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

FSMQ Level 3 (pilot) Data analysis scheme of work

Before starting this Advanced (Level 3) FSMQ, students should have acquired the skills and knowledge associated with the Statistics assessment objective of GCSE Mathematics, or with an Intermediate (Level 2) FSMQ in Data or equivalent.  A suggested work scheme showing topic areas and methods to be covered is given below. The order and time allocations can be varied to suit different groups of students. 

The assignments below could be used as classroom activities or homework, but will not be part of the AQA assessment of this FSMQ.

Topic area

Content

Nuffield resource
(originally written for the 'Using and applying statistics' FSMQ) 
The links below go to pages from which you can download the resources, some recently revised.

Carrying out  investigations

(4 hours)

Identify characteristics that are pertinent to investigations.  Introduce and use statistical terms, including qualitative and quantitative data, primary and secondary data, discrete and continuous variables, population, representative, biased, random, and stratified samples.

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.

(Note that the AQA FSMQ 'Data analysis' concentrates on the analysis of data which has already been obtained, rather than data that students collect themselves.  Therefore time should not be spent on collecting data, but students should be aware of issues relating to the collection and use of data in real situations.)

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.  Teacher notes suggest uses.

Parking permits   
Presentation, activity, information sheet and work sheet including finding random and representative samples, questionnaire design etc.

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.

 

Statistical diagrams

(6 hours)

Draw and interpret back-to-back stem and leaf diagrams and histograms (including grouping of data).  Describe the shape of distributions using terms such as symmetrical, skewed, multi-modal. (Measures of skewness not required.)

Histograms  
Instructions explaining how to construct an accurate histogram and frequency polygon in Excel.

Graphic calculators    
Presentation introducing students to the Casio fx-7400G PLUS calculator.

 

Topic area

Content

Nuffield resource
The links below go to pages from which you can download the resources, some recently revised.

Statistical measures and further diagrams

(8 hours)

Find the mean (\overline x), mode, median, range, inter-quartile range and standard deviation of data (both \sigma_n and \sigma_n_-_1) from a list and from a frequency table.  Use a calculator to find \overline x, \sigma_n and \sigma_n_-_1 (and also a spreadsheet if possible).  Consider the effect of outliers.

Draw and use a cumulative frequency graph to find the median, percentiles, upper and lower quartiles and interquartile range. 

Draw and interpret box and whisker plots.

Casio calculators  
Instructions for using a Casio fx83WA or fx85WA to find the mean and standard deviation.

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.

 

Compare data sets

(8 hours)

Compare and contrast data sets using measures of location and spread and statistical diagrams.

Justify choice of statistical diagrams and measures.

Subject results    
Spreadsheet containing A-level results in 13 subjects. Use for practice of spreadsheet skills.

Election results   
Spreadsheet containing the 2005 and 2010 General Election results.  For practice of spreadsheet skills.

Football figures    
Excel spreadsheet containing 2007-8 data for each premier league club.  Teacher notes suggest uses.

House prices  
Spreadsheet of house price data for 1983 to 2010 which could be used for L3 work.

Bivariate data

(10 hours)

Plot scatter diagrams of bivariate data, including the use of mean values and draw a line of best fit by eye.  Discuss positive, negative, strong, weak and no correlation.

Introduce the principle of least squares, regression lines and Pearson's product moment correlation coefficient (r).  Use a calculator to find r and regression line coefficients and interpret the results.  (Also include the use of a spreadsheet if possible.)

Discuss the fact that correlation does not imply causation, that r is only a measure of linear correlation and that not all relationships are linear.

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.

Graphic calculators 
Presentation introducing students to the Casio fx-7400G PLUS calculator.

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 resource
The links below go to pages from which you can download the resources, some recently revised.

Normal distribution

(10 hours)

The use of theoretical probability distributions to model populations.

Features of a normal distribution, including:
· continuous data
· symmetry
· approximately two-thirds of the distribution lying within one standard deviation of the mean
· approximately 95% of the distribution lying within two standard deviations of the mean

The standard normal distribution with mean 0 and standard deviation 1.

Use of tables to find probabilities and expected frequencies.

Use of tables in reverse calculations.

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. Teacher Notes included.

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, information about hospital waiting lists and so on.

DISCUSS Sampling    
Simulations to aid understanding of how variation occurs within and between samples.  Internet access needed.

Critical thinking

(6 hours, could omit if short of time)

 

Examine statistical work produced by others with a questioning and critical approach. Consider the initial data and the statistical charts, graphs and measures that were used to analyse the data 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. 

Revision (8 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