symmetry, positive and negative skew the distinction between well-presented and poorly presented data Poorly presented data can be misleading, for example, 3D angled pie charts and 3D pie charts with slices pulled out, scales that do not start at 0. the shape and simple properties of frequency distributions symmetrical positive and negative skew that many populations can be modelled by the Normal distribution the potential for visual misuse, by omission or misrepresentation Knowledge of causes such as unrepresentative scales or other measures is expected. the transformation from one presentation to another Bar chart to pie chart, etc. KRZWRGLVFRYHUHUURUVLQGDWDDQGUHFRJQLVHGDWDWKDWGRHVQRW¿WDJHQHUDO trend or pattern, including outliers $QDO\WLFDOGH¿QLWLRQRIDQRXWOLHUwill be required. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 33 A Qualification content (c) Higher Tier Measures of central tendency Students should be taught to: work out and use the mean, mode and median of raw data presented as a list No more than 30 numbers in the list will be examined. work out the mean, mode and median for discrete data presented as a frequency distribution Graphical and other methods for the median are expected. 3 notation is expected. identify the modal class interval for grouped frequency distributions for discrete or continuous data Frequency distributions with equal class intervals only. work out and use estimates for the mean and median of grouped frequency distributions for discrete or continuous data Graphical and other methods for the median are expected. The use of sigma notation is expected understand the effects of transformations of the data on the mean, mode and median Transformations will be restricted to those of the type x m ax + b LHDI¿QHWUDQVIRUPDWLRQV understand the effect on the mean, mode and median of changes in the data including the addition or withdrawal of a population or sample member understand the appropriateness, advantages and disadvantages of each of the three measures of central tendency Explanation of why certain measures are inappropriate is expected. be able to make a reasoned choice of a measure of central tendency appropriate to a particular line of enquiry, nature of the data and purpose of the analysis; Full explanation of why a particular measure is chosen, including cases where a comparison is to be made, is expected. calculate and use a weighted mean No more than four categories are expected. 34 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier (d) Qualification content A Measures of dispersion Students should be taught to: work out and use the range for data presented in a list or frequency distribution The possible effect of an outlier on range is expected. work out the quartiles, percentiles and interquartile range for discrete and continuous data presented either as a list, frequency table or grouped frequency table Graphical and other methods will be expected. Numerical interpolation is expected. work out interpercentile ranges for discrete and continuous data presented as a list, frequency distribution or grouped frequency distribution Numerical interpolation is expected. construct, interpret and use box plots The use of box plots includes comparisons. formally identify outliers 2XWOLHUVDUHGH¿QHGDV less than LQ – 1.5 s IQR and greater than UQ + 1.5 s IQR, where LQ and UQ are lower and upper quartiles and IQR is interquartile range. Effect of anomalous data. calculate and use variance and standard deviation Division by n is expected, as is use of 3 notation. understand the advantages and disadvantages of each of the measures of dispersion range, quartiles, interquartile range, percentiles, deciles, interpercentile range, variance and standard deviation Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 35 A Qualification content Higher Tier Students should be taught to: use an appropriate measure of central tendency together with range, quartiles, interquartile range, percentiles, deciles, interpercentile