# GCSE Statistics

Scheme of work

This scheme of work for GCSE Statistics (8382) is designed to help you plan your teaching. This scheme of work is designed as a suggestion only and not as a prescriptive approach. You are free to organise your teaching in any way that suits the needs of your students.

Assumed coverage

The scheme of work assumes a 60 week course over two years. This gives a total teaching time of 180 hours.

Year one

Term one

 Week number Specification reference Learning objective(s) Suggested timing (hours) Prerequisite knowledge Links to GCSE Maths 8300 1 3.6.1 to 3.6.5 Statistical Enquiry Cycle (SEC) – to become familiar with the steps required to carry out a sound statistical investigation 3 If appropriate it would be helpful to reference KS3 statistical investigations carried out in maths and inspect them for adherence to the SEC 2 3.1.1 A1 3.1.2 A2 Understand what a hypothesis is and how it might be tested Understand factors that may constrain how an investigation is carried out and how a hypothesis might be tested 1 2 3.1.3 A3 Understand the necessary and preferably proactive strategies that might be necessary to avoid the issues raised above when undertaking an investigation 1 2/3 3.2.1 B1a 3.2.4 B2a Know the different types of data that arise and investigate situations when these types arise Understand that a clear knowledge of the data type is key to understanding how to correctly interrogate the data (eg which diagram to use) Understand the potential dangers of using secondary data 2 S2, S3h, S4 3 3.2.3 B1c Understand the terms ‘explanatory’ / ‘response’ and ‘dependent’ / ‘independent’ (through use of examples) 1 P8 3 3.2.5 B2b Understand the difference between a census and a sample, possibly referencing the National Census as an example 1 4 3.2.5 B2b 3.5.4 E2a Understand different types of experiments and observation including the implications for level of control Understand that comparing outcomes with predictions can be used to identify possible bias in the design 1 4 3.2.5 B2b 3.5.10 E3d Understand how to reference and interpret secondary sources – working online if possible to interrogate well known national sources of data including the Office for National Statistics and government 1 4/5 3.2.5 B2b 3.2.14 B4 3.2.7 B2d Understand how to write and evaluate a questionnaire, including considerations in B4, avoiding bias and dealing with sensitive issues 2 5 3.2.5 B2b Understand the use of simulations to obtain data and information 1 5 3.2.6 B2c Understand validity and reliability as detailed in B2c 1 6 3.2.5 B2b Summary lesson – understand the relative benefits of the different methods of data collection recently considered 1 6 – Assessment on work done so far 1 6 3.2.8 B3a 3.2.9 B3b Understand what a population is in different circumstances, the use of sample frames and sampling in general 1 S1 7 3.2.10 B3c 3.2.11 B3d Understand the different types of sampling from the specification in an outline way 1 7 3.2.10 B3c Understand the reasons for use of and dangers of convenience sampling 1 7/8 3.2.11 B3d and 3.2.12 B3e Understand the concept of random sampling and how to carry it out using the different methods listed in the specification 2 8 3.2.11 B3d Understand the concept of and how to carry out a systematic sample 1 8 3.2.11 B3d Understand the concept of and  how to carry out a quota sample 1 9 3.2.13 B3f Understand the concept of stratification and the necessary calculations and rounding issues that may arise 2 Calculating with percentages and fractions (N2) 9/10 3.2.15 B5a Understand how to deal with issues that arise with collected data including sessions on internet collected data 2 10 3.2.16 B5b Understand the possible need to clean data including on spreadsheets and the techniques required 1 10 3.2.17 B5c Understand extraneous variables, how to identify and control them 1 11 – Review of methods for data selection and collection 1 11 3.3.1 C1a and 3.2.2 B1b Understand how to tally and  tabulate data including the use of different labelling systems Understand the implications of merging classes for continuous data 2 Use of double inequalities for ‘between’ two values such as 0 ≤ t ≤ 10 (N1) S2, S3h 12 3.3.1 C1a Understand the use and misuse of pictograms 1 S2 12 3.3.1 C1a Understand how to draw a standard pie chart 1 How to use a protractor (G2) Use of angle and fraction calculations S2 12 3.3.1 C1a Understand how to interpret pie charts already drawn or generated by the student 1 S2 13 3.3.2 C1b Understand how to construct a comparative pie chart for two data sets 1 Knowledge of area of a circle formula and calculations (G17) 13 3.3.2 C1b Understand how to interpret and work with comparative pie charts and other 3D visualisation methods (eg from the media) 1 Knowledge of area of a circle formula and calculations (G17) 13 3.3.1 C1a Understand how to draw a stem-and-leaf diagram including the importance of a key 1 14 3.3.1 C1a Understand how to draw a back-to-back stem-and-leaf diagram including the importance of a key 1 14 3.3.1 C1a Understand how to interpret stem-and-leaf and back-to-back stem-and-leaf diagrams (excluding median and IQR which comes later as a refresher for these diagrams) 1 14 3.3.1 C1a Understand how to interpret Venn diagram (excluding their use for probability which comes later as a refresher for these diagrams) 1 P6 15 3.3.1 C1a Understand how to draw Venn diagrams from information given 1 P6 15 3.3.1 C1a 3.3.7 C4b Understand the types of data for which the diagrams covered so far are suitable 1 S2, S3h 15 – Second assessment on work done so far 1

