Nuffield Mathematics teaching resources are for use in secondary and further education

# FSMQ Level 3 (legacy) Using and applying statistics scheme of work

This AQA FSMQ requires a total of 60 guided learning hours that could be used in a variety of ways such as 2 hours per week for 30 weeks, 4 hours per week for 15 weeks, 5 hours per week for 12 weeks. The order and time allocations can be varied to suit different groups of students.

Note that you will also need to allow time for students to complete a Coursework Portfolio. The Coursework Portfolio requirements are listed in the AQA Advanced FSMQ specification for Using and applying statistics and in the AQA AS Use of Mathematics specification. The assignments below provide some data that your students could use in their portfolios, but if possible you should use data that is more relevant to their other studies or interests.

Before students start the course they should be able to:

• collect and organise data, including the use of questionnaires, grouping and tables (with and without spreadsheets)
• calculate mean, median, mode, range, quartiles and interquartile range for continuous, discrete and grouped data
• draw and interpret bar charts, frequency diagrams, pie charts and line graphs
• draw Cartesian graphs accurately
• substitute values into statistical formulae such as  $\textup{mean}&space;=&space;\frac&space;{\textup{sum&space;of&space;values}}{\textup{number&space;of&space;values}}$

The suggested work scheme below includes some revision of these as well as the other topics and methods that need to be covered.

The following techniques should be introduced as soon as possible and used throughout the course:

• using statistical terms correctly eg qualitative and quantitative data, primary and secondary data, independent and dependent variables, discrete and continuous variables, population, representative and random samples, outliers.
• using spreadsheets to carry out calculations and display results in tables and statistical charts and graphs
• checking calculations using estimates, inverse operations and different methods.

Although the topics are listed separately below, it would be more beneficial to follow a number of statistical investigations through from the initial collection and organisation of data to an analysis of the situation making use of statistical charts and measures.  Where possible these investigations should reflect the students’ other areas of work and interests.

Note that topics given below as Extension Opportunities are optional, but students must do some work outside the main core in their coursework portfolio.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Carrying out  investigations (3 hours) Identify characteristics that are pertinent to investigations.  Use statistical terms - qualitative and quantitative data, primary and secondary data, discrete and continuous variables, population, representative, biased, random and stratified samples etc. Discuss different methods of collecting data –  the use of surveys (including questionnaires), observations and experiments.  Include ideas associated with consistency, repeatability and variability between samples. Results    Data sheets containing A level results and a worksheet with related statements. Students consider the limitations of the data in assessing the truth of the statements. Optional use of spreadsheet. HE applications   Data Sheets, spreadsheet and worksheet using gender, age, ethnic origin and other information about HE applicants. Football figures    Excel spreadsheet containing 2007-8 data for each premier league club. Parking permits  Presentation, activity, information sheet and work sheet including finding random and representative samples, questionnaire design. Music and work      Worksheet requiring students to write an hypothesis and design an experiment to test whether listening to music has any effect on the performance of people doing work. Also includes arithmetic tests that may be used to carry out such an experiment. Price at the pump     Discuss what factors affect petrol prices at different petrol stations and how you could collect data to investigate the ideas generated.  May also be used later in the course when students are able to analyse data they collect.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Statistical charts (6 hours) Drawing and interpreting bar charts (include comparative and component bar charts), pie charts (including comparative pie charts) line graphs and histograms.  Using a spreadsheet to draw charts and graphs. Describe the shape of distributions using terms such as symmetrical, skewed, multi-modal. Interpreting complex charts eg line graph superimposed on bar chart and any charts or graphs related to students’ other studies. Extension Opportunities – other appropriate diagrams eg stem & leaf. Draw pie charts in Excel    Activity showing students how to draw a pie chart in Excel and change its appearance. Draw line graphs in Excel     Activity showing students how to draw line graphs in Excel. Pie charts    Activity showing students how to draw a pie chart by hand. Also includes practice exercise with real data – can be used as follow up to ‘Draw pie charts in Excel’ activity. Histograms    Instructions explaining how to construct an accurate histogram and frequency polygon in Excel. Pareto charts Combination of bar and cumulative frequency charts that are useful in economics, business and management.  Data sheet and worksheet.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Statistical measures (8 hours) Find mean, mode, median, range, quartiles and standard deviation of data from a list and from a frequency table.  Consider outliers and include using both a calculator and spreadsheet. Use of a cumulative frequency graph to find the median, quartiles and percentiles. Compare and contrast data sets using statistical charts and measures. Extension opportunity –  box and  whisker plots. Casio calculators    Instructions for using a Casio fx83WA or fx85WA to find the mean and standard deviation. Graphic calculators  Presentation introducing students to the Casio fx-7400G PLUS calculator. Election results    Spreadsheet containing the 2005 and 2010 General Election results.  For practice of spreadsheet skills or an assignment. House prices    Spreadsheet of house price data for 1983 to 2010 which could be used for L3 work. Pay rates for men and women   Activity showing students how to draw a cumulative frequency graph in Excel. Box and whisker plots    Students can use this Excel spreadsheet to draw up to four box and whisker plots.  Includes instructions. Subject results      Spreadsheet containing A-level results in 13 subjects.  Use for practice of spreadsheet skills or in an assignment. Finding information from complex tables (4 hours) Include calculation of percentages and ‘reverse’ percentages

