Scheme of work (2-year) - Word version · Web viewIssue 2 has been updated by replacing the GCSE...

TheEDEXCEL AWARDS

Edexcel Level 1 Award in Statistical Methods (AST10)Edexcel Level 2 Award in Statistical Methods (AST20)Edexcel Level 3 Award in Statistical Methods (AST30)

For first teaching from January 2013

Issue 2 (September 2016)

Scheme of work

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Contents

Introduction 1Level 1 scheme of work 2Level 1 course overview 4Level 1 modules 6Level 1 concepts and skills (AST10) 26Level 2 scheme of work 28Level 2 course overview 30Level 2 modules 32Level 2 concepts and skills (AST20) 54Level 3 scheme of work 57Level 3 course overview 59Level 3 modules 61Level 3 concepts and skills (AST20) 81Resources Table 83Level 1 83Level 2 84Level 3 85

IntroductionThis scheme of work has been designed for teachers delivering the Edexcel Award in Statistical Methods. This scheme of work is based upon a course model which can be taught over a single year, or more years if desired, for all tier students.

The scheme of work is structured so each topic contains:

Module number Recommended teaching time, though of course this is adaptable according to individual

student needs Level Contents, referenced back to the specification GCSE specification references Prior knowledge and links with the alternative levels Objectives for students at the end of the module Links to the GCSE schemes of work modules At level 3 links to (S1) GCE Mathematics Ideas for differentiation and extension activities Notes for general mathematical teaching points and common misconceptions

Updated versions of this scheme of work will be available via a link from the Edexcel Mathematics Awards website (www.edexcel.com /mathsawards ).

This course can be taught as a stand-alone course.Alternatively it can be taught as an introduction to GCSE Mathematics or GCSE Statistics, with differentiation extending the content from an Awards course into GCSE topics where possible. The links to the GCSE schemes of work are given for this reason. Both the level 1 and level 2 courses can also stand alongside GCSE Statistics and GCSE Mathematics courses at Foundation and Higher respectively. The level 3 course can be used as an introduction to A(S) Mathematics, or even as a bridge between GCSE Mathematics/Statistics and A(S) Mathematics.

This course can be supported by a range of resources. At the end of the document we have provided a table which can be populated with the resources and links of choice to support delivery.

Issue 2 (September 2016)Issue 2 has been updated by replacing the GCSE Mathematics 1MA0 and 2MB01 specification and scheme of work references with those for the new GCSE (9–1) Mathematics 1MA1, for first teaching September 2015. A few small amends have also been made in other places, and these are marked by vertical lines in the margin.

Edexcel Awards in Statistical Methods Scheme of work Issue 2 © Pearson Education Ltd 2016 1

http://www.edexcel.com/

The Edexcel Awardin Statistical Methods

Level 1 (AST10)

Scheme of work

Edexcel Awards in Statistical Methods Scheme of work Issue 2 © Pearson Education Ltd 2016=

2

Level 1 course overview

The table below shows an overview of modules in the Level 1 scheme of work.Teachers should be aware that the estimated teaching hours are approximate and should be used as a guideline only.

Module number Title Estimated teaching hours

1 Types of data 1.52 Population and sampling 23 Data collection 74 Tabulating data 55 Diagrams and representations: discrete data 106 Diagrams and representations: continuous data 107 Measures of central tendency 78 Measures of dispersion 39 Scatter diagrams 5

10 Time series 511 Probability 11

Total 66.5


Module 1 Time: 1 – 2 hours

Awards Tier: Level 1

Contents: Types of data

1.1 Understand and use discrete, continuous and categorical data

GCSE SPECIFICATION REFERENCES

S2 Interpret and construct tables, charts and diagrams … for categorical data, … ungrouped discrete numerical data …

S3 Construct and interpret diagrams for grouped discrete data and continuous data …

S6 Use and interpret scatter graphs of bivariate data …

PRIOR KNOWLEDGESome use of dataWhere data can be found

OBJECTIVESBy the end of the module the student should be able to:

Recognise that data can be obtained from primary and secondary sources Recognise the difference between quantitative and qualitative variables Recognise the difference between discrete and continuous data Recognise and use scales of measurement, eg categorical, rank Categorise data through the use of well-defined, precise definitions or class boundaries Understand, use and define situations for grouped and ungrouped data Understand the meaning of bi-variant data which may be discrete, continuous, grouped

or ungrouped

LINKS TO LEVEL 2 (extension work)Module 1 Types of data

LINKS TO GCSE SCHEME OF WORK (2-year)Foundation Unit 3a and Unit 7

DIFFERENTIATION & EXTENSIONGenerate practical examples of categorical and rank scales of measurementMake a list of possible pairs of bi-variant data, eg height v weightCategories are a range of variables from a variety of everyday contexts


4

NOTESPrimary sources should include raw data, surveys, questionnaires (which may have more than two categories), investigations and experimentsSecondary sources include databases, published statistics, newspapers, internet pages, etcThe use of terms such as class width and class interval is expected




Contents: Population and sampling

1.1 Understand and use discrete, continuous and categorical data

1.2 Design and use simple data collection sheets for discrete and continuous data


S1 Infer properties of populations or distributions from a sample, while knowing the limitations of sampling

PRIOR KNOWLEDGEAn understanding of why data needs to be collected


Understand the meaning of the term population Understand the word census with regard to small scale and large scale populations Understand the reasons for sampling and that sample data is used to estimate

values in a population Understand the terms random, randomness and random sample Understand the use of random numbers Understand, design and use a sampling frame Be able to select a random sample as a method of investigating a population Appreciate how bias in a sampling procedure might occur and how it might be

minimised

LINKS TO LEVEL 2 (extension work)Module 2 Population and sampling At level 2 the range of sample methods will be extended, including stratified sampling

LINKS TO GCSE SCHEME OF WORK (2-year)Foundation Unit 7

DIFFERENTIATION & EXTENSIONTake a stratified sample with more than one category, eg gender and age groupInvestigate other methods of sampling, eg systematic sampling

NOTESRandom numbers may be collected from random number tables, calculators and spreadsheetsAn appreciation of an appropriate sample size is expectedDesigning a sample frame is expected


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Contents: Data collection

1.2 Design and use simple data collection sheets for discrete and continuous data, using tallies including grouped frequencies

1.3 Criticise a question for a questionnaire



S2 Interpret and construct tables, … including frequency tables …

PRIOR KNOWLEDGEExperience of simple tally chartsExperience of inequality notation and signsSome knowledge of the layout of questionnaires


Understand the advantages and disadvantages of using interviews versus questionnaires

Design and use effective data capture sheets and methods of recording data Understand and account for the problems of design, ambiguity of wording, leading

questions, definitions and obtaining truthful responses Understand the advantages and disadvantages of open and closed questions Be aware of the problems related to identifying the appropriate population, the

distribution and collection of surveys, errors in recorded answers, non-response and missing data

LINKS TO LEVEL 2 (extension work)Module 3 Data collectionAt level 2 students are expected to have a better understanding of bias, and to use this to enhance the quality of questioning and the wording of questionsExpected to understand pilot and pre-testing at level 2



DIFFERENTIATION & EXTENSIONInvestigate the usability of real-world data collection sheets, eg tax return, passport application, national censusInvestigate how the manner of an interview could affect the outcome, eg students role-play interviewsInvestigate a leading question — does it really affect the response?

