Number of children in a family: 0, 1, 2, 3… never 2.4. Height of a person: 1.7m, 1.732m, 1.7324m… any value at all. Two fundamentally different kinds of data — and they need different tools.
Discrete data is counted — it takes separate, distinct values (usually whole numbers). Continuous data is measured — it can take any value within a range, limited only by the precision of your instrument.
It decides which chart to use (bar vs histogram), which distribution applies (binomial vs normal), and whether 'the average is 2.4' even makes sense.
Which one is continuous data?
Telling them apart
- Can you count it? → discrete (children, dice rolls, defects, goals).
- Do you measure it? → continuous (height, weight, time, temperature, distance).
- Discrete → bar graph, probability mass function, binomial/Poisson.
- Continuous → histogram, density curve, normal/exponential.
Classify: (a) shoe size, (b) foot length in cm, (c) number of pets, (d) time to run 100m.
Why can't you use a bar graph (with gaps) for continuous data?
Gaps imply 'nothing exists between these values' — but for continuous data, values *do* exist in between. That's why histograms have touching bars: the x-axis is an unbroken number line.
Money is a sneaky case. Strictly it's discrete (down to the cent), but with large amounts we usually treat it as continuous for graphing and modelling. Context decides.
Quick test: 'Could the answer reasonably be 2.5?' If yes, it's continuous (2.5 metres ✓). If 2.5 is nonsense (2.5 children ✗), it's discrete.
- Discrete = counted (distinct values); continuous = measured (any value in a range).
- Discrete → bar graphs, mass functions. Continuous → histograms, density curves.
- Test: would a fractional answer make sense?