Cambridge International AS and A Level Mathematics Statistics

S1 Statistics 1

Chapter 1: Exploring Data

Looking at the Data

Stem-and-Leaf Diagrams

Categorical or Qualitative Data

Numerical or Quantitative Data

Measures of Central Tendency

Frequency Distributions

Grouped Data

Measures of Spread (Variation)

Working with an Assumed Mean

Chapter 2: Representing and Interpreting Data

Histograms

Measures of Central Tendency and of Spread Using Quartiles

Cumulative Frequency Curves

Chapter 3: Probability

Measuring Probability

Estimating Probability

Expectation

The Probability of Either One Event or Another

Independent and Dependent Events

Conditional Probability

Chapter 4: Discrete Random Variables

Discrete Random Variables

Expectation and Variance

Chapter 5: Permutations and Combinations

Factorials

Permutations

Combinations

The Binomial Coefficients

Using Binomial Coefficients to Calculate Probabilities

Chapter 6: The Binomial Distribution

The Binomial Distribution

The Expectation and Variance of B(n, p)

Using the Binomial Distribution

Chapter 7: The Normal Distribution

Using Normal Distribution Tables

The Normal Curve

Modelling Discrete Situations

Using the Normal Distribution as an Approximation for the Binomial Distribution

S2 Statistics 2

Chapter 8: Hypothesis Testing Using the Binomial Distribution

Defining Terms

Hypothesis Testing Checklist

Choosing the Significance Level

Critical Values and Critical (Rejection) Regions

One-Tail and Two-Tail Tests

Type I and Type II Errors

Chapter 9: The Poisson Distribution

The Poisson Distribution

Modelling with a Poisson Distribution

The Sum of Two or More Poisson Distributions

The Poisson Approximation to the Binomial Distribution

Using the Normal Distribution as an Approximation for the Poisson Distribution

Chapter 10: Continuous Random Variables

Probability Density Function

Mean and Variance

The Median

The Mode

The Uniform (Rectangular) Distribution

Chapter 11: Linear Combinations of Random Variables

The Expectation (Mean) of a Function of X, E(g(X))

Expectation: Algebraic Results

The Sums and Differences of Independent Random Variables

More than Two Independent Random Variables

Chapter 12: Sampling

Terms and Notation

Sampling

Sampling Techniques

Chapter 13: Hypothesis Testing and Confidence Intervals Using the Normal Distribution

Interpreting Sample Data Using the Normal Distribution

The Central Limit Theorem

Confidence Intervals

How Large a Sample Do You Need?

Confidence Intervals for a Proportion

Answers

Index