range, variance and standard deviation to compare distributions of data An awareness that a full comparison needs at least both a measure of central tendency and a measure of dispersion is expected. calculate, interpret and use standardised scores to compare values from different frequency distributions Extra measures are included. (e) Further summary statistics Students should be taught to: simple index numbers Price relative = (Price ÷ Price in base years) × 100 chain base index numbers Used to calculate the annual percentage change. weighted index numbers :HLJKWHGLQGH[QXPEHU Ȉ,QGH[QXPEHUî:HLJKW·Ȉ:HLJKW For example, CPI (Consumer Price Index), AEI, (Average Earnings Index). Retail Price Index (RPI) What items are in the index, how items change over time, how prices are established from survey, how the index is used in assessing real price change and the limitations. 36 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier (f) Qualification content A Scatter diagrams and correlation Students should be taught to: plot data as points on a scatter diagram The labelling and scaling of axes is expected. recognise positive, negative and zero correlation by inspection Terms such as strong or weak are expected. understand the distinction between correlation, causality and a non-linear relationship The points lying on the circumference of a circle are related but show zero correlation. GUDZDOLQHRIEHVW¿WSDVVLQJWKURXJK( x , y ) to the points on a scatter diagram Questions will state when ( x , y ) is required. ¿QGWKHHTXDWLRQRIDOLQHRIEHVW¿WLQWKHIRUPy = ax + b and a practical interpretation of a and b in context Commenting on whether a straight line is appropriate will be expected. Finding the values of a and b from the diagram. ¿WQRQOLQHDUPRGHOVRIWKHIRUPVy = axn + b and y = kax The relationship will be suggested; n could be 2, 1 or 1 only. 2 For example, population growth or nuclear decay. understand the pitfalls of interpolation and extrapolation Particularly the problem of extrapolating beyond the range. interpret data presented in the form of a scatter diagram FDOFXODWHLQDSSURSULDWHFDVHV6SHDUPDQ¶VUDQNFRUUHODWLRQFRHI¿FLHQW and use it as a measure of agreement or for comparisons of the degree of correlation The formula will be given. Although students should have experience of dealing with tied ranks, this will not be tested in the examination. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 37 A Qualification content (g) Higher Tier Time series Students should be taught to: plot points as a time series; draw a trend line by eye and use it to make a prediction No more than 20 points is expected. calculate and use appropriate moving averages Up to and including a 7-point moving average. LGHQWLI\DQGGLVFXVVWKHVLJQL¿FDQFHRIVHDVRQDOYDULDWLRQE\LQVSHFWLRQRIWLPH series graphs Students will be expected to work out the average seasonal variation from their time series graphs. draw a trend line based on moving averages; recognise seasonal effect at a given data point and average seasonal effect. Interpretations are expected. 38 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier (h) Qualification content A Quality assurance Students should be taught to: plot sample means, medians and ranges over time on quality control charts that have target values, and action and warning limits For example, in the manufacture of clothes to test that the variation in waist size is within allowable limits and that production may continue; in the manufacture of engineering components that certain measurements are within allowable limits and production may continue. understand that in a process under control almost all of the means, medians or ranges fall inside the action limits, and only 1 in 20 fall outside the warning limits know the action to be taken if a sample mean, median or range falls outside of each type of limit If a sample mean is outside the action limits the process is stopped. If a sample mean is between the warning and action limits