CHAPTER 20

Representing Quantitative Data

Why ‘re’present your numbers?

Few people can extract meaning from arrays of numbers.

Summarising them – whether in numbers or pictures – will make patterns and differences clearer.

How you can summarise them will depend on the nature of the numbers themselves.

Different forms of data

Quantitative data varies in terms of what the numbers signify.

Numbers can:• be merely labels (nominal or categorical)• show order of size or strength (ordinal)• indicate relative size (interval)• measure size in absolute terms (ratio).

The scale can be continuous or discrete.

Combining numbers

It is often useful to combine numbers – eg absence rates will be monthly or yearly averages.

Beware! The type of scale used determines what you can and cannot do with your numbers.

Scales and allowable operations

The mathematical operations that are allowable depend upon the scale –

Nominal: none

Ordinal: none – although averaging scores is common practice

Interval: addition and subtraction

Ratio: addition, subtraction, multiplication and division

Average values

Rather than listing all the values in a set, it may help to give an average of the numbers.

There are three common ways of summarising numbers to indicate the ‘central value’:• the arithmetic mean• the median• the mode

Student Activity 1

Indications of spread

A mean, median or mode does not indicate the degree of ‘scatter’ in your figures. This can be shown by the

• range• inter-quartile range, or• standard deviation.

Graphical representations

Graphical representations can be as clear as summary statistics, while retaining more information.

Typical graphs include:• box and whisker plots• pie charts • bar-charts and histograms• graphs• scatter plots

Box and whisker plots

Pie charts for proportionsPie chart of respondents’ length of service in their current jobs

Bar-charts for proportionsProportion of new and repeat sales for three products

Bar-charts for differenceBar-chart showing distribution of different error types

Graphs Cost and sales values for different production volumes

Scatter plotsScatter plot showing error rates at different operating speeds

Clarity and ‘honesty’

Representations need to be

• clear: do not over-clutter

• clear: label everything clearly

• ‘honest’: avoid using scales to magnify or diminish the apparent significance of results