Controlled Assessment Teacher Guidance for Controlled Assessment For submission May 2012 only

Edexcel GCSE Statistics Unit 2 Theme: Paper and Pencil Controlled Assessment Teacher Guidance for Controlled Assessment For submission May 2012 only Paper Reference 5ST02/01 You do not need any other materials. This teacher guidance for the controlled assessment task is valid from March 2011 to May 2012. Centres must submit their moderation sample(s) by May 2012. Please note that this controlled assessment task will ONLY be valid for assessment in May 2012. Teachers must ensure that students are completing the correct task for a particular year. Further guidance can be found on the Edexcel website (www.edexcel.com). Turn over 2012 Edexcel Limited. 6/5/5 **

THEME: PAPER AND PENCIL Introduction This task gives scope for students of all abilities to produce projects. Students will need guidance in choosing the questions they are going to pose. The questions will need to enable the students to use statistical techniques based on the specification content of this GCSE. They will also need advice about the collection of data. The controlled assessment must be done in three stages. 1: Planning Formal supervision (Classroom/IT suite) (see Specification page 79) 10 marks (1 to 2 weeks curriculum time (approx. 1 2 hours)) This will take place under formal supervision. The students should be supervised at all times, but this is not examination conditions and students should be encouraged to discuss their planning with the teacher. This can take place over more than one lesson but students cannot take any of their work out of the classroom. Student access to resources is determined by what is available in the centre. Whilst word processors and spreadsheets may be useful NO INTERNET ACCESS should be available. Students are not allowed access to their plans outside formal supervision and all word processed material needs to be stored safely. Suggestions as to how the task can be approached can be discussed. Discuss with students: What sort of questions can be asked? Draw out of the students the possible questions they might consider. This will determine the sort of data they might collect. Suggestions for investigation: Comparison of male and female scores when doing a paper based spelling/number test. The time it takes to complete a paper based puzzle. The time it takes to make a paper model (e.g. aeroplane, boat). The distance a model paper aeroplane will fly. Estimation of the areas of regular shapes drawn on paper or the lengths of lines/ curves drawn on paper. Distribution of the errors made when estimating. 2

What data will be needed? This should include discussion of the population and how much data will be needed. (Generally at least 30 pieces required but at least 60 are needed for more complex work.) What is the population from which the data will be collected? How reliable is the data? What data is to be collected and how will it be recorded? Which sampling method will be used and why? How large should the sample be? What problems might arise and how will they be overcome? How might bias arise and how can this be minimised? How could the data be collected? What data sheets will be required? Students may collect data in groups but they will need to give an explicit account in their plan of how they will do this. What statistical techniques can be used? Whilst the use of techniques must be an integral part of the project, students require some guidance as to what is expected at each level. It should be pointed out that making a choice of techniques with reasons is essential if the student is to achieve marks for planning. Students should be encouraged to be selective. Some statistical techniques are more sophisticated than others. Students should choose techniques that suit their ability. The better students should be advised that the complexity of their investigation will be limited if their hypotheses and choice of techniques do not allow them to produce work of a reasonable degree of complexity. Here are some suggested questions and related analyses. Low demand Students undertaking investigations involving low demand activities might consider: The average score/range for females and for males for spelling/number problems. Are males better than females at spelling/number problems? Does age affect how good you are at number problems/spelling? Are males better at estimating areas of paper than females? From these, students could make simple comparisons of single variables involving techniques/calculations such as: totals, measures of central tendency, measures of dispersion (spread), simple random sampling. Representations of data could involve diagrams such as: tally chart, data tables, pictograms, bar charts, multiple bar charts, line/stick graphs, stem and leaf diagrams, scatter diagrams. 3 Turn over