another sample is taken. (i) Estimation Students should be taught to: estimate population means from samples estimate population proportions from samples with applications in opinion polls and elsewhere HVWLPDWHSRSXODWLRQVL]HEDVHGRQWKH3HWHUVHQFDSWXUHUHFDSWXUHPHWKRG The appropriateness of the assumptions in practice. understand the effect of sample size on estimates and the variability of estimates, with a simple quantitative appreciation of appropriate sample VL]H Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 39 A Qualification content Higher Tier Reasoning, interpreting and discussing results Students should be taught to: apply statistical reasoning, explain and justify inferences, deductions, arguments, solutions and decisions &DVHVFOHDUO\UHVWULFWHGWRWKHFRQWHQWRIWKHVSHFL¿FDWLRQDWWKHDSSURSULDWH level. explore connections and look for and examine relationships between variables, LQFOXGLQJ¿WWLQJWKHHTXDWLRQWRDOLQHRIEHVW¿WRUWUHQGOLQH For example, height and weight, age and depreciation of a car, GNP and mortality in infants. Interpretations of gradient and intercept are expected. consider the limitations of any assumptions Simple cases only, for example, honest replies to questionnaires, equally likely outcomes in probabilities, representativeness of sample of population, reliability of secondary data. formally identify outliers using quartiles Dealing with outliers is expected. relate summarised data to any initial questions or observations The relevance of measures of central tendency. interpret all forms of statistical tables, diagrams and graphs To include real published tables and graphs. compare distributions of data and make comparisons using measures of central tendency and measures of dispersion, such as percentiles, deciles, interpercentile range, mean deviation, variance and standard deviation The shapes of distributions and graphs may be used. Formula for variance and standard deviation to be given. 40 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier Qualification content A Students should be taught to: check results for reasonableness and modify their approaches if necessary For example, the mean must lie between the maximum and minimum, ‘the average bicycle speed was 130 km per hour’ is not reasonable. interpret correlation as a measure of the strength of the association between two variables, LQFOXGLQJ6SHDUPDQ¶VUDQNFRUUHODWLRQFRHI¿FLHQWIRUUDQNHG data The use of words such as weak or strong is expected; the closer to p 1 the better the correlation for a given sample size. Beware the use of correlation in small samples. make predictions The use of a trend line by eye, drawing or formula will be expected. FRPSDUHRUFKRRVHE\H\HEHWZHHQDOLQHRIEHVW¿WDQGDPRGHOEDVHGRQ y = axn + b for n = 2, 1 or 1 , y = ax2 + bx or y = kax 2 Based on an informal awareness of the spread of points around a proposed model. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 41 A Qualification content Higher Tier Probability Students should be taught to: understand the meaning of the words event and outcome Tossing a coin is an event with outcomes landing heads or tails. understand words such as: impossible, certain, highly likely, likely, unlikely, possible, evens and present them on a likelihood scale Interpretation of real-life situations is expected, for example, ‘the probability that the horse will win the next race is 0.3’; ‘the probability that I will get a grade C or better in my GCSE Statistics is 3 .’ 