NOTESData collection to include: surveys, counting, questionnaires and measurementMeasurement of data to include an appreciation that the measurement of continuous variables such as time and length is subject to some errorThe minimisation of ambiguity and bias is expectedWork on simulations and experiments can be carried out as part of a general course but will not feature as a requirement in questionsThe use of control groups is not requiredWhich methods of data collection are most appropriate for either primary or secondary data is knowledge that is required


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Contents: Tabulating data

1.2 Design and use simple data collection sheets for discrete and continuous data, using tallies including grouped frequencies

1.4 Understand reliability (including the significance of the number of trials)2.1 Draw two-way tables4.1 Read and interpret data presented in tables4.2 Interpret two-way tables



PRIOR KNOWLEDGEAn understanding of the different types of data: continuous, discrete and categoricalExperience of inequality notation and symbol


Construct frequency tables by tallying raw data where appropriate Tabulate using class intervals for discrete and continuous data Tabulate using various forms of grouping the data, including qualitative or quantitative

categories Combine categories to simplify tables with an understanding of the problems of over

simplification, the effects on readability, the identification or masking of trends and the loss of detail

Read and interpret data presented in tabular or graphical form Design suitable tables, including summary tables and two-way tables

LINKS TO LEVEL 2 Module 4 Tabulating data

LINKS TO GCSE SCHEME OF WORK (2-year)Foundation Unit 3a


DIFFERENTIATION & EXTENSIONFurther examples of tables to collect and/or summarise information in the real worldCompare different methods of tabulating data for ease of useNOTESStudents should be able to list outcomes from single or two successive eventsThe maximum size of 2-way tables will be 16 cells (excluding totals)Students may need reminding about the correct use of tallies


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Contents: Diagrams and representations: discrete data

2.1 Draw pictograms, bar charts, line graphs, dual bar charts, pie charts2.2 Identify simple misuse of visual representations4.1 Read and interpret data presented in tables4.2 Interpret pictograms, bar charts, line graphs, dual bar charts, pie charts4.3 Find totals and modes from frequency tables or diagrams4.7 Make comparisons and predictions from data and representations of data


S2 Interpret and construct tables, charts and diagrams, including … bar charts … and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, … and know their appropriate use

S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data …

PRIOR KNOWLEDGEAn understanding of the different types of data: continuous, discrete and categoricalExperience of inequality notation and symbolFor pie charts some basic fraction work and use of a protractor to measure and draw angles


Construct, draw, use and understand:– Pictograms– Bar charts– Multiple or composite bar charts for qualitative, quantitative and discrete data– Vertical line (stick) graphs for discrete data– Stem and leaf diagrams– Pie charts

Understand the distinction between well-presented and poorly presented data Understand the potential for visual misuse by omission or misrepresentation Transform from one presentation to another Understand how to discover errors in data and recognise data that does not fit a general

trend or pattern


LINKS TO LEVEL 2 (extension work)Module 5 Diagrams and representations: discrete dataAt level 2 the investigation and interpretation of stem and leaf diagrams is extendedPictograms and pie charts at level 1 only but could feature as part of a question at level 2Frequency polygons, stem and leaf diagrams, cumulative frequency diagrams, box plots and histograms are introduced at level 2


DIFFERENTIATION & EXTENSIONFurther examples of these graphs drawn from the real worldInvestigate the misrepresentation of statistics in the mediaCompare information presented in different forms, eg pie chart and bar chart

NOTESStudents should be able to list outcomes from single or two successive eventsThe reasons for choosing particular forms of representation are expectedComparative line graphs are expectedDiscuss misuse of data, this could be done by collecting examples from the media for discussionClearly label all axes on graphs and use a ruler to draw straight linesAngles for pie charts must be correct to within 2°


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Contents: Diagrams and representations: continuous data

2.1 Draw bar charts, line graphs, dual bar charts, pie charts

2.2 Identify simple misuse of visual representations

4.2 Interpret bar charts, line graphs, dual bar charts, pie charts

4.3 Find totals and modes from frequency tables or diagrams

4.7 Make comparisons and predictions from data and representations of data


S2 Interpret and construct tables, charts and diagrams, including … pie charts … for categorical data, … and know their appropriate use


PRIOR KNOWLEDGEAn understanding of the different types of data: continuous, discrete and categoricalExperience of inequality notation and symbolFor pie charts some basic fraction work and use of a protractor to measure and draw angles.


Construct, draw, use and understand:– Pie charts– Frequency diagrams

Transform from one presentation to another Understand how to discover errors in data and recognise data that does not fit a general

trend or pattern

LINKS TO LEVEL 2 (extension work)Module 6 Diagram and Representations: continuous dataAt level 2 the investigation and interpretation of stem and leaf diagrams is extendedPie charts at level 1 only but could feature as part of a question at level 2Frequency polygons, stem and leaf diagrams, cumulative frequency diagrams, box plots and histograms are introduced at level 2

LINKS TO GCSE SCHEME OF WORK (2-year)Foundation Unit 3a and 3b


DIFFERENTIATION & EXTENSIONDiscuss the optimum number of divisions in a pie chartComparative pie charts (simple cases, eg doubling frequency doubles area)

NOTESStudents should be able to list outcomes from single or two successive eventsThe reasons for choosing a particular form of representation is expectedComparative line graphs are expectedDiscuss misuse of data, this could be done by collecting examples from the media for discussionThe properties of the shape of distributions and skew are not needed at level 1Clearly label all axes on graphs and use a ruler to draw straight linesAngles for pie charts must be correct to within 2°Other statistical diagrams such as population pyramids and choropleth maps are not required


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Contents: Measures of central tendency

3.1 Find totals, mean, mode, median and range for lists of data

3.2 Find range and mode from a stem and leaf diagram


4.6 Compare data using frequencies, totals, mean, median, mode and range


S2 Interpret and construct tables, charts and diagrams …S4 Interpret, analyse and compare the distributions of data sets from univariate

empirical distributions through: … appropriate measures of central tendency (median, mean, mode …) and spread (range …)

S5 Apply statistics to describe a population

PRIOR KNOWLEDGEKnowledge of finding the mean, median and mode for small data setsAbility to order and to find the mid-point of two numbers


Convert raw data to summary statistics, design, construct and present summary tables Work out the mean, median and mode of raw data presented as a list Work out the mean, median and mode of discrete data presented as a frequency

distribution Understand the appropriateness, advantages and disadvantages of each of the three

measures of central tendency Be able to make a reasoned choice of a measure of central tendency appropriate to a

particular line of enquiry Write down the mode or median from a stem and leaf diagram or frequency table

LINKS TO LEVEL 2 (extension work)Module 7 Measures of central tendencyAt level 2 finding measures of central tendency from grouped data in tables, stem and leaf diagrams, cumulative frequency diagrams and box plots is expectedFinding a modal class interval or the location of a median within a table is level 2



DIFFERENTIATION & EXTENSIONUse a spreadsheet to calculate summary statisticsUse statistical functions on scientific calculatorsFind the combined mean of two sets of data given the mean for each set of dataShow how the mean can be affected by extreme values

NOTES and x̄ notation is expectedExplain that a quick method for finding the middle value (for the median of an even number of values) is by adding the two values together and dividing the total by two


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Contents: Measures of Dispersion

3.1 Find totals, mean, mode, median and range for lists of data

3.2 Find range and mode from a stem and leaf diagram


4.6 Compare data using frequencies, totals, mean, median, mode and range


S2 Interpret and construct tables, charts and diagrams …S4 Interpret, analyse and compare the distributions of data sets from univariate

empirical distributions through: … appropriate measures of central tendency (median, mean, mode …) and spread (range …)