Mid demand Students undertaking investigations involving mid demand activities might consider: How the distributions of scores for number/spelling tasks differ between boys and girls. Do students who do well at spelling also do well at number problems? How the distributions of times to do a paper puzzle/make a paper model, differ between males and females. Is there a relationship between the time it takes to make a paper aeroplane and the distance it flies? How the estimates vary between boys and girls and between different age groups. From these, students could make comparisons of one or more variables involving techniques/calculations such as: measures of central tendency, measures of dispersion (spread), quartiles, stratified sampling. Representations of data could involve diagrams such as: scatter diagrams (with line of best fit), box plots, cumulative frequency diagrams, histograms with equal intervals. High demand Students undertaking investigations involving high demand activities might consider: How different age groups compare. The correlation between the time it takes to make a paper aeroplane and the distance it flies. Standardised scores for various tests. Whether the time taken to complete a puzzle/make a paper model can be modelled by a normal distribution. Whether the distance flown by paper aeroplanes can be modelled by a normal distribution. Whether the errors in estimating areas/lengths can be modelled by a normal distribution. From these, students could consider the interrelationships between several variables involving advanced techniques/calculations such as: Spearman s rank correlation coefficient, standardised scores, calculation of errors, frequency density, formal identification of outliers, the normal distribution, standard deviation. Representations of data could involve diagrams such as: frequency density, histograms with equal/unequal intervals, normal curves, scatters with lines of best fit/curves, comparative pie charts. Occasionally a very able candidate wants to go beyond the specification and this can be encouraged, however, the highest marks may be awarded for the creative application of techniques within the specification. Candidates going beyond the specification must offer a full explanation and justification for the techniques they use. Students must complete all work independently. Once students have planned their investigation, they should hand their work in to the teacher. The teacher will mark and give feedback on the plan to the student and note the feedback on the Student Record Form. Teachers can give advice, but not undue help, regarding the suitability of the student s choices in their feedback to the students. 4

At this point students can amend their plan in the light of the teacher s comments. The mark given for planning cannot be changed. 2a: Collecting, processing and representing data Informal supervision (see Specification page 79) ICT may be used at this stage. Collecting data (8 marks) (approx 2 3 hours) This should have been planned in Stage 1. Any necessary data collection sheets should be prepared. Data may be collected from the Internet. There are many useful sites (see below for some suggestions). Students may want to collect data in small groups, but their contribution should be recorded in their plan. 2b: Processing, analysing and representing data (12 marks) (approx 2 4 hrs) This means that the students need to draw relevant diagrams and do relevant calculations. The use of ICT is encouraged but not essential. There is no need to show evidence of calculations or hand drawn diagrams as these skills are assessed in the external assessments. It is important that ICT is used sensibly and diagrams have sensible scales and labels. 3: Interpret and evaluate Formal supervision (Classroom/ICT suite) 10 marks (up to 2 hours) Students may bring in work from outside the classroom but the teacher will need to monitor the work in the classroom to ensure it relates to the initial plan. The initial plan may have been developed and adapted and this is to be encouraged, but only following discussion with the teacher. This is to ensure that the project is the work of the individual student. Students must bring all the work they have compiled to the classroom and put together the whole report. Work can be handwritten or word processed. Students will need to produce in final form: The written up hypothesis/es with their planned strategy. The data collection discussion describing exactly what they did. Raw data in an appendix with summary tables in the main body of the report. Problems that arose and limitations of the data should be discussed. Reasons for choice should accompany the analysis. Diagrams and calculations should be interpreted. There should be an interpretation in the context of the whole investigation relating back to the original questions and hypotheses. Conclusions linking together the strands of their enquiry. Evaluation of the work discussing any limitations. A completed Student Record Form to accompany the work and an authentication form signed by the student. When completed the work is handed in. This must be at the end of the highly controlled time there must be no extension for finishing at home. 5 Turn over

The teacher will need to complete the student record form, with their marks and any other information, which should be attached to the front of the project. Possible data sources This is really a theme that uses primary data. The following are some Internet sources that might prove helpful. There are many others. www.printable-puzzles.com/ Crosswords, word searches, logic www.users.tpg.com.au/users/puzzles/ Number/word puzzles www.bestpaperairplanes.com/ Aeroplane templates www.funpaperairplanes.com/ Aeroplane templates 6