4 put outcomes in order in terms of probability Use of b is expected. put probabilities in order on a probability scale Labelling of the scale is expected. understand the terms random and equally likely understand and use measures of probability from a theoretical perspective and from a limiting frequency or experimental approach )RUPDOGH¿QLWLRQDQGQRWDWLRQRIDOLPLWZLOOQRWEHUHTXLUHGEXWWHUPLQRORJ\ such as ‘as the number of trials increases’ is expected. Understand that increasing sample size generally leads to better estimates of probability and population parameters. understand that in some cases the measure of probability based on limiting frequency is the only viable measure The probability of a sports team winning can only be measured from a limiting frequency perspective. For example, medical statistics for the assessment of health risks. compare expected frequencies and actual frequencies 42 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Higher Tier Qualification content A Students should be taught to: use simple cases of the binomial and discrete uniform distribution The expansion of (p + q)2 is expected. In all other cases the expansion of (p + q)n will be given. (n will be limited to 5) use simulation to estimate more complex probabilities use probability to assess risk Examples may be taken from insurance scenarios. produce, understand and use a sample space Listing all outcomes of single events and two successive events, in a systematic way is expected. understand and use Venn diagrams and Cartesian grids IRUH[DPSOHXVLQJDî&RUWHVLRQJULGWRVKRZWKHVXPRIWZRGLFH understand the terms mutually exclusive and exhaustive and to understand the addition law P(A or B) = P(A) + P(B) for two mutually exclusive events ‘Mutually exclusive’ means that the occurrence of one outcome prevents another, 3(probabilities) = 1 when summed over all mutually exclusive outcomes. know, for mutually exclusive outcomes, that the sum of the probabilities is 1 and in particular the probability of something not happening is 1 minus the probability of it happening If P(A) = p then P(not A) = 1 – p draw and use tree diagrams and probability tree diagrams for independent events and conditional cases Listing all possible joint or compound outcomes with and without replacement for up to three outcomes and three sets of branches. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 43 A Qualification content Higher Tier Students should be taught to: understand, use and apply the addition for mutually exclusive events, general addition and multiplication laws for independent events and conditional events and outcomes To correctly apply P(A and B) = P(A) u P(B), P(A or B) = P(A) + P(B), P(A B) = P(A) + P(B) – P(A B), P(A B) = P(B \ A) s P(A). the shape and simple properties of the Normal distribution The distribution is symmetrical with mean, mode and median equal; approximately 95% of values are within p 2 standard deviations of the mean; virtually all values are within p 3 standard deviations of the mean. Use of the Normal distribution to model some populations. Use of Normal distribution tables will not be required. 44 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 B Assessment Assessment summary • 2QHZULWWHQSDSHU • 2QHLQWHUQDODVVHVVPHQWZLWKFRQWUROOHGFRQGLWLRQV Summary table of assessment Unit 1 Paper 1F Unit code: 5ST1F/01 • RIWKH¿QDODVVHVVPHQW • Content aimed at grades C–G • &RYHUVDOO$VVHVVPHQW2EMHFWLYHV • 2QHZULWWHQSDSHUODVWLQJKRXUDQGPLQXWHV • PDUNVLQWRWDO • Consists of questions in familiar and unfamiliar contexts • &RQWDLQVVKRUWDQVZHUDQGORQJDQVZHUTXHVWLRQV • 4XHVWLRQVVHWRQVWDQGDUGVWDWLVWLFDOWHFKQLTXHVGLDJUDPVDQGSUREDELOLW\ • 4XHVWLRQVZKLFKJLYHVWXGHQWVWKHRSSRUWXQLW\WRDQDO\VHZULWWHQDQGVWDWLVWLFDOHYLGHQFH Unit 1 Paper 1H Unit code: 5ST1H/01 • RIWKH¿QDODVVHVVPHQW • &RQWHQWDLPHGDWJUDGHV$±' • &RYHUVDOO$VVHVVPHQW2EMHFWLYHV • 2QHZULWWHQSDSHUODVWLQJKRXUV • PDUNVLQWRWDO • Consists of questions in familiar and unfamiliar contexts • &RQWDLQVVKRUWDQVZHUDQGORQJDQVZHUTXHVWLRQV • 4XHVWLRQVVHWRQVWDQGDUGVWDWLVWLFDOWHFKQLTXHVGLDJUDPVDQGSUREDELOLW\ • 4XHVWLRQVZKLFKJLYHVWXGHQWVWKHRSSRUWXQLW\WRDQDO\VHZULWWHQDQGVWDWLVWLFDOHYLGHQFH Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 45 B Assessment Unit 2 Unit code: 5ST02 • RIWKH¿QDODVVHVVPHQW • 8QWLHUHGJUDGHV$±*DYDLODEOH • &RYHUVDOODVVHVVPHQWFULWHULD • 7KHWDVNVFRQVLVWRIWKUHHVWDJHV { planning { data collection and processing and representing data { LQWHUSUHWLQJDQGHYDOXDWLQJGDWD • PDUNVLQWRWDO • $SSUR[LPDWHO\±KRXUVFXUULFXOXPWLPH • 