## Investigations

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 and organisations require statistics for a wide range of purposes.

 e.g. The Ministry of Transport may need to know the different causes of accidents. MAF, the Ministry of the Agriculture may need to know what percentage of kiwifruit are lost to bad weather each year. A TV company may want to know how many people are watching certain programmes. 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 or survey.

Types of Data

There are two main types of data that can be collected:

Discrete data This is data that is usually whole numbers and is often collected by counting.

e.g. The number of people at a sports game or the number of cars sold.

Continuous data This data is usually the result of measuring and can be any type of number.

e.g. The heights of people or the weights of passengers' bags at an airport.

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 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.

Problems with questionnaires include misleading questions, questions designed to produce a desired answer, questions which offend people, and questions on topics which people give untrue answers. e.g. How many houses have you burgled in the past year?!

Organising and displaying the data

 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.

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.