CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract...
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Transcript of CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract...
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