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(Confidential for teachers use only) Assessment criteria Theme: Paper and Pencil 1: Planning Mark Performance descriptor Exemplification 0 The student supplies no evidence of an implicit plan to process or display some data. 1 The student provides evidence of an implicit plan to process or display some data. Decides to do some sort of task involving Paper and Pencil. 2 The student gives a clear aim to process or display some data. Poses a question relating to the task decided upon. 3 The student chooses a simple aim providing a strategy to use a simple statistical technique to process or display data. Poses a question relating to the task decided upon and suggests at least one technique that might be used. The technique can be low demand. 4 The student chooses a simple aim providing a strategy to use a simple statistical technique (diagram or calculation) to make a comparison. Poses a question relating to the task decided upon and suggests at least one low demand technique (diagram or calculation) that might be used to compare. 5 The student chooses a simple aim providing a strategy to use a diagram and calculation to make a comparison. Poses a question relating to the task decided upon and suggests a statistical diagram and a calculation that might be used to compare. These should be appropriate to the aim. They can be mid/low demand. 6 The student chooses a more complex line of enquiry to use statistical techniques, to make a comparison. They give a clear aim with sensible reasons for the diagrams and calculations they will use. The student poses a question/aim relating to the task decided that requires the use of mid demand techniques. These should be simply justified and appropriate to the hypothesis. Where appropriate comparisons should be made. 7 The student chooses a more complex line of enquiry to use statistical techniques to make a comparison. They give clear aims and justify which diagrams and calculations they use. They identify potential problems with the data (e.g. anomalies, different sized populations, scales etc.) As for a mark of 6 but a detailed justification of chosen techniques is required. Students should note possible problems that might arise in the data collection. Results should be predicted. 8 The student plans to test a hypothesis, which has been carefully specified in clear statistical terms. They give a clear aim and justify all of the diagrams and calculations they use ensuring that diagrams are drawn so that comparisons can be made. They plan how they will deal with any potential problems with the data. Students must plan to use at least one high demand technique. All techniques must be appropriate to clearly specified hypothesis/es. Students must justify in detail all the techniques they choose to use. Possible problems should be identified and a way of tackling them, should they arise, suggested. 8

9 The student plans to test hypotheses, which have been carefully specified in clear statistical terms. They should consider a number of interrelated variables and justify their plan to use a number of different techniques. They must plan and justify how they will deal with any potential problems with the data. 10 The student plans to test hypotheses, which have been carefully specified in clear statistical terms. They must foresee possible problems, which might arise and justify their methods for dealing with these. They should consider a number of interrelated variables and plan to use a number of different advanced techniques. More than one hypothesis should be posed. More than one variable should be considered and they should be related in some way. Data collection must be explicitly described. Possibility of bias should be discussed. A suggestion as to how possible outliers could be identified needs to be given. At least one high demand technique should be used. Supporting mid/low level demand work should be used where appropriate. The student should be planning to use a number of different but appropriate high demand techniques. Supporting mid/low level demand work should be used where appropriate. Problems should be dealt with. Discussion of anomalies/outliers etc on the validity of the data should be considered. 9 Turn over

2a: Data collection Mark Performance indicator Exemplification 0 The student does not use any data. 1 The student uses some data. The student collects some data (this may be implied) or produces a test or template. 2 The student collects some data (at least 10 items). The student shows evidence of collecting at least 10 pieces of data. 3 The student collects some data, indicates its source and how it was collected. The data should be shown in some way. They may use the whole population but should indicate that they are doing so. (The word census is not required at this level) The data source both for the task and the subjects doing the task is stated and there is some effort to explain how the actual data was collected. If the whole population is used this should be stated. The data is shown in a list or table. The task to be used should be clearly presented. This is low demand work. 4 The student uses a recognised sampling method and gives a brief account of how the data was collected and its source. The student collects enough data in two or more data sets to make comparisons. If a census is used reasons for this must be given. At least two sets of 25 pieces of data are collected using one or more tasks. A recognised sampling method should be used if sampling takes place. If internet data puzzles/tests are used a simple reason for their choice should be given. This is mid demand work. 5 The student uses a recognised sampling method and gives a detailed account of how they collected their data. They discuss the type(s) of data which may be discrete, continuous, qualitative or quantitative. Any anomalies in the data should be identified as they occur. There is a detailed account of how the data was collected. The method should be appropriate. Task sheets are presented in the appendix and their appropriateness discussed. Anomalies and possible bias is discussed. 6 The student gives a detailed account of the sampling mechanism for their data collection and justifies the size of the sample. Any anomalies should be identified as they occur and a decision made, with reasons as to whether they should be included or omitted. The sample sizes are appropriate and justified (or a census if that is used). If sampling is used the mechanism should be explicitly explained. The effect of leaving in or omitting outliers, if they exist, should be discussed. This is high demand work. 7 The student justifies their choice of a particular sampling technique. Limits for outliers set at the planning stage should have been used. Problems in data collection and which were identified at the planning stage (for example, different sized populations or samples, missing data) have been acted upon. As well as the requirements for 6, any outliers/anomalies should be identified and dealt with. Problems suggested in the plan should be considered and identified if they have arisen. 10

8 Reliability of the data source should be discussed with reference to source, collection strategy and the proportion of anomalies found. Bias, how it may arise and what is being done to avoid it should be discussed. All of the techniques used for sampling and dealing with problems must be justified. There should be discussion as to whether the sample collected is a good representation of the population. There should be some discussion on the reliability of the data (e.g. difficulty of timing/measuring). If it is not then consideration should be given as to whether another sample would improve the investigation. There should be detailed discussion of the problems that arose in collecting the data and what was done to solve the problems. (e.g. problems with people understanding the tasks, cheating etc.) 11 Turn over

2b: Processing, analysing and representing data Mark Performance criteria Exemplification 0 The student does not attempt to draw a simple diagram or perform a calculation. 1 The student attempts to draw a simple diagram or perform a calculation. The student attempts to draw a low demand diagram (e.g. pictogram simple bar chart, line graph, data table, simple pie chart) or calculate a total, average or range. Some errors acceptable. 2 The student produces a simple diagram (correct labels and scales) or calculation successfully. The student attempts to draw a low demand diagram or calculate a total, average or range. The work is mostly correct. 3 The student produces a simple correct statistical diagram or calculation. The student attempts to draw an appropriate low demand diagram or calculate a total, average or range. The work is all correct. 4 The student produces simple correct statistical diagrams and calculations. These may be simply to display or summarise the data. The student attempts to draw a low demand diagram and calculate a total, average or range. The work is correct. It may not be interpreted in any way. 5 The student provides a diagram or calculation to make a simple comparison following on from their planning. In addition to mark 4 the candidate considers two data sets and makes a simple comparison. This could be by commenting on a multiple bar chart or comparing a measure of centrality. 6 The student uses diagrams and calculations to make simple comparisons following on from their planning. At least one of the statistical techniques should be more complex than the techniques used for mark 4. The diagrams must be correct with scales and labels. The student makes a comparison using both a diagram and a calculation. 7 The student uses diagrams and calculations to make a comparison at least one of which must be more complex. The student needs to compare using at least one mid demand technique. (e.g. scatters with lines of best fit for correlation, cf diagrams, ranges, quartiles). 8 The student use diagrams and calculations to make comparisons which must be more complex. The student needs to compare using more than one mid demand technique. (e.g. box plots for comparison). 9 The student justifies their use of diagrams and calculations having ensured that diagrams enable comparisons to be made. They draw a series of diagrams and perform calculations to explore one or more variables without making connections between the variables. Students need to use a variety of techniques that are appropriate. Comparative diagrams must have the same scale. All diagrams and calculations are justified in writing in the plan or as a result of intermediate interpretations. 12

