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Develop advanced mathematical skills with a real-world focus

Table of Contents

Syllabus matching grid
1 Introduction to statistical thinking
1.1: What is statistics and why is it important?
1.2: Types of data
2 Measures of location and spread
2.1: Averages
2.2: Quartiles and the interquartile range
2.3: Variance and standard deviation
2.4: Which average should you use?
2.5: Coding
3 Representing and analysing data
3.1: Stem-and-leaf diagrams
3.2: Box-and-whisker plots
3.3: Histograms
3.4: Cumulative frequency graphs
3.5: Skewness
3.6: Comparing distributions
Review exercise A
Maths in real-life: Seeing the wood and the trees
4 Probability
4.1: Basic concepts and language f probability
4.2: Two (or more) events
4.3: Tree diagrams
4.4: Conditional probability
4.5: Relationships between events
5 Probability distributions and discrete random variables
5.1: Discrete random variables
5.2: The probability function, p(x)
5.3: Expectation of a discrete random variable
5.4: The variance of a discrete random variable
6 Permutations and combinations
6.1: Permutations of n distinct objects in a straight line
6.2: Permutations of k objects from distinct objects in a straight line
6.3: Allowing constraints on permutations (for n distinct objects)
6.4: Permutations when some objects are not distinguishable
6.5: Combinations
6.6: Evaluate probabilities by calculation sing permutations or combinations
Review exercise B
Maths in real-life: Sporting statistics
7 The binomial distribution
7.1: Introducing the binomial distribution
7.2: Mean and variance of the binomial distribution
7.3: Modelling with the binomial distribution
8 The geometric distribution
8.1: Introducing the geometric distribution
8.2: The mean of the geometric distribution
9 The normal distribution
9.1: Continuous probability distributions and the normal distribution
9.2: Standard normal distribution
9.3: Calculating probabilities for the (µ, *s2) distribution
9.4: Using the normal distribution
10 The normal approximation to the binomial distribution
10.1: Normal shape of some binomial distributions
10.2: Continuity correction
10.3: The parameters for the normal approximation
Review exercise C
Maths in real-life: Statistics is definitely not a lonely world
Exam-style paper A
Exam-style paper B
Answers
Data sets
Glossary of terms
Index