Term two

 Week number Specification reference Learning objective(s) Suggested timing (hours) Prerequisite knowledge Links to GCSE Maths 8300 1 3.3.2 C1b Understand how to interpret choropleth maps 1 1 3.3.2 C1b Understand how to interpret and compare data sets shown in population pyramids 1 1 3.3.3 C2 Understand how to draw and interpret a basic bar chart and bar line chart 1 S2 2 3.3.3 C2 Understand how to draw and interpret dual and composite bar charts 1 2 3.3.3 C2 Understand how to draw and interpret percentage bar charts 1 2 3.3.3 C2 Understand how to draw and interpret line charts 1 S2 3 3.3.3 C2 A basic understanding of time series and scatter charts (both to be covered in more detail later) 1 S2, S6 3 3.3.3 C2 Understand how to draw a frequency polygon 1 3 3.3.3 C2 Understand how to interpret a frequency polygon 1 4 3.3.3 C2 Understand the features of and how to construct a histogram with equal width classes 1 S3h 4 3.3.3 C2 3.3.5 C3b Understand the correct method of frequency density to construct histograms with unequal width classes 2 Area of a rectangle (G16) S3h 5 3.3.3 C2 Understand how to interpret histograms of equal and unequal width classes 1 S3h 5 3.3.3 C2 3.3.4 C3a 3.3.7 C4b Look in detail at the types of data which can be used in the different types of diagram encountered so far, understand when various types of diagram can and cannot be used in terms of the nature of the data to be visualised 2 S2, S3, S4h 6 3.3.5 C3b 3.3.2 C1b Understand the misrepresentations that occur in visualisations, including those in media and the internet 3 [suggested project for one week] 7 All of section C Summary of different visualisation methods including assessment 3 8 3.4.1 D1a 3.4.2 D1b Understand the basic measures of average and their strengths and weaknesses 1 S4 8 3.4.1 D1a 3.5.7 E3a Understand how to find the mode or modal group and how to compare two data sets through the comparison of their modes (in context) 1 S4 8 3.4.1 D1a Understand how to calculate the mean for a set of data and a discrete frequency distribution 1 S4 9 3.4.1 D1a Understand how to calculate an estimate of the mean for a grouped frequency distribution including why it is an estimate 1 S4 9 3.4.1 D1a 3.4.2 D1b Understand how to calculate a geometric mean and the circumstances in which this is a better measure than arithmetic mean 1 9 3.5.7 E3a Comparing two data sets through the comparison of their means (in context) 1 S5 10 3.4.1 D1a 3.5.7 E3a Understand how to calculate the median for a set of data and how to compare two data sets through the comparison of their medians (in context) 1 S4, S5 10 3.4.1 D1a Understand how to identify the median for tabulated discrete data 1 S4 10 3.4.1 D1a Understand how to estimate the median for a grouped frequency distribution (calculation methods) 1 S4 11 3.4.1 D1a Understand the concept of a weighted mean and how it is calculated 2 11 3.4.3 D2 Understand the basic concept of a symmetric distribution and of skew by inspection 1 12 3.4.3 D2 Understand how to calculate skew from a given formula 1 12 3.5.13 E5a Understand how to interpret the skewness of a distribution or compare the skewness of two distributions from inspection or from calculation 1 12 – Summary of measures encountered so far, optional assessment 1

