Course Outline

Section
1 Representation of data
1.1 Introduction
1.2 Stem-and-leaf diagrams
1.3 Histograms and frequency polygons
1.4 Cumulative frequency graphs
1.5 Practical activities
2 Measures of location
2.1 Introduction
2.2 Median
2.3 Finding the median from a frequency table
2.4 The mean
2.5 Summation notation
2.6 Calculating the mean from a frequency table
2.7 Making the calculation of the mean easier
2.8 The mode and the modal class
2.9 Comparison of the mean median and mode
2.10 Practical activities
3 Measures of spread
3.1 Introduction
3.2 The range
3.3 The interquartile range
3.4 Box plots
3.5 Outliers
3.6 Variance and standard deviation
3.7 Proof of the equivalence of the variance formulae
3.8 Calculating variance from a frequency table
3.9 Making the calculation of variance easier
3.10 Practical activities
4 Probability
4.1 Assigning probability
4.2 Probabilities of events
4.3 Addition of probabilities
4.4 Conditional probability and the multiplication law
4.5 Independent events
4.6 Practical activities
5 Permutations and combinations
5.1 Permutations
5.2 Permutations when the objects are not distinct
5.3 Combinations
5.4 Applications of permutations and combinations
6 Probability distributions
6.1 Random variables
6.2 An important property of a probability distribution
6.3 Using probability distribution as a model
7 The binomial and geometric distribution
7.1 The binomial distribution
7.2 Practical activity
7.3 The geometric distribution
7.4 Practical activity
8 Expectation and variance of a random variable
8.1 Expectation
8.2 The variance of a random variable
8.3 The expectation and variance of a binomial distribution
8.4 The expectation of a geometric distribution
8.5 Proof that E(X) = 1/p for a geometric distribution
9 Correlation
9.1 Scatter diagrams
9.2 Measurement of correlation
9.3 Making the calculation of r easier
9.4 Practical activities
9.5 Interpretation of a correlation coefficient
9.6 Rank correlation
9.7 Another method of calculating Spearman's rank correlation coefficient
9.8 Practical Activities
9.9 A comparison of the two correlation coefficients
10 Regression
10.1 Linear relationships
10.2 The method of least squares
10.3 Making predictions with a regression line
10.4 Practical activities
10.5 Two possible regression lines
10.6 Practical activity
10.7 Controlled variables
10.8 Practical activity