PRIOR KNOWLEDGEKnowledge of finding the range of a small list of numbers


Convert raw data to summary statistics, design, construct and present summary tables Work out and use the range for data presented in a list or frequency distribution Use an appropriate measure of central tendency, eg to compare distributions of data Understand how to discover errors in data and recognise data that does not fit a general

trend or pattern

LINKS TO LEVEL 2 (extension work)Module 8 Measures of dispersionAt level 2 finding measures of dispersion from grouped data in tables, stem and leaf diagrams, cumulative frequency diagrams and box plots is expectedQuartiles, percentiles, and outliers are all considered at level 2


DIFFERENTIATION & EXTENSIONDiscuss which measure of dispersion is most appropriate in a given situationStudents compare themselves to published statistics, eg BMI, birth weight charts


NOTES

and x̄ notation is expectedThe range should be written as a single number and not two numbers separated by a dash (or other symbol)


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Contents: Scatter Diagrams

2.1 Draw simple time-series graphs and scatter graphs

4.2 Interpret simple time-series graphs, and scatter graphs

4.4 Describe correlation in scatter graphs


S6 Use and interpret scatter graphs of bivariate data data; recognise correlation …; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends while knowing the dangers of so doing

PRIOR KNOWLEDGEPlotting coordinatesAn understanding of the concept of a variableRecognition that a change in one variable can affect anotherBasic scaling on axes


Plot points as points on a scatter diagram Recognise positive, negative and zero correlation by inspection Draw a line of best fit Understand the pitfalls of interpolation and extrapolation Interpret data presented in the form of a scatter diagram

LINKS TO LEVEL 2 (extension work)Module 9 Scatter diagramsAt level 2 use of the mean point is introducedSimple descriptions of the correlation are extended

LINKS TO GCSE SCHEME OF WORK (2-year)Foundation Unit 3c


DIFFERENTIATION & EXTENSIONInvestigate the relationship between variables, eg hand span v foot length, volume v surface area of cubesScatter graphs where the scaling on the axis is not easyInvestigate how the line of best fit is affected (visually) by the choice of scales on the axes

NOTESClearly label all axes on graphs and use a ruler to draw straight linesStudents should appreciate that the line of best fit does not necessarily go through the origin or ‘corner point’ of the graph


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Contents: Time Series

4.5 Identify trend in time-series graphs

4.7 Make comparisons and predictions from data and representations of data


S2 Interpret and construct tables, charts and diagrams, including … tables and line graphs for time series data and know their appropriate use

PRIOR KNOWLEDGEPlotting coordinatesAn understanding of the concept of a variableBasic scaling on axesKnowledge of units of time (minutes, hours, days, weeks, months, and quarters)


Plot points as a time series; draw a trend line by eye and use it to make a prediction Identify and discuss the significance of seasonal variation by inspection of time series

graphs

LINKS TO LEVEL 2 (extension work)Module 10 Time seriesAt level 2 the significance of seasonal variation is introduced, only trends are required at level 1Moving averages are introduced


DIFFERENTIATION & EXTENSIONAnalyse real-world time series graphs for trends, eg FT100 index over 3 years

NOTESClearly label all axes on graphs and use a ruler to draw straight linesTrend lines may be required and these may be drawn ‘by eye’ but need to be a straight line




Contents: Probability

5.1 Use and interpret a probability scale

5.2Write down theoretical/experimental probabilities ( and )

5.3 Estimate probabilities from practical situations

5.4 Add two probabilities (including 1− p)5.5 List outcomes in theoretical and practical situations


P2 Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments

P3 Relate relative expected frequencies to theoretical probability, using appropriate language and the 0-1 probability scale

P4 Apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one

N5 Apply systematic listing strategies …

PRIOR KNOWLEDGEUnderstand that a probability is a number between 0 and 1Know how to add simple fractions and decimalsRecognise the language of statistics, eg likely, certainty, impossible, etc


Understand the meaning of the words event and outcome Understand the meaning of the words impossible, certain, highly likely, likely, unlikely,

possible, evens and present them on a likelihood scale Put outcomes in order in terms of probability Put probabilities in order on a probability scale 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 Understand that in some cases the measure of probability based on limiting frequency

is the only viable measure Compare expected frequencies and actual frequencies Work out probability


22

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

Know, for mutually exclusive outcomes, that the sum of probabilities is 1, and in particular the probability of something not happening is 1 minus the probability of it happening

Write down the probability from a 2-way table

LINKS TO LEVEL 2 (extension work)Module 11 ProbabilitySample spaces and tree diagramsThe need to make decisions as to whether a sum or product of probabilities is needed is considered in greater detail at level 2


DIFFERENTIATION & EXTENSIONDo calculations without the use of a calculator, eg probabilities with harder fractionsExperiments with dice and spinners or ICT simulations show how a large number of trials lead to more accuracy, this is not a requirementShow that P(Double 6) can be found by seeing that there is only 1 outcome from 36 in considering possible outcomes or by P(6) = 1/6 × 1/6 = 1/36)

NOTESProbabilities may be expressed as fractions, decimals or percentages, ie not as ratios (odds)Formal definition and notation of a limit is not requiredProbabilities written as fractions do not have to be cancelled to the simplest form, unless requested


Level 1 concepts and skillsWhat students need to learn:

Topic Concepts and skills1. Data 1. Understand and use discrete, continuous and

categorical data2. Design and use simple data collection sheets

for discrete and continuous data, using tallies including grouped frequencies

3. Criticise a question for a questionnaire4. Understand reliability (including the

significance of the number of trials)2. Displaying data 1. Draw pictograms, bar charts, line graphs, dual

bar charts, two-way tables, pie charts, simple time-series graphs and scatter graphs

2. Identify simple misuse of visual representations3. Calculating with data 1. Find totals, mean, mode, median and range for

lists of data2. Find range and mode from a stem and leaf

diagram4. Interpreting data 1. Read and interpret data presented in tables

2. Interpret pictograms, bar charts, line graphs, dual bar charts, two-way tables, pie charts, simple time-series graphs, and scatter graphs

3. Find totals and modes from frequency tables or diagrams

4. Describe correlation in scatter graphs5. Identify trend in time-series graphs6. Compare data using frequencies, totals, mean,

median, mode and range7. Make comparisons and predictions from data

and representations of data5. Probability 1. Use and interpret a probability scale

2. Write down theoretical/experimental

probabilities (

1n and

an )

3. Estimate probabilities from practical situations4. Add two probabilities (including 1− p)5. List outcomes in theoretical and practical

situations


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Level 2 (AST20)

Scheme of work





1 Types of data 1.52 Population and sampling 53 Data collection 64 Tabulating data 3.55 Diagrams and representations: discrete data 86 Diagrams and representations: continuous data 107 Measures of central tendency 78 Measures of dispersion 69 Scatter diagrams 7

10 Time series 711 Probability 6

Total 67


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Contents: Types of data

1.1 Classify discrete, continuous and categorical data






LINKS TO LEVEL 1 CONTENTModule 1 Types of data


Recognise that data can be obtained from primary and secondary sources Recognise the difference between quantitative and qualitative variables Recognise the difference between discrete and continuous data Recognise and use scales of measurement, eg categorical, rank Categorise data through the use of well-defined, precise definitions or class boundaries Appreciate the implication of grouping for loss of accuracy in presentations Understand, use and define situations for grouped and ungrouped data Understand the meaning of bi-variant data which may be discrete, continuous, grouped

or ungrouped

LINKS TO LEVEL 3 (extension work)Module 1 Data



DIFFERENTIATION & EXTENSIONUse other scales for data, eg ordinal scale, ratio scaleMake a list of possible pairs of bi-variant data, eg height v weightCategories are a range of variables from a variety of everyday contexts

NOTESPrimary sources should include raw data, surveys, questionnaires (which may have more than two categories), investigations and experimentsSecondary sources include databases, published statistics, newspapers, internet pages, etcThe use of terms such as class width and class interval is expected


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Contents: Population and sampling

1.2 Recognise the difference between a sample and a population and give a simple reason for sampling

1.4 Identify possible sources of bias in sampling methods1.5 Calculate a stratified sample using one category



PRIOR KNOWLEDGEAn understanding of why data needs to be collected

LINKS TO LEVEL 1 CONTENTModule 2 Population and samplingReasons for sampling and the differences of census and sampling should be described in greater detail Use of random numbers is extendedThe range of sampling methods is extended; students should now begin to appreciate which sampling method is most appropriate


Understand the meaning of the term population Understand the word census with regard to small scale and large scale populations Understand the reasons for sampling and that sample data is used to estimate values in

a population Understand the terms random, randomness and random sample Understand the use of random numbers Understand design and use a sampling frame Be able to select a random sample or stratified sample from one category as a method

of investigating a population Appreciate how bias in a sampling procedure might occur and how it might be

minimised Understand and use systematic, quota and cluster sampling Understand the strengths and weaknesses of various sampling methods, including bias,

influences and convenience


LINKS TO LEVEL 3 (extension work)Module 2 Population sampling

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 14a (NB stratified sampling is not included in the 9-1 specification)

DIFFERENTIATION & EXTENSIONDiscuss the size of the sample needed for particular sampling proceduresDiscuss the feasibility of taking a census in large populationsConsider the role of pilot samples and trialling of questionnaires, including pre-testing

NOTESRandom numbers may be collected from random number tables, calculators and spreadsheetsAn appreciation of an appropriate sample size is expectedDesigning a sample frame is expectedUnderstand the types of question used for a census and how the collected data is usedEmphasise the differences between primary and secondary data


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Contents: Data collection

1.3 Design a question for a questionnaire1.4 Identify possible sources of bias in sampling methods



PRIOR KNOWLEDGEExperience of simple tally chartsExperience of inequality notation and signsSome knowledge of the layout of questionnaires

LINKS TO LEVEL 1 CONTENTModule 3 Data collectionThe quality of the design of questions for a questionnaire should be betterRather than discrete data, a far deeper understanding of what is needed for continuous data is needed here, extending to grouping and class intervals


Understand the advantages and disadvantages of using interviews versus questionnaires

Design and use effective data capture sheets and methods of recording data Understand the role of pilot studies and pre-testing Understand and account for the problems of design, ambiguity of wording, leading

questions, definitions and obtaining truthful responses with simplest form of random response in sensitive cases

Understand the advantages and disadvantages of open and closed questions Be aware of the problems related to identifying the appropriate population, the


Understand the need for identification of the variables to be investigated and the meaning of explanatory and response variables



LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 14a

DIFFERENTIATION & EXTENSIONInvestigate the collection of primary data in the real world, eg tax return, passport application, National CensusInvestigate how the manner of an interview could affect the outcome, eg students role-play interviewsInvestigate a leading question – to what extent does it affect the response?Investigate psychometric testingConsider the role of pilot samples and trialling of questionnaires, including pre-testing

NOTESData collection to include: surveys, counting and questionnairesMeasurement of data to include an appreciation that the measurement of continuous variables such as time and length is subject to some errorThe minimisation of ambiguity and bias is expectedStudents may need reminding about the correct use of talliesEmphasise the differences between primary and secondary data


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Contents: Tabulation

2.1 Draw two-way tables, complete grouped frequency tables

4.1 Interpret and compare




LINKS TO LEVEL 1 CONTENTModule 4 TabulationThe work at level 1 is extended here to include detailed comparisons of data that is tabulatedThe tables at level 2 can now be grouped


Construct frequency tables by tallying raw data were appropriate, including open- ended class intervals and classes of varying width

Tabulate using class intervals for discrete and continuous data Tabulate using various forms of grouping the data, including qualitative or quantitative

categories Combine categories to simplify tables with an understanding of the problems of over

simplification, the effects on readability, the identification or masking of trends and the loss of detail

Read and interpret data presented in tabular or graphical form Design suitable tables, including summary tables and two-way tables




DIFFERENTIATION & EXTENSIONFurther examples of tables to collect and/or summarise information in the real worldCompare different methods of tabulating data for ease of useTabulate data with two or more characteristics

NOTESPresent and interpret data collected for courseworkStudents should be able to list outcomes from single or two successive eventsThe maximum size of 2-way tables will be 16 cells (excluding totals)


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Contents: Diagrams and representations: discrete data

2.1 Draw composite bar charts, ordered and unordered stem and leaf diagrams, frequency polygons, cumulative frequency diagrams, box plots, histograms (equal class interval)

2.2 Identify misuse of visual representations


S2 Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use


PRIOR KNOWLEDGEAn understanding of the different types of data: continuous, discrete; categoricalExperience of inequality notation and symbol

LINKS TO LEVEL 1 CONTENTModule 5 Diagrams and representations: discrete dataExtended to include the drawing of diagrams and graphs of data that is grouped


Construct, draw, use and understand:– Multiple or composite bar charts for qualitative, quantitative and discrete data– Stem and leaf diagrams

Identify simple properties of the shape of distributions of data including symmetry, positive and negative skew


trend or pattern


LINKS TO LEVEL 3 (extension work)Module 3 Diagrams and representations

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 3b

DIFFERENTIATION & EXTENSIONFurther examples of these graphs (particularly graphs used for comparison), eg back-to-back stem and leaf diagramsInvestigate the misrepresentation of statistics in the mediaCompare information presented in different forms, eg stem and leaf v bar chartCollect examples of charts and graphs in the media which have been misused and discuss the implicationsConsider the shape of distributions and skew

NOTESStudents should be able to list outcomes from single or two successive eventsReasons for choosing a particular form of representation are expectedComparative line graphs are expectedClearly label all axes on graphs and use a ruler to draw straight lines


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Contents: Diagrams and representations: continuous data

2.1 Draw composite bar charts, ordered and unordered stem and leaf diagrams, frequency polygons, cumulative frequency diagrams, box plots, histograms (equal class intervals).

