## Description

This is the second in a series of books written to support the Statistics modules in MEI Structured Mathematics, but you may also use them for an independent course in the subject. Throughout the course the emphasis is on understanding, interpretation and modelling, rather than on mere routine calculations. This is the third edition of this book.

There are four chapters in this book. The Poisson distribution is covered in the first chapter and this is followed by the Normal distribution in Chapter 2. Chapter 3 is about samples and hypothesis testing. The book ends with a chapter on bivariate data, covering correlation and regression lines; you meet two correlation coefficients (Pearson’s product moment and Spearman’s rank) and use them as statistics for suitable hypothesis tests.

Several examples are taken from the pages of a fictional local newspaper, The Avonford Star. Much of the information that you receive from the media is of a broadly statistical nature. In these books you are encouraged to recognise this and shown how to evaluate what you are told.

**Contents****1 The Poisson distribution 1**

The Poisson distribution 3

Modelling with a Poisson distribution 7

The sum of two or more Poisson distributions 12

The Poisson approximation to the binomial distribution 18**2 The Normal distribution 32**

Using Normal distribution tables 34

The Normal curve 39

Modelling discrete situations 49

Approximating the binomial distribution so

Approximating the Poisson distribution 52**3 Samples and hypothesis testing es**

Interpreting sample data using the Normal distribution 68

Contingency tables 81

The \2 test for independence in a contingency table 87**4 Bivariate data 104**

Describing variables 106

Interpreting scatter diagrams 107

Product moment correlation 110

Rank correlation 132

The least squares regression line 142

**Appendices 159**

1. Mean and variance of the Poisson distribution 159

2. The sum of two independent Poisson distributions 160

3. The equivalence of Spearman’s rank correlation

coefficient and Pearson’s product moment correlation

coefficient 161

4. The least squares regression line 162**Answers ies**

Chapter 1 165

Chapter 2 167

Chapter 3 171

Chapter 4 173