ETF1100 Chap.2 Data Visualisation
Data Visualisation
Data Visualisation turns tables into defensible comparisons. The chapter selects bars for categories, histograms for numerical distributions, lines for ordered time and scatterplots for two numerical variables. It also distinguishes counts from proportions, explains why unequal group sizes require normalisation, and diagnoses truncated axes, unordered lines and decorative geometry that exaggerate a business difference.
What this chapter covers
- 01
Frequency and relative-frequency tables
- 02
Bar charts for categories
- 03
Histograms for distributions
- 04
Line charts for time
- 05
Scatterplots for relationships
- 06
Normalised rates and honest scales
Worked example · free
Compare late-delivery counts and rates
- 1Compute 48 / 1,600 = 3.0% for metropolitan deliveries.
- 1Compute 30 / 600 = 5.0% for regional deliveries.
- 1State that metropolitan operations have more late cases to resolve.
- 1State that regional operations have the worse late-delivery rate.
Key terms
- Frequency Table
- A table counting observations in mutually exclusive categories or intervals.
- Relative Frequency
- A frequency divided by its relevant total and expressed as a proportion or percentage.
- Histogram
- A display using adjacent bins to show the distribution of a numerical variable.
- Normalised Rate
- A count divided by an exposure total to support comparison across unequal groups.
- Truncated Axis
- An axis beginning away from the natural baseline and potentially exaggerating differences in length.
Data Visualisation FAQ
When should I use percentages instead of counts?
Use percentages or rates when group sizes or exposure totals differ and the question concerns relative performance or risk. Keep counts when workload or absolute volume matters. Many business decisions need both views, because a small rate can still generate many cases in a large group.
Why is a line chart wrong for unordered categories?
A connecting line implies continuity and meaningful movement between adjacent positions. Unordered categories have no such path, so bars on a common baseline are more honest. Preserve line charts for time or another genuinely ordered sequence.
Does normalising make a comparison fair?
Normalising fixes one denominator problem but does not control every difference between groups. Product mix, opening hours, customer characteristics or case complexity may remain. State the rate denominator and name important uncontrolled differences before recommending action.
How do I verify a chart before sharing it?
Reconcile plotted values with the source table, confirm that filters and denominators are intentional, and check title, axes, units, order and missing groups. Estimate the visible pattern from the numbers first. If the software display contradicts that expectation, inspect the selected range and series mapping before interpreting it.
Exam move
Create a four-row chart selector: category comparison uses bars, numerical distribution uses a histogram, time order uses a line and two numerical variables use a scatterplot. For every practice display, write the business question and denominator before choosing geometry. Rebuild frequency tables as both counts and relative frequencies so you can explain what changes when group sizes differ.
Train yourself to inspect axes, units, category order, legends and missing groups before interpreting colour or shape. When a rate appears, calculate the underlying count as well; operational workload and relative performance can point to different priorities. Practise writing two-sentence conclusions that name the visible pattern and one factor the chart does not control.
Avoid three-dimensional effects, broken baselines and sorted time labels. In the exam, identify whether the option preserves proportion, order and scale. On your notes sheet, include one warning: percentages are only comparable when their denominators answer the same question. Recreate one dashboard from its underlying table rather than copying its styling.
First calculate totals, within-group percentages and any rate per exposure unit; then decide which of those quantities answers workload, performance or composition. Draw a rough chart by hand and predict what should be longest, highest or most concentrated before using Excel. After plotting, reconcile every mark with the table and inspect whether filters or hidden rows changed the denominator.
Practise three repairs: restore chronological order to a time series, replace an area or three-dimensional display with a common baseline, and show both a count and a rate when group sizes differ. For each repair, explain how the original encoding could change a decision. Test titles by covering the rest of the page: the title should still reveal measure, population or group, and period.
Check that colour is not the only carrier of meaning and that category labels remain readable. When a graph highlights a small difference, calculate its absolute and relative scale and compare it with operational relevance. Add one limitation tied to data collection rather than a generic caution. Finally, write a one-line recommendation that follows from the displayed evidence without claiming causation.
This deliberate chart audit turns visual literacy into a repeatable decision process.
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