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Statistics Definitions

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Statistics is the Maths of recording and interpreting data.

A piece of data is any observation of measurement. The source of the data is a variable or variate. Examples of variables are

	The amount of rainfall in one hour.
	The colour of cars.
	The number of radioactive decays.
	The height of trees.

Variables are divided into two categories:

Qualitative	These cannot be assigned a numerical value. For example, the colour of cars is a qualitative variable.
Quantitative	These variables are defined by a numerical value. The other 3 examples above are quantitative variables.

Quantitative data can itself be broken down into two distinct categories, discrete and continuous.

Discrete	Discrete data comes in lumps, and can be counted. Discrete variables can only take on certain values, usually they have to be whole numbers. Examples of discrete variables would be the number of radioactive decays or the number of cars passing a point.
Continuous	Continuous data can take any value within a range. For example, the height of a population, whilst being restricted to being no more than around 2m, can take any value up to that limit. Continuous data cannot be counted, but must be measured. It is important, when taking measurements of continuous variables, that you know the accuracy of your measurements.

Collecting data

We often take statistics to give an impression of the properties of a large group. The obvious example is an opinion poll. Whether you want to predict the result of a general election or gauge public opinion on a local road development, you will want to conduct a poll. There is no way that you could conduct a poll of the entire electorate, so you have to choose a sample. A sample is a small selection from the entire population, which is supposed to be representative of the population as a whole.

In order that your sample really is representative of the whole population, it is important that its make up should mirror that of the population, so for example, an election opinion poll should include an equal number of men and women, the correct proportions from all ethnic groups and should cover people in all the socio-economic groups.

It is important, however, that while ensuring the correct make up of the sample, the individuals taken for the sample should be random, wherever possible.

Describing Your Results

The number of results for a particular value (or range of values), is called the frequency.

In the case of continuous variables, since no two units will have the same value (exactly) you will only get a useful frequency (greater than 1) by grouping results. This may also be useful with discrete variables. The frequency will now be the number of results over a range of values.

Since it may be convenient to vary the width of the different groups, a more useful measure can be the frequency density. This divides the frequency of a group by its width. For example, in a survey of heights, you might find that 5 people fall into the range 185cm-190cm, while only 4 people fall into the range 175cm-176cm. This is clearly misleading, since the first range is 5 times larger than the second. You will get a fairer idea of the heights of the population if you say that the groups have frequency densities of 1 and 5 respectively.

The next page will look in detail at grouping data.

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