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
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 
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 
HE applications 

Football figures 

Parking permits 

Music and work 

Price at the pump 
Topic area 
Content 
Nuffield resources 
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, multimodal. 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 
Draw line graphs in Excel 

Pie charts 

Histograms 

Pareto charts 
Topic area 
Content 
Nuffield resources 
Statistical measures 
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 
Graphic calculators 

Election results 

House prices 

Pay rates for men and women 

Box and whisker plots 

Subject results 

Finding information from complex tables 
Include calculation of percentages and ‘reverse’ percentages 
Topic area 
Content 
Nuffield resources 
Correlation and regression 
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 productmoment 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, nonlinear models. 
DISCUSS regression and correlation 
Casio calculators 

Correlation 

Music Festival 

Anthropometric data 

Mammals (assignment) 

Module results 
Topic area 
Content 
Nuffield resources 
The Normal Distribution 
The use of theoretical probability distributions to model populations.
Features of normal distributions: 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, chisquared. 
Stature 
Pulse rates 

Health data 

DISCUSS Sampling 

Critical thinking 
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) 
Critical thinking (assignment) 

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