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...
![Page 1: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/1.jpg)
CHAPTER 20
Representing Quantitative Data
![Page 2: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/2.jpg)
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.
![Page 3: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/3.jpg)
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.
![Page 4: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/4.jpg)
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.
![Page 5: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/5.jpg)
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
![Page 6: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/6.jpg)
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
![Page 7: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/7.jpg)
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.
![Page 8: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/8.jpg)
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
![Page 9: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/9.jpg)
Box and whisker plots
![Page 10: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/10.jpg)
Pie charts for proportionsPie chart of respondents’ length of service in their current jobs
![Page 11: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/11.jpg)
Bar-charts for proportionsProportion of new and repeat sales for three products
![Page 12: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/12.jpg)
Bar-charts for differenceBar-chart showing distribution of different error types
![Page 13: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/13.jpg)
Graphs Cost and sales values for different production volumes
![Page 14: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/14.jpg)
Scatter plotsScatter plot showing error rates at different operating speeds
![Page 15: CHAPTER 20 Representing Quantitative Data. Why ‘re’present your numbers? Few people can extract meaning from arrays of numbers. Summarising them – whether.](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c05c60/html5/thumbnails/15.jpg)
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