# Different kinds of Variables: Numerical Variables

In this chapter we look at Variables with indefinitely large sets of Levels, such as anything we can *count* or *measure*.

```
The child's weight is ((continuous))kg.
The class size is ((counting numbers)).
```

Numerical Variables include integer Variables, counting Variables, percentages and so on.

In particular, we look at what happens at the extremes. Can you have a reading age of 1000, and if not, why not?

You’ll notice that in this chapter and in many other chapters, we just say “Variable” whenever we don’t need to distinguish between “Variable” and “Variable-sign”.

We call these Variables “numerical”, though we explicitly exclude pseudo-numerical Variables such as discrete ordinal Variables which are sometimes given “numerical” Levels^{10}.

Obviously there is no such thing as specifying the Levels of these Variables by listing them: instead we use some kind of iterative rule, such as “0 is one of the Levels; if x is a Level, x+1 is a Level”.

## Count (natural number) Variables

Rather than trying to list all (!) the counting numbers, we can just write `((count))`

`This week there were about *20--* ((count)) visitors to the youth centre.`

Count Variables are integer Variables for which there is one Level which has the property of being less than all the other Level, namely zero.

## Integer Variables

Addition and subtraction are allowed on each and every pair of Levels. Same as count Variables, but can be negative.

`I have *minus 200--* ((integers)) EUR in my bank account.`

## Continuous (rational) Variables

There are plenty of scales which allow for accurate measurement on rational number scales, like the rate of inflation or average income, or a child’s weight.

`The average weight of the children was *30--* ((positive continuous numbers)) kg.`

### Percent and proportion Variables

Percent Variables are (usually continuous) Variables between 0 and 100.

`*33--* ((0-100)) percent of the students passed the exam. `

e.g. in SPSS↩