1 Introduction to descriptive statistics

Many students taking degree courses involving the sciences and technology have to study statistics. This Workbook will enable you to understand the meaning and interpretation of numerical and diagrammatic statements involving data.

Consider the following ‘everyday’ statements, all of which contain numbers:

1. My son plays in his school cricket team, his batting average over the season was 28.9 runs.
2. Police estimate that 4,000 people took part in the protest march.
3. About 11,000,000 drivers will take to the roads during the coming Bank Holiday.
4. The average life of this type of tyre is between 20,000 and 25,000 miles.

The four statements are all of the type that you may meet in the course of your everyday life. In a sense, there is nothing special about them and yet they all use numbers in different ways. Statement 1 implies that a numerical calculation has been performed on a data set, statement 2 implies that a point estimate can represent a data set, statement 3 is making a prediction about an event which has not yet happened and statement 4 is making a prediction about an event which depends on several interrelated factors and is based on past experience.

All four statements are concerned with the collection, organisation and analysis of data.

Essentially, this last sentence summarises descriptive statistics. We start with the organisation of data and look at techniques for examining data $-$ these are called exploratory techniques and enable us to understand and communicate to others meaning that may be hidden within a given data set.