10 The student uses diagrams and calculations to test a complex hypothesis. They draw a series of diagrams and perform calculations to explore one or more variables without making connections between the variables. The work is accurate with few errors. There is little irrelevant work present and outliers are considered if they occur. 11 The student should consider a number of interrelated variables and use a number of different techniques to explore possible connections or effects. They draw a series of diagrams and perform calculations to explore one or more variables making connections between all of the variables. At least one of the techniques they use must be complex. 12 The student should consider a number of interrelated variables and plan to use a number of different techniques beyond those associated with mark 11. They link diagrams and calculations to explore possible connections, distributions or effects. The student must deal with the problems they foresaw in their plan and justify their approach. A series of appropriate and correct diagrams are drawn and correct calculations are carried out. At least one needs to be high demand (e.g. Spearman, standard deviation, frequency density histograms, normal curves). There is little redundancy. Outliers are calculated and acted upon. A number of inter-related variables are used. A series of appropriate and correct techniques are carried out. Connections between variables are carefully explained. At least one technique needs to be high demand. There should be a clear attempt to interpret and use ALL the diagrams and calculations. The student uses a number of high demand techniques that are appropriate to the investigation. The work is done correctly. The whole study is linked and flows in a meaningful way. The techniques are interpreted and used to further the investigation. The presentation of diagrams and calculations is complete and clear. 13 Turn over

3: Interpretation and discussion of results Marks Performance criteria Exemplification 0 The student makes no comments about the data. 1 The student makes a comment about the data, e.g. I collected 10 pieces of data. Makes any simple comment about the investigation. 2 The student makes a comment to draw a conclusion about the data, e.g. the largest is... Makes a comment that summarises the data, e.g. a total. 3 The student makes a simple statistical comment about the diagram or calculation. e.g. The mode is... Uses their graph, chart or calculation. 4 The student uses a diagram or calculation to make a simple statistical comparison. e.g. The bar charts show that the most popular drink is X. Drink Y is the least popular. Compares graphs, charts or calculations. 5 The student interprets diagram and calculation to make a simple statistical comparison. In the case of multiple conclusions at least one but not all need to be correct. Compares both a diagram and a calculation to make a statistical comparison. 6 The student summarises their results and comments upon their work. They make some simple comparison. Summarises which statistical techniques were used and what evidence they produced. Makes some comparisons using mid demand techniques. 7 The student summarises and makes detailed explanations of their results with correct interpretations of statistical techniques. They correctly interpret their data making comparisons. Summarises which statistical techniques were used and what evidence they produced. Interprets their results in the context of their original aims. Some of the techniques discussed must be high demand. 8 The student summarises and makes detailed explanations of their results with correct interpretations of statistical techniques. They correctly interpret their data making in depth comparisons and commenting on the effect of outliers and anomalies in their data. They evaluate their sampling or strategy. Provides a full account of the high demand techniques they have used and interprets their results. Shows statistical understanding by evaluating their strategy and commenting on their data collection. Comments on their strategy for outliers and anomalies if they exist. Considers whether their aims were achieved and whether their predictions were correct. 14

9 The student summarises their strategy discussing the interrelationships between the variables, interpreting their results and evaluating their planning. They relate summary statistics to confirm or refute their hypothesis. All techniques, some of which must be complex, must be used and commented upon. 10 The student summarises and evaluates as above to use a number of different techniques at least one of which must be more complex than those for mark 9. All commentaries should be correct and concise. Any limitations are discussed and quantified. Provides a more formal account relating back to the original hypotheses. Gives a full account of all techniques they have used, some of which should be high demand techniques, and interprets their findings in the context of their investigation. Summarises their results giving detailed explanations and correct interpretations relating back to the hypotheses. All work must be concise and should flow. All techniques should be efficient. Limitations should be discussed. 15

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