3ODQQLQJDQGLQWHUSUHWLQJVWDJHVXQGHUIRUPDOVXSHUYLVLRQGDWDFROOHFWLRQDQGSURFHVVLQJDQG UHSUHVHQWLQJGDWDXQGHULQIRUPDOVXSHUYLVLRQ Assessment Objectives and weightings % in GCSE $2 $QDO\VHDVWDWLVWLFDOSUREOHPDQGSODQDQDSSURSULDWHVWUDWHJ\ ± $2 'HVFULEHDQGXVHDSSURSULDWHPHWKRGVWRVHOHFWDQGFROOHFWGDWD ± $2 3URFHVVDQDO\VHDQGSUHVHQWGDWDDSSURSULDWHO\ ± $2 8VHVWDWLVWLFDOHYLGHQFHWRLGHQWLI\LQIHUHQFHVPDNHGHGXFWLRQV ± TOTAL 100% Relationship of assessment Objectives to assessments Assessment Assessment Objective AO1 AO2 AO3 AO4 Total for AO1, AO2, AO3 and A04 8QLW ± ± ± ± 75% 8QLW 5% 7.5% Total for GCSE 10–20% 10–20% 40–50% 25–35% 100% 46 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Assessment B External assessment Examination papers 1F and 1H • ([DPLQDWLRQSDSHUV)DQG+ZLOOEHFRPELQHGTXHVWLRQDQGDQVZHU ERRNVFRQWDLQLQJERWKVKRUWHUDQGORQJHUTXHVWLRQV • ([DPLQDWLRQSDSHUVZLOODVVHVVDFURVVDOOWKHJUDGHVDYDLODEOHLQWKH tier. • 4XHVWLRQVRQWKH+LJKHU7LHUH[DPLQDWLRQSDSHU+ZLOODVVXPH NQRZOHGJHIURPWKH)RXQGDWLRQ7LHU) • 'LDJUDPVZLOOQRWQHFHVVDULO\EHGUDZQWRVFDOHDQGPHDVXUHPHQWV VKRXOGQRWEHWDNHQIURPGLDJUDPVXQOHVVLQVWUXFWLRQVWRWKLVHIIHFW DUHJLYHQ • )RUPXODHVKHHWVZLOOEHSURYLGHGLQWKHTXHVWLRQDQGDQVZHUERRNOHWV IRUERWKWKH)RXQGDWLRQDQGWKH+LJKHU7LHU Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 47 B Assessment Calculators • 6WXGHQWVZLOOEHH[SHFWHGWRKDYHDFFHVVWRDVXLWDEOHHOHFWURQLF calculator for the examination papers. • 7KHHOHFWURQLFFDOFXODWRUWREHXVHGE\VWXGHQWVDWWHPSWLQJ H[DPLQDWLRQSDSHU)VKRXOGKDYHDVDPLQLPXPWKHIROORZLQJ IXQFWLRQV +, –, ×, ÷, x¥xPHPRU\FRQVWDQWIXQFWLRQEUDFNHWVxƶxƶfx, DUDQGRPQXPEHUNH\DQGWKHIDFLOLW\WRHQWHUGDWDIRUVWDWLVWLFDO calculation. • 7KHHOHFWURQLFFDOFXODWRUWREHXVHGE\VWXGHQWVDWWHPSWLQJ H[DPLQDWLRQSDSHU+VKRXOGKDYHDVDPLQLPXPWKHIROORZLQJ IXQFWLRQV +, –, ×, ÷, x¥xPHPRU\FRQVWDQWIXQFWLRQEUDFNHWVxƶxƶfx, ıDUDQGRPQXPEHUNH\DQGWKHIDFLOLW\WRHQWHUGDWDIRUVWDWLVWLFDO calculation. • &DOFXODWRUVZLWKDQ\RIWKHIROORZLQJIDFLOLWLHVDUHSURKLELWHGIURPDQ\ H[DPLQDWLRQ { GDWDEDQNV { UHWULHYDORIWH[WRUIRUPXODH { 4:(57<NH\ERDUGV { EXLOWLQV\PEROLFDOJHEUDPDQLSXODWLRQ { V\PEROLFGLIIHUHQWLDWLRQRULQWHJUDWLRQ Entering your students for assessment Student entry 'HWDLOVRIKRZWRHQWHUVWXGHQWVIRUWKLVTXDOL¿FDWLRQFDQEHIRXQGLQ Edexcel’s Information ManualDFRS\LVVHQWWRDOOH[DPLQDWLRQVRI¿FHUV 7KHLQIRUPDWLRQFDQDOVREHIRXQGRQ(GH[FHO¶VZHEVLWH ZZZHGH[FHOFRP 6WXGHQWVVWXG\LQJWKLVXQLWLVHG*&6(TXDO¿FDWLRQDUHUHTXLUHGWR FRPSOHWHDWOHDVWSHUFHQWRIWKHRYHUDOODVVHVVPHQWUHTXLUHPHQWVDV terminal assessment. 48 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Assessment B Forbidden combinations and Classification Code &HQWUHVVKRXOGEHDZDUHWKDWVWXGHQWVZKRHQWHUIRUPRUHWKDQRQH *&6(TXDOL¿FDWLRQZLWKWKHVDPHFODVVL¿FDWLRQFRGHZLOOKDYHRQO\RQH JUDGHWKHKLJKHVWFRXQWHGIRUWKHSXUSRVHRIWKHVFKRRODQGFROOHJH SHUIRUPDQFHWDEOHV 6WXGHQWVVKRXOGEHDGYLVHGWKDWLIWKH\WDNHWZRVSHFL¿FDWLRQVZLWKWKH VDPHFODVVL¿FDWLRQFRGHVFKRROVDQGFROOHJHVDUHYHU\OLNHO\WRWDNHWKH YLHZWKDWWKH\KDYHDFKLHYHGRQO\RQHRIWKHWZR*&6(V7KHVDPHYLHZ PD\EHWDNHQLIVWXGHQWVWDNHWZR*&6(VSHFL¿FDWLRQVWKDWKDYHGLIIHUHQW FODVVL¿FDWLRQFRGHVEXWKDYHVLJQL¿FDQWRYHUODSRIFRQWHQW6WXGHQWVZKR KDYHDQ\GRXEWVDERXWWKHLUVXEMHFWFRPELQDWLRQVVKRXOGFKHFNZLWK WKHLQVWLWXWLRQWRZKLFKWKH\ZLVKWRSURJUHVVEHIRUHHPEDUNLQJRQWKHLU programmes. 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Students can explore the practical applications RIWKHLUZRUNLQWKH¿HOGVRIEXVLQHVVDQG¿QDQFLDOVHUYLFHV Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Appendix 2 Appendices D Further skills development 7KHVWXG\RIVWDWLVWLFVFDQDQGVKRXOGSURYLGHRSSRUWXQLWLHVWRSURPRWH • general thinking skills: WKURXJKGHYHORSLQJSUREOHPVROYLQJ FRPPXQLFDWLRQDQGGHGXFWLYHUHDVRQLQJVNLOOVLHZK\µOLQHVRIEHVW¿W¶ DUHOLPLWHGRQDPRGHOOLQJRIXVHGFDUSULFHVRUZK\µDIRRWEDOOWHDPLV DWLWVPRVWYXOQHUDEOHVKRUWO\DIWHULWVFRUHVDJRDO¶LVQRQVHQVH • economic skillsWKURXJKXVLQJDQGDSSO\LQJVWDWLVWLFVLQSUREOHPV VHWLQHFRQRPLFGLVFLSOLQHVIRUH[DPSOHWKHUHODWLRQVKLSEHWZHHQWKH Retail Price Index and house prices • entrepreneurial and enterprise skillsGHYHORSLQJVWXGHQWV¶ DELOLWLHVWRDSSO\VWDWLVWLFDOWHFKQLTXHVLQEXVLQHVVWHFKQRORJ\VFLHQFH