2.2 Identify misuse of visual representations


S2 Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use

S3 Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal … class intervals and cumulative frequency graphs, and know their appropriate use

S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data, including box plots …


LINKS TO LEVEL 1 CONTENTModule 6 Diagrams and representations: continuous dataExtended to grouped dataSome extra graphs are now considered in addition to those at level 1, including histograms, cumulative frequency diagrams with polygons, box plots and stem and leaf diagrams



Construct, draw, use and understand:– Frequency diagrams – Frequency polygons – Histograms with equal and unequal class intervals and the concept of frequency

density – Cumulative frequency diagrams – Box plots – Stem and leaf diagrams


Transform from one presentation to another Understand how to discover errors in data and recognise data that does not fit a general

trend or pattern Compare distributions

LINKS TO LEVEL 3 (extension work)Module 3 Diagrams and representations

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 3bHigher Unit 14b

DIFFERENTIATION & EXTENSIONFurther examples of these graphs (particular graphs used for comparison), eg cumulative frequency diagrams used for comparison, normal distributions, etcInvestigate the misrepresentation of graphs used to represent continuous data in the media or on the InternetUse frequency polygons to compare histogramsUse box plots to compare heights of students in each year group of the schoolConsider the shape of distributions and skew

NOTESStudents should be able to list outcomes from single or two successive eventsReasons for choosing a particular form of representation are expectedComparative line graphs are expectedThe use of box plots includes comparisonsDiscuss misuse of data, this could be done by collecting examples from the media for discussionOther statistical diagrams such as population pyramids and choropleth maps are not required


38




3.1 Calculate means for grouped and ungrouped data3.2 Find the median for grouped and ungrouped data4.2 Find the modal class interval from a frequency table or diagram4.3 Find the class interval which contains the median


S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: … appropriate measures of central tendency (median, mean, mode and modal class) …


PRIOR KNOWLEDGEKnowledge of finding the mean, median and mode for small data setsAbility to order and to find the mid-point of two numbersFind the mean, median and mode of a simple list of discrete numbers

LINKS TO LEVEL 1 CONTENTModule 7 Measures of central tendencyExtended to grouped dataWorking with class intervals is needed at level 2



Work out the mean, median and mode of:– Raw data presented as a list – Discrete data presented as a frequency distribution

Identify the modal class interval for grouped frequency distributions for discrete and continuous data

Work out and use estimates for the mean and median of grouped frequency distributions for discrete and continuous data

Understand the effects of transformations of the data on the mean, mode and median 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


particular line of enquiry, nature of data and purpose of the analysis Understand that increasing sample size generally leads to better estimates of

population parameters Find the median from:

– Stem and leaf diagrams – Cumulative frequency diagrams – Box plots

LINKS TO LEVEL 3 (extension work)Module 4 Measures of central tendency


DIFFERENTIATION & EXTENSIONUse a spreadsheet to calculate summary statisticsUse statistical functions on scientific calculatorsFind the combined mean of two sets of data given the mean for each set of dataShow how the mean can be affected by extreme valuesConsider ways to use scientific calculators and statistical functions in order to perform calculations

NOTESGraphical and other methods for the median are expected and x̄ notation is expected


40



Contents: Measures of dispersion

3.2 Find the median, quartiles and interquartile ranges for grouped and ungrouped data

3.4 Calculate means and standard deviation 3.5 Understand and use summation notation in statistical calculations4.4 Identify outliers4.6 Identify and describe skew4.7 Compare data using interquartile range, skew and standard deviation


S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: … appropriate measures of … spread (range, including consideration of outliers, quartiles and inter-quartile range)


PRIOR KNOWLEDGEKnowledge of finding the range of a list of numbers

LINKS TO LEVEL 1 CONTENTModule 8 Measures of dispersionThis work is now extended into interquartile range and distributions


Work out and use the range for data presented in a list or frequency distribution Work out the quartiles and interquartile range for discrete and continuous data

presented either as a list, frequency table or grouped frequency table Formally identify outliers Calculate and use variance and standard deviation Understand the advantages and disadvantages of each of the measures of dispersion,

range, quartiles, interquartile range, variance and standard deviation Find the range or interquartile range from:

– Box plots – Cumulative frequency diagrams – Stem and leaf diagrams


LINKS TO LEVEL 3 (extension work)Module 5 Measures of dispersion


DIFFERENTIATION & EXTENSIONDiscuss which measure of dispersion is most appropriate in a given situationStudents compare themselves to published statistics, eg BMI, birth weight chartsConsider ways to use scientific calculators and statistical functions in order to perform calculationsConsider percentiles and deciles

NOTESThe possible effect of an outlier on range is expectedAwareness that a full comparison of distributions needs at least both a measure of central tendency and a measure of dispersion and x̄ notation is expected


42



Contents: Scatter diagrams

4.1 Interpret and compare scatter diagrams4.5 Draw lines of best fit on scatter graphs and trend lines by eye with or without

mean point4.8 Make comparisons and predictions from data and representations of data


S6 Use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends while knowing the dangers of so doing

PRIOR KNOWLEDGEPlotting coordinatesAn understanding of the concept of a variableRecognition that a change in one variable can affect anotherBasic scaling on axesAn understanding of correlation

LINKS TO LEVEL 1 CONTENTModule 9 Scatter diagrams


Plot points as points on a scatter diagram Recognise positive, negative and zero correlation by inspection Draw a line of best fit

Draw a line of best fit through to the points on a scatter diagram Understand the pitfalls of interpolation and extrapolation Interpret data presented in the form of a scatter diagram

LINKS TO LEVEL 3 (extension work)Module 7 Correlation



DIFFERENTIATION & EXTENSIONInvestigate the relationship between variables, eg hand span v foot length, volume v surface area of cubesStart work on some easy examples of Spearman’s rank correlation coefficient

NOTES

Questions will state when is required


44



Contents: Time series

2.1 Draw time-series graphs with or without moving averages4.8 Make comparisons and predictions from data and representations of data and

describe trend4.9 Interpret and compare moving averages and fixed base index numbers


S2 Interpret and construct tables, charts and diagrams, including … tables and line graphs for time series data and know their appropriate use

PRIOR KNOWLEDGEPlotting coordinatesAn understanding of the concept of a variableBasic scaling on axesKnowledge of units of time (minutes, hours, days, weeks, months and quarters)

LINKS TO LEVEL 1 CONTENTModule 10 Time seriesPlotting of basic seasonal graphs and inserting a trend line on graphs


Plot points as a time series; draw a trend line by eye and use it to make a prediction Calculate and use appropriate moving averages Identify and discuss the significance of seasonal variation by inspection of time series

graphs Draw a trend line based on a moving average Use and interpret index numbers in the real world

LINKS TO LEVEL 3 (extension work)Module 8 Time series

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 3b (NB moving averages and average seasonal trends are not in the 9–1 specification)


DIFFERENTIATION & EXTENSIONStudents may be required to work out the average seasonal variation from their time series graphChain base index numbersRecognise seasonal effect at a given data point and average seasonal effect

NOTESIndex numbers using a fixed base only


46




2.1 Draw sample space diagrams4.1 Interpret sample space diagrams.5.1 Compare theoretical and experimental probabilities5.2 Add two or more probabilities (including 1− p)5.3 Use sample space diagrams to calculate probabilities5.4 Use probability to estimate outcomes5.5 Multiply probabilities using tree diagrams





P6 Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams

P7 Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

P8 Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

P9 Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

PRIOR KNOWLEDGEUnderstand that a probability is a number between 0 and 1Know how to add simple fractions and decimalsKnow how to work out and state probabilities using fractions, decimals or percentages

LINKS TO LEVEL 1 CONTENTModule 11 ProbabilitySimple probability is extended to consider multiple events and multiplication of probabilities



Understand the meaning of the words: event, outcome, random and equally likely Put outcomes in order in terms of probability Understand and use measures of probability from a theoretical perspective and from a

limiting frequency or experimental approach, and that increasing sample size generally leads to better estimates of probability

Understand that in some cases the measure of probability based on limiting frequency is the only viable measure

Compare expected frequencies and actual frequencies Calculate probabilities Produce, understand and use a sample space 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 Know, for mutually exclusive outcomes, that the sum of probabilities is 1; and in

particular the probability of something not happening is 1 minus the probability of it happening

Draw and use probability tree diagrams for independent events and conditional cases Understand, use and apply the addition for mutually exclusive events, general addition,

and multiplication laws for independent events and conditional events and outcomes

LINKS TO LEVEL 3 (extension work)Module 9 Probability

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 10

DIFFERENTIATION & EXTENSIONDo calculations without the use of a calculator, eg probabilities with harder fractionsGenerate sample spaces which require careful specification, eg drawing cards from a pack of cardsInvestigate probability in real life situations, eg National Lottery

NOTESProbabilities may be expressed as fractions, decimals or percentages, ie not as ratios (odds)Formal definition and notation of a limit is not requiredIn tree diagrams, up to three sets of branches are required


48

Level 2 concepts and skillsWhat students need to learn:All level 1 content is assumed knowledge and can be tested at level 2.

