What is Statistics?

Statistics involves the gathering and organisation of data and information.

Data is collected and then processed. It can be displayed using graph and listed in tables. Calculations can be made to summarise the data. Finally the data is presented, discussed and conclusions are made.

Statistics are often used to help to show or prove something. When this happens an investigation or survey is often carried out.

Designing a Statistical Investigation

You may be asked to carry out an investigation or survey. The information below may help.

The collection of data
Many people require statistics for a wide range of purposes.

 e.g. A movie-making company may need to know information about the number of people watching their movies. A sports coach my need information on how well each member of the team are playing. The Prime Minister may want to know how popular he or she is. A medical researcher may need to know if a certain drug is effective at curing patients.

The collection of data takes time and is therefore expensive.
Much thought must be put into the planning of any statistical investigation.

Choosing a sample
The first thing to decide on the number of people or items to be surveyed. This is called asample. This size of the sample needs to be large enough to be truly representative but not too large as this would be too expensive and time-consuming.

 Number of people in sample Comments 4 or 5 people Generally too small a number to give accurate results. 30 people Suitable for a survey of, say, your school. 1000 people The number often used by political polls. 10000 A large number only used for big surveys. Everyone in the country Called a census. Very expensive, held every 5 years.

A sample must be evenly spread over the population. Choosing a random sample, where evey item has an equal chance of being chosen, helps to remove bias.
Bias
occurs when a sample does not accurately represent the group from which it is taken.
There are several ways to obtain a random sample:
• Draw names out of a hat.
• Choose names at regular intervals from an alphabetical list.
• Give every person or item a number and choose the numbers at random, using special tables, a computer or a draw.

Questionnaires and Interviews

questionnaire is a form used to obtain information. Careful preparation of questionnaires is essential and may require special training. Questionnaires can then be sent to people, which often results in a low return rate. Interviewers can be used to stop people in the street or to ring people to ask the questions. Surveys using these kinds of techniques can often produce biased samples unless they are well designed.

Organising and displaying the data

 When the data has been collected, it can be summarised into tables and graphs. Stem and Leaf diagrams, pictographs, column and pie graphs are common ways of displaying this data. These are covered in more detail in Topic 44.

Analysis of the data

Calculations can be made and statistics such as the meanmedianmode and range can be found. See Topic 45.

Finally, and most importantly, the data, tables, graphs and calculations can be analysed and the results of a survey presented, summarised and any conclusions drawn.

As you can see, there is a lot to statistics.