HFRQRPLFVHWF)RUH[DPSOHZKDWDUHWKHLPSOLFDWLRQVRIDGURSLQ VKDUHSULFHVRUWKHFDXVDOLW\RIVPRNLQJDQGKHDUWGLVHDVH • work-based skillsE\GHYHORSLQJVWXGHQWV¶DELOLWLHVWRDSSUHFLDWH DQGDSSO\VWDWLVWLFDOWHFKQLTXHVLQDUDQJHRIµZRUNSODFH¶VLWXDWLRQVDQG DQDO\VHUHODWHGUHDOOLIHSUREOHPVIRUH[DPSOHWKHPLQLPXPKRXUO\ ZDJHDVUHODWHGWRSURGXFWLRQVKDUHSULFHVSUR¿WVDQGSRWHQWLDO JURZWKRUFORVXUHRIWKHFRPSDQ\ Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 71 Appendix 3 D Appendices Appendix 3 Codes Type of code Use of code Code number National FODVVL¿FDWLRQFRGHV (YHU\TXDOL¿FDWLRQLVDVVLJQHGWRDQDWLRQDO FODVVL¿FDWLRQFRGHLQGLFDWLQJWKHVXEMHFWDUHDWR ZKLFKLWEHORQJV&HQWUHVVKRXOGEHDZDUHWKDW VWXGHQWVZKRHQWHUIRUPRUHWKDQRQH*&6( TXDOL¿FDWLRQZLWKWKHVDPHFODVVL¿FDWLRQFRGHZLOO KDYHRQO\RQHJUDGHWKHKLJKHVWFRXQWHGIRUWKH SXUSRVHRIWKHVFKRRODQGFROOHJHDFKLHYHPHQWDQG DWWDLQPHQWWDEOHV National 4XDOL¿FDWLRQV )UDPHZRUN14) codes (DFKTXDOL¿FDWLRQWLWOHLVDOORFDWHGD4&$1DWLRQDO 4XDOL¿FDWLRQV)UDPHZRUN14)FRGH The QAN for the TXDOL¿FDWLRQLQWKLV SXEOLFDWLRQLV Unit code Each unit is assigned a unit code. 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Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 73 Appendix 4 D Appendices Edexcel GCSE in Statistics Formulae Sheet Foundation Tier Mean of a frequency distribution Mean of a grouped frequency distribution 74 Edexcel GCSE in Statistics = ∑ fx ∑f = ∑ fx , where x is the mid-interval value. ∑f Specification © Edexcel Limited 2008 Appendix 4 Appendices D Edexcel GCSE in Statistics Formulae Sheet Higher Tier Mean of a frequency distribution = ∑ fx ∑f Mean of a grouped frequency distribution = ∑ fx , where x is the mid-interval value. ∑f Variance = ∑ (x − x ) 2 n Standard deviation (set of numbers) or x 2 x 2 n n ( x x )2 n where x is the mean set of values. Standard deviation (discrete frequency distribution) 2 fx 2 fx f f or f ( x x )2 f 6SHDUPDQ¶VUDQNFRUUHODWLRQFRHI¿FLHQW Edexcel GCSE in Statistics 1− 6∑ d 2 n(n 2 − 1) Specification © Edexcel Limited 2008 75 Appendix 5 D Appendices Appendix 5 Controlled assessment Nature of controlled assessment &RQWUROOHGDVVHVVPHQWZLOOFRQVLVWRIRQHPDMRUSURMHFW 7KHWDVNFKRVHQDQGGDWDFROOHFWHGVKRXOGJLYHVWXGHQWVRSSRUWXQLWLHVWR VDWLVI\DOORIWKHFRQWUROOHGDVVHVVPHQWREMHFWLYHV Setting, administering and supervising controlled assessment 7KHFRQWUROOHGDVVHVVPHQWFRPSRQHQWFRQWULEXWHVWRWKH¿QDO DVVHVVPHQW7KHWLPHGHYRWHGWRWKHFRQWUROOHGDVVHVVPHQWDQG DVVRFLDWHGVNLOOVVKRXOGUHÀHFWWKHZHLJKWLQJRIWKHFRPSRQHQW 6WXGHQWVPD\FKRRVHDQ\OLQHRIHQTXLU\IRUWKHLUSURMHFWZLWKLQWKH WDVNVHWE\(GH[FHO&HQWUHVVKRXOGDGDSWWKHWDVNWRVXLWWKHLURZQ FLUFXPVWDQFHVDQGDFFHVVWRUHVRXUFHV7KHSURMHFWPD\UHÀHFWSHUVRQDO LQWHUHVWVRIWKHVWXGHQWRUORFDOLQWHUHVWVEXWVKRXOGEHFKRVHQWRHQVXUH WKDWWKHIXOOUDQJHRIVWDWLVWLFDOWHFKQLTXHVRSHQWRWKHVWXGHQWFDQEH demonstrated. 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(DFKVWDJHVKRXOGEHFDUULHGRXWZLWKLQWKHVXJJHVWHGWLPHDOORZDQFHV ZLWKWKHDSSURSULDWHOHYHORIVXSHUYLVLRQ Supporting evidence 6WXGHQWVXEPLVVLRQVPXVWEHDQQRWDWHGWRVKRZZKHUHWKHFUXFLDO HYLGHQFHEHKLQGWKHDZDUGLQJRIDPDUNLQHDFKVWUDQGFDQEHIRXQG :KHQWKHDVVHVVPHQWVDUHFRPSOHWHWKHPDUNVDZDUGHGXQGHUHDFK RIWKHVWUDQGVDQGDQRYHUDOOPDUNRXWRIPXVWEHHQWHUHGRQ the Student Record FormZLWKZKHUHDSSURSULDWHDQ\VXSSRUWLQJ LQIRUPDWLRQLQWKHVSDFHVSURYLGHG Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 79 Appendix 5 D Appendices Standardisation Internal standardisation (DFKFHQWUHLVUHTXLUHGWRVWDQGDUGLVHDFURVVWHDFKHUVPDUNLQJWKH controlled assessment component and teaching groups entering the H[DPLQDWLRQ,QFDVHVZKHUHPRUHWKDQRQHWHDFKHUKDVEHHQLQYROYHG LQWKHPDUNLQJRIWKHFRQWUROOHGDVVHVVPHQWRQHWHDFKHUPXVWEH GHVLJQDWHGDVEHLQJUHVSRQVLEOHIRUWKH¿QDOPDUNVLJQLQJWKHStudent Record FormDQGIRUWKHVWDQGDUGLVDWLRQRIVWXGHQWZRUN &HQWUHVDUHDGYLVHGWRKROGWUDLQLQJVHVVLRQVIRULQWHUQDOPDUNHUV Moderation The sample for moderation &HQWUHVZLOOEHLQIRUPHGEHIRUHWKHH[DPLQDWLRQRIWKHVDPSOHWKH\ VKRXOGVHQGIRUPRGHUDWLRQ7KLVVDPSOHZLOOEHFKRVHQDWUDQGRP +RZHYHULWVKRXOGDOZD\VFRQWDLQERWKWKHKLJKHVWDQGORZHVWPDUN DZDUGHGE\WKHFHQWUHVRLIWKHVHDUHQRWLQFOXGHGLQWKHVHOHFWHG UDQGRPVDPSOHWKHFHQWUHZLOOEHDVNHGWRDGGWKHPWRWKHVDPSOH The moderator :HZLOODVVLJQDPRGHUDWRUWRHDFKFHQWUH7KHVDPSOHIRUPRGHUDWLRQ VKRXOGEHVHQWGLUHFWO\WRWKHPRGHUDWRUE\WKHFHQWUH Feedback 7KHFHQWUHZLOOUHFHLYHEULHIIHHGEDFNQRWHVIURPWKHPRGHUDWRU ZKLFKZLOOKLJKOLJKWDQ\SUREOHPDUHDVLQWKHPDUNLQJRIWKHFRQWUROOHG assessment. 