Why we draw charts
Tables of numbers are precise but hard to read. Our eyes are very good at comparing lengths and positions and at spotting trends, clusters and unusual points. A well-chosen chart turns data into a picture that answers a question at a glance. Scientists, doctors, journalists and governments rely on charts to make decisions, which is why it matters that they are drawn honestly.
Types of data
- Categorical: named groups, such as favourite fruit or blood group.
- Numerical (discrete or continuous): counts or measurements, such as test scores or height.
- Paired data: two measurements for each item, such as temperature and sales on the same day.
- Time series: measurements taken one after another, such as monthly rainfall.
Choosing the right chart
| Chart | Best for |
|---|---|
| Bar chart | Comparing categories or totals |
| Line graph | Change over time |
| Scatter graph | The relationship between two numerical variables |
| Histogram | The distribution of one numerical variable |
| Pie chart | Parts of a whole, with only a few categories |
Research on how people read charts shows we judge positions and lengths far more accurately than angles or areas, which is why bar charts are usually clearer than pie charts.
Averages, spread and outliers
The mean adds up all values and divides by how many there are; the median is the middle value when they are sorted. An outlier, a value far from the rest, can drag the mean a long way while barely moving the median. That is why house prices and incomes are usually reported as medians. Therange (largest minus smallest) gives a quick sense of spread.
Correlation is not causation
The correlation coefficient r measures how closely paired data follow a straight line, from −1 (perfect negative) through 0 (none) to +1 (perfect positive). A strong correlation does not prove that one thing causes the other. Ice-cream sales correlate with shark attacks because hot weather increases both: aconfounding variable. To show cause and effect, scientists use controlled experiments.
How charts can mislead
- Truncated axes: starting the y-axis above zero makes small differences look huge.
- Wrong chart type: joining unrelated points with lines suggests a trend that is not there.
- Cherry-picking: showing only the time period that supports a claim.
- Hidden sample size: a dramatic pattern from five people may be pure chance.
- 3D effects and pie charts distort how big slices and bars appear.
Sample size and noise
Real data always contains random variation, or noise. With a small sample, noise can create or hide patterns by chance; with a larger sample, the true pattern stands out. Try 5 points and then 200 in the simulator and watch how much more stable the trend line and correlation become.
Key terms
- Outlier
- A value much larger or smaller than the rest of the data.
- Trend line (line of best fit)
- A straight line that best summarises the relationship in a scatter graph.
- Distribution
- How values are spread out: where they cluster and how far they range.
Common misconceptions
- “A strong correlation proves cause.” A third factor may be responsible, or it may be chance.
- “The mean is always the best average.” With outliers or skewed data, the median is often more representative.
- “Any chart will do.” The wrong chart can hide the pattern or invent one.
Key takeaways
- Match the chart to the data: bars for categories, lines for time, scatter for relationships, histograms for distributions.
- Outliers pull the mean much more than the median.
- Correlation measures association, not cause.
- Check axes and sample sizes before trusting a chart.
Model note: the datasets are generated from fixed random seeds with realistic patterns, so every visitor sees the same data for the same settings.