Term three

Time within this term has been allocated to summer exams and other possible events, such as work experience, by reducing the teaching load to 10 weeks between Easter and summer.

 Week number Specification reference Learning objective(s) Suggested timing (hours) Prerequisite knowledge Links to GCSE Maths 8300 1 3.4.4 D3a Understand the concept of (measures of) spread and the most basic of those, the range 1 S4 1 3.4.4 D3a Understand what quartiles are from a list of values and the concept of inter-quartile range 1 S4h 1 3.4.4 D3a Understand what deciles and percentiles are and the concept of inter-percentile and inter-decile range 1 2 3.3.3 C2 Understand the concept of cumulative frequency and how to find cumulative frequencies for a grouped or discrete frequency distribution 1 S3h 2 3.3.3 C2 Understand how to construct a cumulative frequency graph for a grouped frequency distribution 2 S3h 3 3.3.3 C2 Understand how to construct a cumulative frequency step polygon for a discrete frequency distribution 2 3/4 3.3.3 C2 3.4.1 D1a 3.4.4 D3a Understand how to obtain estimates of median and inter-quartile range from different cumulative frequency graphs and comparing the results in context 2 S4h 4 3.3.3 C2 3.4.4 D3a Understand how to obtain estimates of inter-decile range and inter-percentile range from different cumulative frequency graphs and comparing the results in context 1 4 3.4.4 D3a Understand the concept of standard deviation and what it is measuring 1 5 3.4.4 D3a Understand how to calculate standard deviation for a list of values 1 5 3.4.4 D3a 3.4.1 D1a Understand how to calculate standard deviation (and mean) using Sigma notation and frequency tables 2 6 3.4.5 D3b Understand the concept of outliers and looking for them by inspection 1 S4, S6 6 3.3.3 C2 Understand how to construct a box plot 1 S4h 6 3.3.3 C2 and 3.4.5 D3b Understand the construction of a box plot with statistical outliers included (of the LQ –1.5IQR  and UQ +1.5IQR type) 1 7 3.4.5 D3b An understanding of outliers for the mean and standard deviation method 1 7 3.5.14 E5b Understand how to comment on outliers with reference to the original data 1 7 SEC 3.6 Revisit the Statistical Enquiry Cycle and discuss in light of content now covered 1 8 or 9 All specification references so far Revision of material in Year 10 3 9 or 8 All specification references so far Suggested statistical investigation (the previous specification’s Controlled Assessment is a good source) 3 10 All specification references so far End of Year assessments, review and feedback 3