80 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Appendix 6 Appendix 6 Appendices D Controlled assessment marking criteria Introduction &RQWUROOHGDVVHVVPHQWLVPDUNHGRQDFRPPRQPDUNVFDOHDFURVVERWK WLHUVRIHQWU\7KHPD[LPXPPDUNLVZKLFKZHWKHQFRQYHUWWRD PDUNRXWRIE\DGLUHFWVFDOLQJIDFWRUIRUHDFKWLHURIHQWU\ (DFKSLHFHRIZRUNPXVWEHDVVHVVHGXQGHUWKHIROORZLQJVWUDQGKHDGLQJV ZLWKWKHPDUNIRUHDFKVWUDQGUHFRUGHGRQWKHStudent Record FormVHH Appendix 7 7KHDVVHVVPHQWFULWHULDDUHVXEGLYLGHGLQWRIRXUVWUDQGVWKHVHEHLQJ 1 3ODQQLQJ 2a Data collection 2b 3URFHVVLQJDQDO\VLQJDQGUHSUHVHQWLQJGDWD 3 ,QWHUSUHWDWLRQDQGGLVFXVVLRQRIUHVXOWV 6WUDQGVDQGZLOOEHRQDPDUNVFDOH6WUDQGDZLOOEHRQDQ PDUNVFDOHDQG6WUDQGEZLOOEHRQDPDUNVFDOH 7KHPDUNDZDUGHGLQHDFKVWUDQGPXVWUHÀHFWWKHGHJUHHRIGLI¿FXOW\ DQGVRSKLVWLFDWLRQRIWKHOLQHRIHQTXLU\ Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 81 Appendix 6 D Appendices Quality of Written Communication (QWC) &RQWUROOHGDVVHVVPHQWVIRUWKH(GH[FHO*&6(LQ6WDWLVWLFVSURYLGH RSSRUWXQLWLHVDFURVVDELOLW\UDQJHVWRDVVHVV4XDOLW\RI:ULWWHQ &RPPXQLFDWLRQ4:& (DFKVWDJHRIWKHFRQWUROOHGDVVHVVPHQWRIIHUVRSSRUWXQLWLHVZKHUH i) student ensures text is legible spelling, punctuation and grammar are accurate that meaning is clear ii) students select and use a form and style of writing appropriate to purpose and to complex subject matter iii) students organise information clearly and coherently, using specialist vocabulary when appropriate. 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QWC (ii) 7KHGDWDVKRXOGEHVKRZQLQVRPHZD\ 7KH\PD\XVHWKHZKROHSRSXODWLRQEXWVKRXOGLQGLFDWHWKDWWKH\DUHGRLQJVR7KHZRUG FHQVXVLVQRWUHTXLUHGDWWKLVOHYHO 4 7KHVWXGHQWXVHVDUHFRJQLVHGVDPSOLQJPHWKRGDQGJLYHVDEULHIDFFRXQWRIKRZWKHGDWD ZDVFROOHFWHGDQGLWVVRXUFH 7KHVWXGHQWFROOHFWVVXI¿FLHQWGDWDLQWZRRUPRUHGDWDVHWVWRPDNHFRPSDULVRQV ,IDFHQVXVLVXVHGUHDVRQVIRUWKLVPXVWEHJLYHQ 5 QWC (iii) 7KHVWXGHQWXVHVDUHFRJQLVHGVDPSOLQJPHWKRGDQGJLYHVDGHWDLOHGDFFRXQWRIKRZWKH\ collected their data. 7KH\GLVFXVVWKHW\SHVRIGDWDZKLFKPD\EHGLVFUHWHFRQWLQXRXVTXDOLWDWLYHRU TXDQWLWDWLYH $Q\DQRPDOLHVLQWKHGDWDFROOHFWHGVKRXOGEHLGHQWL¿HGDVWKH\RFFXU 6 7KHVWXGHQWJLYHVDGHWDLOHGDFFRXQWRIWKHsampling mechanism for their data collection DQGMXVWL¿HVWKHVL]HRIWKHVDPSOH $Q\DQRPDOLHVVKRXOGEHLGHQWL¿HGDVWKH\RFFXUDQGDGHFLVLRQPDGHZLWKreasons, as to ZKHWKHUWKH\VKRXOGEHLQFOXGHGRURPLWWHG 7 7KHVWXGHQWMXVWL¿HVWKHLUFKRLFHRIDSDUWLFXODUVDPSOLQJWHFKQLTXH /LPLWVIRURXWOLHUVVHWDWWKHSODQQLQJVWDJHVKRXOGKDYHEHHQXVHG 3UREOHPVLQGDWDFROOHFWLRQZKLFKZHUHLGHQWL¿HGDWWKHSODQQLQJVWDJHIRUH[DPSOHGLIIHUHQW VL]HGSRSXODWLRQVRUVDPSOHVPLVVLQJGDWDKDYHEHHQDFWHGXSRQ 8 QWC (ii) and QWC (iii) 84 5HOLDELOLW\RIWKHGDWDVRXUFHVKRXOGEHGLVFXVVHGZLWKUHIHUHQFHWRVRXUFHFROOHFWLRQ VWUDWHJ\DQGWKHSURSRUWLRQRIDQRPDOLHVIRXQG %LDVKRZLWPD\DULVHDQGZKDWLVEHLQJGRQHWRDYRLGLWVKRXOGEHGLVFXVVHG $OORIWKHWHFKQLTXHVXVHGIRUVDPSOLQJDQGGHDOLQJZLWKSUREOHPVPXVWEHMXVWL¿HG Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Appendix 6 2b: Appendices D Processing, analysing and representing data (12 marks) Mark Performance descriptor 0 7KHVWXGHQWGRHVQRWDWWHPSWWRGUDZDVLPSOHGLDJUDPRUSHUIRUPDFDOFXODWLRQ 1 7KHVWXGHQWDWWHPSWVWRGUDZDVLPSOHGLDJUDPRUSHUIRUPDFDOFXODWLRQ 2 7KHVWXGHQWSURGXFHVDVLPSOHGLDJUDPFRUUHFWODEHOVDQGVFDOHVRUFDOFXODWLRQ VXFFHVVIXOO\ 3 The student produces a simple correct statistical diagram or calculation. 4 7KHVWXGHQWSURGXFHVVLPSOHFRUUHFWVWDWLVWLFDOGLDJUDPVDQGFDOFXODWLRQV7KHVHPD\EH VLPSO\WRGLVSOD\RUVXPPDULVHWKHGDWD 5 7KHVWXGHQWSURYLGHVDGLDJUDPorFDOFXODWLRQWRPDNHDVLPSOHFRPSDULVRQIROORZLQJRQ from their planning. QWC (iii) 6 The student uses diagrams andFDOFXODWLRQVWRPDNHVLPSOHFRPSDULVRQVIROORZLQJRQIURP their planning. $WOHDVWRQHRIWKHVWDWLVWLFDOWHFKQLTXHVVKRXOGEHPRUHFRPSOH[WKDQWKHWHFKQLTXHVXVHG IRUPDUN 7KHGLDJUDPVPXVWEHFRUUHFWZLWKVFDOHVDQGODEHOV 7 7KHVWXGHQWXVHVGLDJUDPVDQGFDOFXODWLRQVWRPDNHDFRPSDULVRQDWOHDVWRQHRIZKLFK PXVWEHPRUHFRPSOH[ 8 7KHVWXGHQWXVHERWKGLDJUDPVDQGFDOFXODWLRQVZKLFKPXVWEHPRUHFRPSOH[WRPDNH comparisons. 