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Introduction

1. About this module and CAST
   1. Aim of the module
   2. Full version of CAST
   3. About the author
   4. Copyright


2. Variability
   1. Sources of variability
   2. Sorting a set of marks

Chapter 1: Looking at marks

1. Displaying individual marks
   1. Dot plots
   2. Stem and leaf plots
   3. Split stems
   4. Creating the plots


2. What does a distribution show?
   1. Outliers
   2. Clusters
   3. Centre, spread and shape
   4. Displaying other information
   5. Dangers of over-interpretation

Chapter 2: Graphical summaries of marks

1. Density and histograms
   1. Histograms
   2. Best histogram class width
   3. Interpretation
   4. More about histogram bin width
   5. Frequency polygons
   6. Drawing histograms


2. Normal distributions
   1. Smooth curves to describe distributions
   2. Normal distributions
   3. Normal probabilities and area


3. Discrete and categorical data
   1. Discrete and continuous data
   2. Bar charts and histograms
   3. Categorical data
   4. Stacked bar charts and pie charts
   5. Drawing bar charts

Chapter 3: Numerical summaries of marks

1. Describing centre
1. Centre and spread
2. Mean, median, and mode
3. Comparison of mean and median
4. Mean for discrete data
5. Quartiles, deciles, and percentiles


2. Describing spread
   1. Range and interquartile range
   2. Distance from k
   3. Standard deviation

Chapter 4: Marks on other scales

1. Z-scores and stanines
   1. The normal parameters
   2. The standard normal distribution
   3. 70-95-100 rule
   4. Standardising marks
   5. Stanines


2. Reference populations
   1. National distributions of marks
   2. Obtaining percentiles from a reference population
   3. Obtaining stanines from a reference population


3. Scaling marks
   1. Linear scaling
   2. Piecewise linear scaling
   3. Scaling with Excel

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