Year two

Term one

 Week number Specification reference Learning objective(s) Suggested timing (hours) Prerequisite knowledge Links to GCSE Maths 8300 1 3.3.6 C4a 3.3.7 C4b Understand and review the different types of presentations and visualisations for data including comparisons Focus on the type of data and consequent choices for the type of diagram which can be used 2 S2, S3, S4 1/2 3.4.2 D1b 3.5.7 E3a 3.5.8 E3b Understand and review the different types of measures of average and spread Focus on the context and type of data with the consequent choice of measure used 2 S4 2 3.3.3 C2 3.4.6 D4 Review of time series graphs and understand the basic notion of trends over time and within a cycle gleaned by inspection 1 S2 2/3 3.4.6 D4 Understand the common scenarios where four-point moving averages are useful and why Understand how to plot four-point moving averages and join with line of best fit by eye to see trend 2 3 3.4.6 D4 Understand how to determine appropriate point moving averages according to the context, their plotting and interpretation 1 3 3.5.15 E6 Understand how to interpret seasonal and cyclic trends in context 1 4 3.5.15 E6 Understand how to use identified trends to make predictions about the future values in a time series 1 S2 4 3.4.1 D1a 3.5.15 E6 Understand how to calculate and use mean seasonal variation in prediction about the future values in a time series 1 4 3.3.3 C2 3.4.7 D5 Review of scatter diagrams including determining the line of best fit by eye 1 S6 5 3.4.7 D5 Understand the technique of determining a line of best fit using the plotted double mean 1 5 3.4.7 D5 Understand the technique of determining (and plotting) the equation of the regression line 2 Understand y = mx + c, including the plotting of such lines (A10) 6 3.5.19 E8a Understand the meaning of the terms ‘interpolation’ and ‘extrapolation’ and their relative reliability. 1 S6 6 3.5.19 E8a 3.5.20 E8b Understand all the vocabulary surrounding correlation for type and strength 1 S6 6 3.5.21 E8c Understand that correlation does not necessarily imply causation and that other factors may or will interact 1 S6 7 3.5.19 E8b 3.5.22 E9a Understand the Spearman’s –1 to +1 scale to strength of correlation as outlined in the specification and interpreting results in context 1 7 3.4.8 D6 3.5.22 E9a Understand how to calculate Spearman’s correlation coefficient using the formula (or by calculator as this is acceptable in assessments) 1 7 3.5.23 E9b 3.5.24 E9c Understand that there are other ways of measuring correlation (namely Pearson’s product moment correlation coefficient) and be able to interpret on the –1 to +1 scale 1 8 3.5.24 E9c Understand how Pearson’s and Spearman’s methods compare 1 8 3.5.16 E7a Understand how to interpret data that relates to ‘rates of change’ over time eg birth rates 1 R15h 8 3.5.17 E7b Understand how to calculate rates of change using given formulae and interpret the results 1 R15h 9 3.5.18 E7c Understand the different common index numbers that occur as detailed in specification, including but not limited to, retail price index, consumer price index and gross domestic product 1 9 3.5.18 E7c Understand how to calculate and interpret weighted index numbers 2 10 All previous work this term Review and assessment 2 10 3.5.1 E1a Understand the scales that are used to work with probability (fractions, decimals and percentages) 1 Fractions, decimals and percentages (N1) P3 11 3.5.6 E2c Understand the concept of a sample space diagram and how to complete one 1 P7 11/12 3.5.1 E1a 3.4.9 D7 Understand how to calculate probabilities for equally likely outcomes in contexts of one and two events including use of sample spaces 3 P7 12 3.5.11 E4a Understand the concept of independent events and relevant notation 1 P8 12/13 3.5.11 E4a Understand how to calculate probabilities involving independent events and how to use probabilities to determine if events are independent 2 P8 13 3.5.12 E4b Understand the concept of conditional probability and relevant notation 1 P9h 13 3.5.12 E4b Understand how to calculate probabilities conditional on other events having occurred 1 P9h 14 3.3.1 C1a Understand how to construct a two-way table from given information 1 P7 14 3.5.6 E2c Understand how to use a two-way table to calculate basic probabilities (not conditional) 1 P8 14 3.5.6 E2c Understand how to use a two-way table to calculate conditional probabilities 1 P9h 15 3.5.6 E2c Understand how to use a Venn diagram to calculate basic probabilities (not conditional) 1 P6 15 3.5.6 E2c Understand how to use a Venn diagram to calculate conditional probabilities 1 P9h 15 – Overview of learning so far 1

