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 The use of statistics involves the gathering of data or information.
This data is then processed and organised in tables and displayed using graphs.
Finally the data is presented, discussed and conclusions are made.
Designing a Statistical Survey
The collection of data
Many people require statistics for a wide range of purposes.
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A music company may need to know information about the people buying their Cds and tapes. |
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The Ministry of the Environment may need to know how many Kakapo there are left |
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A political party may want to know how popular it is. |
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A medical researcher may need to know if a certain drug is effective at fighting a disease. |
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 is the size of the sample. This would need 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
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| 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
A 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
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When the data has been collected, it is often summarised into table and graphical form.
Pictographs, column and pie graphs are common ways of displaying this data.
Data can also be sorted into a frequency distribution and displayed in a histogram or a stem and leaf diagram. Statistical calculations can then be carried out to find information such as the mean, median and quartiles and these can then be shown on a box and whisker diagram.
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Analysis of the data
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.
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