Spot misleading charts, check claims against the real numbers, and compare two distributions with an average and a measure of spread.
What you will learn
- Say why a chart misleads: an axis that does not start at 0, an uneven scale, bars of different widths
- Turn pie chart angles and percentages into numbers before comparing groups of different sizes
- Choose the average that suits the data, and explain why an extreme value pulls the mean
- Compare two distributions with an average and the range or (Higher) the interquartile range, in context
- Spot claims that rest on a small or biased sample, or read cause into correlation
Charts that mislead
Read the axes before the bars.
Here the vertical axis starts at 400:
The bar for March looks 2.5 times as tall as the bar for February, but the real values are 450 and 420: 450 ÷ 420 = 1.07, only about 7% more. The bars as drawn are measured from where the axis starts: (450 − 400) ÷ (420 − 400) = 50 ÷ 20 = 2.5. "How many times as much" always means divide the real values. Other tricks to look for: uneven steps on an axis (0, 10, 20, 50, 100 spaced equally) and bars of different widths, which look bigger than their heights say.
The rest of this lesson and its 9 practice questions are locked.
In this lesson
- Charts that mislead
- Proportions are not numbers
- Comparing distributions
- Claims to question
- Try it: First question
9 practice questions, marked as you go; about 30 minutes in all.
Key terms
Uneven steps, Different widths, Fractions
In this unit: Probability and statistics: trees, experiments, samples and claims
More probability and statistics: tree diagrams in depth, expected outcomes from experiments, sampling and populations, critiquing charts and claims, and sample spaces in harder contexts.
- Tree diagrams in depth
- Expected outcomes and experiments
- Sampling and populations
- Critiquing charts and claims
- Sample spaces and combined events
All of Probability and statistics: trees, experiments, samples and claims