Term two

 Week number Specification reference Learning objective(s) Suggested timing (hours) Prerequisite knowledge Links to GCSE Maths 8300 1 3.5.6 E2c Understand how to construct a tree diagram for a given context 1 P7, P8 1 3.5.6 E2c Understand how to use a tree diagram to calculate probabilities in ‘with replacement’ (independent) situations 2 P8, P9h 2 3.5.6 E2c Understand how to use a tree diagram to calculate probabilities in ‘without replacement’ (dependent / conditional) situations 2 P8, P9h 2 3.5.2 E1b Understand how probability values can be used to find expected frequencies 1 3 3.5.3 E1c Understand the concept of risk as probabilities which can be compared 1 3 3.5.2 E1b 3.5.3 E1c Understand that risk probabilities can be used to generate frequencies of outcomes for characteristics within a population either on their own or as comparisons 2 4 3.5.5 E2b Understand that increasing trials improves the proximity of experimental probability (relative frequency) to theoretical probability 1 Ability to compare fractions or decimals (N1) P5 4 3.5.25 E10a Understand how to comment on differences between experimental and theoretical values in an experiment in the context of possible bias 1 4 All probability and related work Review of work done on probability 1 5 All probability and related work Optional assessment on probability 1 5 3.5.26 E10b Understand the basic conditions for a binomial distribution to be valid and the features of the distribution 1 5/6 3.5.26 E10b Understand the method of calculating probabilities for a binomial situation for n up to and including 5 (using formula if desired) 2 6 3.5.27 E11a Understand the general features of a Normal distribution and its common place in real data 1 6 3.5.28 E11b Understand the specific features of a Normal distribution relating to probabilities of being specific numbers of standard deviations from the mean 1 7 3.5.27 E11a 3.5.28 E11b Understand how to sketch one or more Normal distributions showing the key features they exhibit 1 7 3.5.30 E11d Understand the concept of how to standardise using the mean and standard deviation as a method of comparing Normal samples 1 7 3.5.30 E11d Understand how to work with given or calculated standardised scores to make comparisons 1 8 3.5.29 E11c Understand the concept of quality assurance and the charts used (mean, median and range) 1 8 3.5.29 E11c Understand how to use warning and action line for quality assurance sampling applications (mean, median and range) 2 9 All of E12 and E13 Understand the concept of using samples to estimate values in a population 1 S1 9 3.5.31 E12a Understand how to use summary data to make estimates of population characteristics 1 S4, S5 9/10 3.4.1 D1a 3.5.32 E12b Understand how to use samples to estimate a population mean. Revise all aspects of obtaining measures of average from lists, tables and diagrams 4 S4, S5 11 3.5.33 E12c Understand how to use sample data to estimate the proportion of a characteristic in a population 1 11 3.5.34 E12d Understand the concept and assumptions being made during the implementation of the Petersen capture-recapture technique 1 11 3.5.34 E12d Understand how to calculate population estimates using the Petersen capture-recapture technique 1 12 3.5.35 E13a 3.2.6 B2c Understand the impact of sample size on issues such as reliability and replication 1 12 3.5.36 E13b Understand at a basic level the notion that a set of sample means will be more closely distributed than individual values from the same population 1 12 – Assessment 1

Term three

 Week number Specification reference Learning objective(s) Suggested timing (hours) Prerequisite knowledge Links to GCSE Maths 8300 1 3.3.6 C4a 3.5.7 E3a 3.5.8 E3b 3.5.9 E3c Review the comparison of different samples, or a sample and a population, to include the comparison of a measure of location and the comparison of a measure of spread, concluding in the context that the data is within 3 2/3 3.3.7 C4b Review the selection of appropriate forms of diagrammatic representation based on the nature of the data (review of all visualisations in this context of data types) 3–6 S2, S3, S4, S6 4 onwards as time allows – Other revision and past papers (eg specimen and practice papers) according to the needs of the students