Topic Concepts and skills1. Data 1. Classify discrete, continuous and categorical

data2. Recognise the difference between a sample and

a population and give a simple reason for sampling

3. Design a question for a questionnaire4. Identify possible sources of bias in sampling

methods5. Calculate a stratified sample using one category

2. Displaying data 1. Draw composite bar charts, two-way tables and time-series graphs with or without moving averages, ordered and unordered stem and leaf diagrams, complete grouped frequency tables, frequency polygons, cumulative frequency diagrams, box plots, histograms (equal class interval) and sample space diagrams

2. Identify misuse of visual representations3. Calculating with data 1. Calculate means for grouped and ungrouped

data2. Find the median, quartiles and interquartile

ranges for grouped and ungrouped data3. Calculate moving averages, combined means

and fixed base index numbers4. Calculate means and standard deviation5. Understand and use summation notation in

statistical calculations4. Interpreting data 1. Interpret and compare composite bar charts,

frequency polygons, scatter diagrams, cumulative frequency diagrams and box plots, histograms with equal class intervals, and sample space diagrams

2. Find the modal class interval from a frequency table or diagram

3. Find the class interval which contains the median

4. Identify outliers5. Draw lines of best fit on scatter graphs and

trend lines by eye with or without mean point6. Identify and describe skew7. Compare data using interquartile range, skew

and standard deviation 8. Make comparisons and predictions from data


and representations of data and describe trend

9. Interpret and compare moving averages and fixed base index numbers

6. Probability 1. Compare theoretical and experimental probabilities

2. Add two or more probabilities (including 1− p)3. Use sample space diagrams to calculate

probabilities4. Use probability to estimate outcomes5. Multiply probabilities using tree diagrams


50


Level 3 (AST30)

Scheme of work





1 Data 1.52 Population sampling 63 Diagrams and representations 94 Measures of central tendency 105 Measures of dispersion 106 The normal distribution 27 Correlation 98 Time series 79 Probability 11

Total 65.5


52



Contents: Data

1.1 Understand and explain discrete, continuous, categorical, qualitative, quantitative, primary and secondary data






LINKS TO LEVEL 2 CONTENTModule 1 Types of data


Recognise that data can be obtained from primary and secondary sources Recognise the difference between quantitative and qualitative variables Recognise the difference between discrete and continuous data Recognise and use scales of measurement, eg categorical, rank Categorise data through the use of well-defined, precise definitions or class boundaries Appreciate the implication of grouping for loss of accuracy in presentations Understand, use and define situations for grouped and ungrouped data Understand the meaning of bi-variant data which may be discrete, continuous, grouped

or ungrouped

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 3aHigher Unit 3bHigher Unit 14

LINKS TO (S1) GCE MATHEMATICSNone


DIFFERENTIATION & EXTENSIONUse other scales for data, eg ordinal scale, ratio scaleMake a list of possible pairs of bi-variant data, eg height v weightCategories are a range of variables from a variety of everyday contexts

NOTESPlan and collect data for courseworkPrimary sources should include raw data, surveys, questionnaires (which may have more than two categories), investigations and experimentsSecondary sources include databases, published statistics, newspapers, internet pages, etcThe use of terms such as class width and class interval is expected


54



Contents: Population sampling

1.1 Understand and explain census, population and sampling frame1.2 Calculate a stratified sample using two categories1.3 Use Peterson’s capture and recapture method to estimate the size of

populations



PRIOR KNOWLEDGEAn understanding of why data needs to be collectedBias and the measures that can be taken to reduce biasRandom sampling methodsSome knowledge of the layout of questionnairesRatios and calculations relating to proportion

LINKS TO LEVEL 2 CONTENTModule 2 Population and samplingModule 3 Data collectionModule 4 Tabulating dataExtended to consider stratified sampling by more than one category and other types of sampling methodAt level 3 students should be expected to bring an understanding and critical analysis of sampling and sampling methods which is more detailed than at level 2


Understand the meaning of the term population Understand the word census with regard to small scale and large scale populations Understand the reasons for sampling and that sample data is used to estimate values in

a population Understand the terms random, randomness and random sample Understand the use of random numbers Understand, design and use a sampling frame Be able to select a random sample or stratified sample from at least one category as a

method of investigating a population Appreciate how bias in a sampling procedure might occur and how it might be

minimised


Understand and use systematic, quota and cluster sampling Understand the strengths and weaknesses of various sampling methods, including bias,

influences and convenience Understand the advantages and disadvantages of using interviews versus

questionnaires Design and use effective data capture sheets and methods of recording data Understand the role of pilot studies and pre-testing Understand and account for the problems of design, ambiguity of wording, leading

questions, definitions and obtaining truthful responses with simplest form of random response in sensitive cases

Understand the advantages and disadvantages of open and closed questions Be aware of the problems related to identifying the appropriate population: the


Understand the processes that need to be in place in order to carry out Peterson’s capture and recapture method

Understand the assumptions that need to be in place to assure some reliability of the Peterson capture and recapture method

Understand the limitations of the Peterson capture and recapture method

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 14a (NB stratified sampling is not in the 9-1 specification)


DIFFERENTIATION & EXTENSIONDiscuss the size of the sample needed for particular sampling proceduresDiscuss the feasibility of taking a census in large populationsInvestigate the collection of primary data in the real world, eg tax return, passport application, National CensusInvestigate how the manner of an interview could affect the outcome, eg students role-play interviewsInvestigate a leading question – to what extent does it affect the response?Investigate psychometric testing

NOTESRandom numbers may be collected from random number tables, calculators and spreadsheetsAn appreciation of an appropriate sample size is expectedDesigning a sample frame is expectedUnderstand the types of question used for a census and how the collected data is usedData collection to include: surveys, experiments (including controlled experiments), counting, data logging, convenience sampling, questionnaires and measurementThe minimisation of ambiguity and bias is expected


56



Contents: Diagrams and representations

2.1 Draw back-to-back stem and leaf diagrams, box plots (with outliers) and generated from cumulative frequency graphs, histograms (unequal class intervals) and Venn diagrams

3.3 Use LQ – 1.5 × IQR and UQ + 1.5 × IQR to identify outliers4.6 Interpret back to back stem and leaf diagrams, box plots with outliers,

Venn diagrams, and data from a variety of representations to solve a problem


S3 Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use

S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data, including box plots; appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)

P6 Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams …

PRIOR KNOWLEDGEUnderstand correlationProduce frequency diagrams and frequency polygons