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Correlation and regression (7 hours) Definition of independent and dependent (controlled and response) variables. Plot scatter diagrams of bivariate data, including the mean point and draw a line of best fit by eye.  Understand positive, negative, strong, weak and no correlation. Calculation and interpretation of the product-moment correlation coefficient (using both a calculator and spreadsheet). Include the fact that correlation does not necessarily imply cause and effect, that a third variable may underlie correlation and that not all relationships are linear. Discuss the principle of least squares.  Find the equation of a regression line using both a calculator and spreadsheet. Draw the regression line (by hand and spreadsheet) and interpret regression coefficients in context. Extension opportunity – rank correlation coefficients, non-linear models. DISCUSS regression and correlation    Simulations to aid understanding.  Internet access needed. Casio calculators    Instructions for using a Casio fx83WA or fx85WA to find the product moment correlation coefficient and regression line of y on x. Correlation    Students find product moment correlation coefficients, draw scatter graphs and summarise the results Music Festival  This L2 activity includes an Excel spreadsheet containing sunshine, rainfall and temperature data for England and Wales, Northern Ireland and Scotland for each month in every year from 1961 to 2010. This could be used for a variety of work at L3. Anthropometric data   Students investigate relationships between anthropometric variables and write a report on their findings. This may include the use of scatter diagrams, lines of best fit, regression lines, and correlation coefficients. Mammals (assignment)   Data sheets giving body mass, brain mass, sleep duration, life span, gestation time and danger index for small, medium and large mammals. Assignment based on the data and suggestions for alternative uses. Optional use of spreadsheet. Module results    Students analyse and compare results for two modules.  Includes use of Excel and Autograph as well as diagrams and calculations done by hand.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. The Normal Distribution (8 hours) The use of theoretical probability distributions to model populations. Features of normal distributions: · continuous variable · unimodal · symmetrical · mean = mode = median · approximately two-thirds of the distribution lies within one standard deviation of the mean · approximately 95% of the distribution lies within two standard deviations of the mean The standard normal distribution with mean 0 and variance 1. Use of the standard normal table to find probabilities and expected frequencies. Use of the standard normal table in reverse calculations. Extension Opportunities – other probability distributions eg uniform, binomial, Poisson.  Significance tests – t, z, Mann Whitney, Wilcoxin signed rank, chi-squared. Stature   Data sheet gives the heights of samples of men and women from 8 countries.  Student worksheet leads to main features of samples from normal distributions.  Optional use of spreadsheet. Pulse rates    Experiment to find the effect of exercise on pulse rates.  Spreadsheet gives results from such an experiment carried out over a number of years by Dr Richard Wilson at the University of Queensland. Health data    Data sets involving the health of adults and children in the UK and information about hospital waiting lists etc. DISCUSS Sampling  Simulations to aid understanding of how variation occurs within and between samples.  Internet access needed. Critical thinking (6 hours) Examine statistical work produced by others with a questioning and critical approach. Consider all aspects of the initial data and the statistical charts, graphs and measures used to analyse the data.  Also consider how findings may be extrapolated from the sample studied to the wider population and the validity of any conclusions reached. Global warming  (assignment)   Gives a list of websites with reports or articles about global warming including statistical evidence.  Students analyse one or more of these reports to meet the second AQA portfolio requirement. Critical thinking (assignment)   Gives general instructions for the report that learners must include in their AQA portfolio and a list of useful weblinks. Revision (6 hours) Revise topics. Work through revision questions and practice papers. Discuss the data sheet - make up and work through questions based on it.

Page last updated on 26 March 2012