9 7KHVWXGHQWMXVWL¿HVWKHLUXVHRIGLDJUDPVDQGFDOFXODWLRQVKDYLQJHQVXUHGWKDWGLDJUDPV HQDEOHFRPSDULVRQVWREHPDGH QWC (ii) 7KH\GUDZDVHULHVRIGLDJUDPVDQGSHUIRUPFDOFXODWLRQVWRH[SORUHRQHRUPRUHYDULDEOHV ZLWKRXWPDNLQJFRQQHFWLRQVEHWZHHQWKHYDULDEOHV 10 7KHVWXGHQWXVHVGLDJUDPVDQGFDOFXODWLRQVWRWHVWDFRPSOH[K\SRWKHVLV QWC (ii) and QWC (iii) 7KH\GUDZDVHULHVRIGLDJUDPVDQGSHUIRUPFDOFXODWLRQVWRH[SORUHRQHRUPRUHYDULDEOHV ZLWKRXWPDNLQJFRQQHFWLRQVEHWZHHQWKHYDULDEOHV 7KHZRUNLVDFFXUDWHZLWKIHZHUURUV 7KHUHLVOLWWOHLUUHOHYDQWZRUNSUHVHQWDQGRXWOLHUVDUHFRQVLGHUHGLIWKH\RFFXU 11 7KHVWXGHQWVKRXOGFRQVLGHUDQXPEHURILQWHUUHODWHGYDULDEOHVDQGXVHDQXPEHURI GLIIHUHQWWHFKQLTXHVWRH[SORUHSRVVLEOHFRQQHFWLRQVRUHIIHFWV 7KH\GUDZDVHULHVRIGLDJUDPVDQGSHUIRUPFDOFXODWLRQVWRH[SORUHRQHRUPRUHYDULDEOHV PDNLQJFRQQHFWLRQVEHWZHHQallWKHYDULDEOHV $WOHDVWRQHRIWKHWHFKQLTXHVWKH\XVHPXVWEHFRPSOH[ 12 QWC (ii) and QWC (iii) 7KHVWXGHQWVKRXOGFRQVLGHUDQXPEHURILQWHUUHODWHGYDULDEOHVDQGSODQWRXVHDQXPEHU RIGLIIHUHQWWHFKQLTXHVEH\RQGWKRVHDVVRFLDWHGZLWKPDUN7KH\OLQNGLDJUDPVDQG FDOFXODWLRQVWRH[SORUHSRVVLEOHFRQQHFWLRQVGLVWULEXWLRQVRUHIIHFWV 7KHVWXGHQWPXVWGHDOZLWKWKHSUREOHPVWKH\IRUHVDZLQWKHLUSODQDQGMXVWLI\WKHLU approach. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 85 Appendix 6 D Appendices 3: Interpreting and evaluating data Marks Performance indicator 0 7KHVWXGHQWPDNHVQRFRPPHQWVDERXWWKHGDWD 1 7KHVWXGHQWPDNHVDFRPPHQWDERXWWKHGDWD (10 marks) )RUH[DPSOH,FROOHFWHGSLHFHVRIGDWD 2 7KHVWXGHQWPDNHVDFRPPHQWWRGUDZDFRQFOXVLRQDERXWWKHGDWD )RUH[DPSOH7KHODUJHVWLV 3 7KHVWXGHQWPDNHVDVLPSOHVWDWLVWLFDOFRPPHQWDERXWWKHGLDJUDPRUFDOFXODWLRQ )RUH[DPSOH7KHPRGHLV 4 7KHVWXGHQWLQWHUSUHWVDGLDJUDPRUFDOFXODWLRQXVLQJDVLPSOHWHFKQLTXHVWRPDNHDVLPSOH statistical comparison. )RUH[DPSOH7KHEDUFKDUWVVKRZWKDWWKHPRVWSRSXODUGULQNLV;'ULQN<LVWKHOHDVWSRSXODU 5 The student interprets a diagram andFDOFXODWLRQWRPDNHDVLPSOHVWDWLVWLFDOFRPSDULVRQ QWC (iii) ,QWKHFDVHRIPXOWLSOHFRQFOXVLRQVDWOHDVWRQHEXWQRWDOOQHHGWREHFRUUHFW 6 The student summarises their resultsDQGFRPPHQWXSRQWKHLUZRUN QWC (ii) 7KH\PDNHVRPHVLPSOHZULWWHQFRPSDULVRQV 7 7KHVWXGHQWVXPPDULVHVDQGPDNHVGHWDLOHGH[SODQDWLRQVRIWKHLUUHVXOWVZLWKFRUUHFW interpretations of statistical techniques. 7KH\FRUUHFWO\LQWHUSUHWWKHLUGDWDDQGPDNHFRPSDULVRQV 8 QWC (ii) and QWC (iii) 9 QWC (ii) and QWC (iii) 10 QWC (ii) and QWC (iii) 7KHVWXGHQWVXPPDULVHVDQGPDNHVGHWDLOHGH[SODQDWLRQVRIWKHLUUHVXOWVZLWKFRUUHFW LQWHUSUHWDWLRQVRIVWDWLVWLFDOWHFKQLTXHV7KH\FRUUHFWO\LQWHUSUHWWKHLUGDWDPDNLQJLQGHSWK comparisons and commenting on the effect of anomalies in their data. 7KH\HYDOXDWHWKHLUVDPSOLQJRUVWUDWHJ\ 7KHVWXGHQWVXPPDULVHVWKHLUVWUDWHJ\GLVFXVVLQJWKHLQWHUUHODWLRQVKLSVEHWZHHQWKH YDULDEOHVLQWHUSUHWLQJWKHLUUHVXOWVDQGHYDOXDWLQJWKHLUSODQQLQJ 7KH\UHODWHVXPPDU\VWDWLVWLFVWRFRQ¿UPRUUHIXWHWKHLUK\SRWKHVLV $OOWHFKQLTXHVVRPHRIZKLFKPXVWEHFRPSOH[PXVWEHXVHGDQGFRPPHQWHGXSRQ 7KHVWXGHQWVXPPDULVHVDQGHYDOXDWHVDVDERYHWRXVHDQXPEHURIGLIIHUHQWWHFKQLTXHVDW OHDVWRQHRIZKLFKPXVWEHDWPRUHFRPSOH[WKDQWKRVHIRUPDUN$OOFRPPHQWDULHVVKRXOG EHFRUUHFWDQGFRQFLVH $Q\OLPLWDWLRQVDUHGLVFXVVHGDQGTXDQWL¿HG GE6?/7?3'?*&6(?*&6(67$7,67,&663(&,668(,1''± 86 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 Appendix 7 Appendix 7 Appendices D Student Record Form &DQGLGDWHQDPH Total mark out of 40: &DQGLGDWHQXPEHU &HQWUHQDPH &HQWUHQXPEHU Date completed Planning (10 marks) Teacher’s advice to student Student’s changes to initial plan Please record marks and additional comments on the next page. Edexcel GCSE in Statistics Specification © Edexcel Limited 2008 87 Appendix 7 D Appendices For the teacher-examiner’s, and moderator’s use Assessment Objective Centre mark Moderator mark Comments $GGLWLRQDOFRPPHQWVWRMXVWLI\PDUN Planning (10 marks) Data collection (8 marks) Processing, analysing and representing data (12 marks) Interpreting and discussing data (10 marks) Other comments: 88 Edexcel GCSE in Statistics Specification © Edexcel Limited 2008