LINKS TO LEVEL 2 CONTENTModule 5 Diagrams and representations: discrete dataModule 6 Diagrams and representations: continuous dataThe work on histograms at level 2 is extended to class intervals of unequal widthWork on scatter diagrams and box plots should now involve formal consideration of outliers





trend or pattern, including outliers Construct, draw, use and understand:

– Histograms with equal and unequal class intervals and the concept of frequency density

– Cumulative frequency diagrams – Box plots – Stem and leaf diagrams


Transform from one presentation to another. Determine whether a data item is an outlier Compare distributions


LINKS TO (S1) GCE MATHEMATICS2 Representation and summary of data

DIFFERENTIATION & EXTENSIONFurther examples of these graphs (particularly graphs used for comparison), eg cumulative frequency diagrams, normal distributions, back-to-back stem and leaf diagrams, etcInvestigate the misrepresentation of statistics in the mediaCompare information presented in different forms, eg stem and leaf v bar chartInvestigate the misrepresentation of graphs used to represent continuous data in the media or on the Internet

NOTESReasons for choosing a particular form of representation are expectedAnalytical definitions of an outlier will be expectedEvidence of use of frequency density could be required as part of work on histogramsStem and leaf diagrams to include back to back stem and leaf diagramsWork on Venn diagrams includes drawing Venn diagrams using a list of data and interpretationDrawing a box plot from a cumulative frequency graph requires the max/min values which cannot necessarily be assumed from the graph


58




3.1 Calculate geometric means4.4 Interpret and compare data using mean/median/mode4.5 Interpret and compare geometric means


S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: … appropriate measures of central tendency (median, mean, mode and modal class) …


PRIOR KNOWLEDGEKnowledge of finding the mean, median and mode for data setsFinding the modal class interval and median from data that is grouped

LINKS TO LEVEL 2 CONTENTModule 7 Measures of central tendency


Work out the mean, median and mode of:– Raw data presented as a list – Discrete data presented as a frequency distribution

Work out and use estimates for the mean and median of grouped frequency distributions for discrete and continuous data

Understand the effects of transformations of the data on the mean, mode and median 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


particular line of enquiry, nature of data and purpose of the analysis Understand that increasing sample size generally leads to better estimates of

population parameters Calculate a geometric mean



LINKS TO (S1) GCE MATHEMATICS2 Representation and summary of data

DIFFERENTIATION & EXTENSIONUse a spreadsheet to calculate summary statisticsUse statistical functions on scientific calculatorsFind the combined mean of two sets of data given the mean for each set of dataShow how the mean can be affected by extreme valuesConsider ways to use scientific calculators and statistical functions in order to perform calculations

NOTESGraphical and other methods for the median are expected

and x̄ notation is expectedThe weighted mean is not required


60



Contents: Measures of dispersion

3.2 Calculate means and standard deviations for grouped and ungrouped data, including using summation notation

3.5 Calculate variances Sxx and Syy and Sxy from given information [NB Questionswill state the expected formulae used to calculate variance: typically

Sxx = or equivalent3.6 Calculate standardised scores4.4 Interpret and compare data using frequencies, totals,

mean/median/mode/range, interquartile range, skew and standard deviation and standardised scores


S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data, including box plots; appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)


PRIOR KNOWLEDGEFinding the range of a list of numbersKnowledge of median and quartilesFormal identification of outliersBox plots and work on outliers

LINKS TO LEVEL 2 CONTENTModule 8 Measures of dispersion Work on median and quartiles could be extended to percentiles and deciles.


Work out and use the range for data presented in a list or frequency distribution Work out the quartiles, percentiles and interquartile range for discrete and continuous

data presented either as a list, frequency table or grouped frequency table Calculate and use variance and standard deviation


Understand the advantages and disadvantages of each of the measures of dispersion, range, quartiles, interquartile range, percentiles, deciles, interpercentile range, variance and standard deviation

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

Calculate, interpret and use standardised scores to compare values from different distributions


LINKS TO (S1) GCE MATHEMATICS2 Representation and summary of data4 Correlation and regression

DIFFERENTIATION & EXTENSIONInvestigate standard scores in a real world context, eg decathlonRelate mean and standard deviation to the normal distributionCentral limit theoremInvestigate the use of percentile range in real-world statistics

NOTESThe possible effect of an outlier on range is expectedNumerical interpolation is expectedFormal definition of the quartiles (eg Q1 as ¼ (n+1)th value) is not required but could be usefulThe use of box plots includes comparisonsAwareness that a full comparison of distributions needs at least both a measure of central tendency and a measure of dispersion is expected

and x̄ notation is expectedKnowledge of the following formulae is required:

Variance =

Standard deviation (set of numbers) or


62



Contents: The normal distribution

2.1 Sketch normal distributions4.1 Compare histograms and normal distributions

GCSE SPECIFICATION REFERENCESNone

PRIOR KNOWLEDGEUnderstand the shape of distributionsA basic knowledge of skewMeans, medians and modesStandard deviation and variance

LINKS TO LEVEL 2 CONTENTNone


Understand that many populations can be modelled by the normal distribution Recognise a graphical interpretation of a normal distribution Sketch the shape of a normal distribution Carry out some comparisons between histograms and the normal curve Understand the symmetry of a normal distribution and how this relates to the mode,

median and mean Know that 95% of the observations lie within ±two standard deviations of the mean Know that virtually all (98.9%) lie within ±three standard deviations of the mean Use tables for the normal distribution

LINKS TO GCSE SCHEME OF WORK (2-year)None

LINKS TO (S1) GCE MATHEMATICS2 Representation and summary of data4 Correlation and regression6 The Normal distribution


DIFFERENTIATION & EXTENSIONTransformation of any normal distribution into Z and use of tablesUse of tables to find μ and σUse of the normal distributions in applications of a real life context

NOTESKnowledge of Normal Distribution Tables is required as given by the tabulated function

of Φ(z), defined as Φ(z) = (See specification for reproduction of the necessary table, which will be provided in the examination)


64



Contents: Correlation

3.4 Calculate measures of correlation including Spearman’s coefficient of rank correlation and Product-moment correlation coefficient (PMCC)

4.2 Identify and describe correlation in scatter graphs and interpret measures of correlation


S6 Use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends while knowing the dangers of so doing

PRIOR KNOWLEDGEAn understanding of correlationScatter graphs and lines of best fit

LINKS TO LEVEL 2 CONTENTModule 9 Scatter diagrams The work on scatter graphs and correlation is extended into more formal approaches such as Spearman’s rank correlation coefficient.


