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## Introduction

This free course, Prices, location and spread, examines aspects of the question:

Are people getting better or worse off?

The course concentrates on the statistical aspects of the question, focusing on statistics about prices. However, it is not the case that statistics can provide all the answers – or even the best answer – to the question of whether people are getting better or worse off. There are many non-statistical issues which are relevant and it is important to put the statistical approach in its correct perspective.

In the question, people does not refer specifically to you, the readers of the course, but to the whole of society in the UK. That is quite a big batch (more than 62 million in 2010, according to an estimate from the UK’s Office for National Statistics), consisting of men, women and children, living alone, in large or small households, or in institutions; some of them working, others unemployed, some retired and others still at school.

It is not possible, using statistical techniques, to provide a complete answer to this one question covering such a big theme, particularly an answer which is valid for all these people and their varied economic and social circumstances; data and techniques both have to be used with common sense. Instead, the aim of this text is more modest: to explore small batches of data relevant to the question (and relating to some individuals and groups in society), using basic analytical and graphical techniques. The sections in this course cover the following:

• Section 1 looks at ways to measure the overall ‘location’ (the typical value) of a batch of data. Two very important measures looked at are the ‘median’ and the ‘arithmetic mean’. The section also looks at patterns in data using diagrammatic methods.

• Section 2 shows how to calculate the ‘weighted mean’, which is a quantity related to the arithmetic mean. You will learn about some circumstances where it makes sense to calculate a weighted mean.

• Section 3 shows how to calculate one particular measure of spread for a batch: the ‘interquartile range’. It also shows some diagrammatic methods for representing the spread and shape of the distribution of values in a batch.

• Section 4 introduces the notion of a ‘price index’ for indicating changes in the price of a single item and for two or more different items.

• Section 5 looks at the UK’s Retail Prices Index (RPI) and Consumer Prices Index (CPI), which measure changes in prices over time. (This section is longer than all the other sections, so you should plan your study time accordingly.)

This OpenLearn course is an adapted extract from the Open University course M140 Introducing statistics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .