92526 Chap.8 Summarising and Graphing Categorical Data
Summarising and Graphing Categorical Data
Week 3 begins with categorical data, which is summarised by counting each category and converting the counts to proportions. The chapter sets out the population proportion and the sample proportion that estimates it, builds a frequency table for a season of 40 injuries by body region, and turns each proportion into a pie-slice angle out of 360 degrees.
It then weighs the two standard pictures.
Pie charts show one dominant share well but rely on angles, which people judge poorly, and they struggle with small percentages, many categories and labelling. Bar charts start every category from a common zero baseline, so lengths can be compared directly; the Week 4 tutorial makes the point by resetting a truncated axis to zero.
The chapter also separates horizontal bar charts from vertical column charts and works through an axis that exaggerates a close season.
What this chapter covers
- 01
Counting categories and computing proportions
- 02
Population and sample proportions
- 03
Frequency tables and slice angles
- 04
What pie charts do well and badly
- 05
Bar charts from a zero baseline
- 06
Truncated axes that exaggerate differences
- 07
Bar charts versus column charts
Worked example · free
Turn a season's injury counts into proportions and slice angles
- 1Proportions: divide each count by 40, giving ankle 0.35, knee 0.25, hamstring 0.20, shoulder 0.125 and other 0.075.
- 1Angles: multiply each proportion by 360 degrees, giving 126, 90, 72, 45 and 27 degrees.
- 1Checks: the proportions sum to 1.000 and the angles to 360 degrees, so no category is missing or double-counted.
- 1Reading: ankles are the largest share at 35%, more than a third of the season, while shoulder and other differ by only two injuries.
Key terms
- Sample proportion
- The count of a category in a sample divided by the sample size, used to estimate the population proportion.
- Relative frequency
- A category's count expressed as a share of all observations.
- Pie chart
- A circular chart that splits a whole into slices sized by each category's proportion.
- Bar chart
- A chart in which each category is a bar whose length, measured from zero, shows its count or value.
Summarising and Graphing Categorical Data FAQ
How is categorical data summarised?
By counting how often each category occurs and converting those counts into proportions or relative percentages. The Week 3 slides define the population proportion as the number belonging to a category divided by the population size, and the sample proportion, written with a hat, as the same ratio within a sample, used to estimate the population value.
How do you work out a pie slice's angle?
Find the category's proportion, its count divided by the total, and multiply by 360 degrees. In a season of 40 injuries, 14 ankle injuries give a proportion of 0.35 and a slice of 126 degrees. The slice angles for all categories should add to exactly 360 degrees.
Why are pie charts often criticised?
The slides give several reasons. People are not good at estimating quantities from angles, matching labels to slices can be hard work, small but important percentages are difficult to show, and with many categories you can run out of distinguishable colours. More categories make a pie visibly more cluttered.
Why should a bar chart's axis start at zero?
Because readers compare bar lengths. If the axis starts above zero, small differences look large: average crowds of 8,600 and 8,200 drawn from 8,000 make one bar three times the other. The Week 4 tutorial resets the axis minimum to 0 for exactly this reason, so lengths reflect the true ratio.
When should you use a horizontal bar chart instead of a column chart?
The Week 3 page suggests horizontal bars cope better with a large number of categories and long labels, while vertical columns show positive and negative values more intuitively, because people read up and down as more and less faster than left and right. Both start from a common baseline.
Exam move
Work one frequency table by hand from raw counts: proportions, percentages and slice angles, with both totals checked. Then take the same table into Excel and draw a pie and a bar chart, add data labels, and set the axis minimum to zero, as the Week 4 tutorial does. Write a one-sentence explanation of which chart is easier to read and why, using the words angle, length and baseline.
Practise spotting a truncated axis in charts you see in sport media, and keep the sample-versus-population distinction in mind whenever a proportion from one club is used to describe a whole league.
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