Recognise positive, negative and zero correlation by inspection Understand the distinction between correlation, causality and a non-linear relationship Draw a line of best fit

Draw a line of best fit through to the points on a scatter diagram Understand the pitfalls of interpolation and extrapolation Interpret data presented in the form of a scatter diagram Calculate, in appropriate cases, Spearman’s rank correlation coefficient and use it as a

measure of agreement or for comparisons of the degree of correlation


LINKS TO (S1) GCE MATHEMATICS4 Correlation and regression


DIFFERENTIATION & EXTENSIONInvestigate the relationship between variables, eg hand span v foot length, volume v surface area of cubes

NOTESExplain that correlation does not guarantee a causal relationship between the variables; unrelated variables may exhibit linear correlation

Questions will state when is required

Spearman’s rank correlation coefficient is


66



Contents: Time series

3.1 Calculate geometric means, mean seasonal variation and moving base index numbers

4.3 Identify trend and seasonality in time-series graphs (including moving averages)


S2 Interpret and construct tables, charts and diagrams, including … line graphs for time series data and know their appropriate use

PRIOR KNOWLEDGEKnowledge of units of time (minutes, hours, days, weeks, months and quarters)Interpretation of a time series graph

LINKS TO LEVEL 2 CONTENTModule 10 Time series Time series interpretation is extended into use of the seasonal effects of the graph to make predictions


Plot points as a time series; draw a trend line by eye and use it to make a prediction Calculate and use appropriate moving averages Identify and discuss the significance of seasonal variation by inspection of time series

graphs Draw a trend line based on moving averages Recognise seasonal effect at a given data point and average seasonal effect Use and interpret index numbers in the real world Calculate, in appropriate cases, the Product-moment correlation coefficient

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 3b (NB moving averages and average seasonal trends are not in the 9-1 specification)



DIFFERENTIATION & EXTENSIONAnalyse real-world time series graphs for trends, eg FT100 index over three yearsUse a spreadsheet to fit a line (and curve) to given bi-variant dataStudents may be required to work out the average seasonal variation from their time series graphChain base index numbers

NOTESAnalytical definitions of an outlier will be expectedThe value of n in a non-linear relationship (see above) could be 2, -1 or ½ only


68




5.1 Use probability and relative frequency to estimate outcomes or make predictions

5.2 Use sample space and Venn diagrams to calculate probabilities5.3 Multiply and add probabilities using tree diagrams5.4 Understand mutually exclusive and independent events, that

P(A or B) = P(A) + P(B)5.5 Use P(A and B) = P(A) × P(B) for independent events A and B

P(A or B) = P(A U B) = P(A) + P(B) – 5.6 Find conditional probabilities and use

P(A U B) = 5.7 Identify and calculate binomial probabilities5.8 Find probabilities using standard normal distribution tables


P1 Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees




P5 Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

P6 Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams

P7 Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

P8 Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions


P9 Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

PRIOR KNOWLEDGEUnderstand that a probability is a number between 0 and 1Know how to add simple fractions and decimalsKnow how to work out and state probabilities using fractions, decimals or percentagesExpansion of (p + q)n

LINKS TO LEVEL 2 CONTENTModule 11 Probability


Understand and use measures of probability from a theoretical perspective and from a limiting frequency or experimental approach, and that increasing sample size generally leads to better estimates of probability

Understand that in some cases the measure of probability based on limiting frequency is the only viable measure

Compare expected frequencies and actual frequencies Calculate probabilities Produce, understand and use a sample space Understand and use Venn diagrams and Cartesian grids 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 Use simple cases of the binomial and discrete uniform distribution Draw and use probability tree diagrams for independent events and conditional cases Understand probability distributions Understand, use and apply the addition for mutually exclusive events, general addition,

and multiplication laws for independent events and conditional events and outcomes

LINKS TO GCSE SCHEME OF WORK (2-year)Higher Unit 10

LINKS TO (S1) GCE MATHEMATICS3 Probability

DIFFERENTIATION & EXTENSIONDo calculations without the use of a calculator, eg probabilities with harder fractionsGenerate sample spaces which require careful specification, eg. drawing cards from a pack of cardsInvestigate probability in real life situations, eg National Lottery


70

NOTESProbabilities may be expressed as fractions, decimals or percentages, ie not as ratios (odds)Formal definition and notation of a limit is not requiredThe expansion of (p + q)n is expectedIn tree diagrams, up to three sets of branches are required


Level 3 concepts and skillsWhat students need to learn:All level 2 content is assumed knowledge and can be tested at level 3.

Topic Concepts and skills1. Data 1. Understand and explain census, population,

sampling frame, discrete, continuous, categorical, qualitative, quantitative, primary and secondary data

2. Calculate a stratified sample using two categories

3. Use Peterson’s capture and recapture method to estimate the size of populations

2. Displaying data 1. Draw back-to-back stem and leaf diagrams, box plots (with outliers) and generated from cumulative frequency graphs, histograms (unequal class intervals), sketch normal distributions and Venn diagrams

3. Calculating with data 1. Calculate geometric means, mean seasonal variation and moving base index numbers

2. Calculate means and standard deviations for grouped and ungrouped data, including using summation notation

3. Use LQ – 1.5 × IQR and UQ + 1.5 × IQR to identify outliers

4. Calculate measures of correlation including Spearman’s coefficient of rank correlation and Product-moment correlation coefficient (PMCC)

5. Calculate variances Sxx, Syy and Sxy from given information [NB Questions will state the expected formulae used to calculate

variance: typically Sxx = or equivalent

6. Calculate standardised scores4. Interpreting data 1. Compare histograms and normal distributions

2. Identify and describe correlation in scatter graphs and interpret measures of correlation

3. Identify trend and seasonality in time-series graphs (including moving averages)

4. Interpret and compare data using frequencies, totals, mean/median/mode/range, interquartile range, skew and standard deviation and standardised scores


72

5. Interpret and compare geometric means and chain base index numbers

6. Interpret back to back stem and leaf diagrams, box plots with outliers, venn diagrams, and data from a variety of representations to solve a problem

5. Probability 1. Use probability and relative frequency to estimate outcomes or make predictions

2. Use sample space and Venn diagrams to calculate probabilities

3. Multiply and add probabilities using tree diagrams

4. Understand mutually exclusive and independent events, that P(A or B) = P(A) + P(B)

5. Use P(A and B) = P(A) × P(B) for independent events A and B P(A or B) = P(A U B) = P(A) + P(B) –

6. Find conditional probabilities and use

P(A U B) = 7. Identify and calculate binomial probabilities8. Find probabilities using standard normal

distribution tables


Resources TableLevel 1

Module number Title Resources Web resources

1 Types of data

2 Population and sampling

3 Data collection

4 Tabulating data

5 Diagrams and representations: discrete data

6 Diagrams and representations: continuous data

7 Measures of central tendency

8 Measures of dispersion

9 Scatter diagrams

10 Time series

11 Probability

Edexcel Awards in Statistical Methods Scheme of work © Pearson Education Ltd 2013 74

Level 2


1 Types of data

2 Population and sampling

3 Data collection

4 Tabulating data

5 Diagrams and representations: discrete data

6 Diagrams and representations: continuous data

7 Measures of central tendency


9 Scatter diagrams

10 Time series

11 Probability


Level 3


1 Data

2 Population sampling

3 Diagrams and representations

4 Measures of central Tendency


6 The normal distribution

7 Correlation

8 Time series

9 Probability


Edexcel, a Pearson company, is the UK’s largest awarding body, offering academic and vocational qualifications and testing to more than 25,000 schools, colleges, employers and other places of learning in the UK and in over 100 countries worldwide. Qualifications include GCSE, AS and A Level, NVQ and our BTEC suite of vocational qualifications from entry level to BTEC Level 2 National Diplomas, recognised by employers and Level 2 education institutions worldwide.We deliver 9.4 million exam scripts each year, with more than 90% of exam papers marked onscreen annually. As part of Pearson, Edexcel continues to invest in cutting-edge technology that has revolutionised the examinations and assessment system. This includes the ability to provide detailed performance data to teachers and students which help to raise attainment.

AcknowledgementsThis document has been produced by Edexcel on the basis of consultation with teachers, examiners, consultants and other interested parties. Edexcel would like to thank all those who contributed their time and expertise to its development.

References to third-party material made in this document are made in good faith. Edexcel does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)

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Further copies of this publication are available fromEdexcel Publications, Adamsway, Mansfield, Notts NG18 4FN

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