SQL, data modeling, data quality, EDA, visualization · insight-0073
Use a log scale for ratios and multiplicative growth, and label the original values
- Evidence type
- practitioner heuristic
- Difficulty
- easy
- Roles
- Data analyst, Data scientist
- Industries
- aviation, retail, finance
Summary: situation, action, reason, boundary
Situation
A chart compares route revenue that spans from thousands to millions, or shows growth multiples above and below 1.
Action
Plot on a log axis with tick labels in original units (1k, 10k, 100k), state the base, and title the axis with the variable rather than "log(revenue)". Explain once to non-technical readers that equal distances mean equal ratios.
Reason
Multiplication on a log scale becomes addition, so ratios of 2 and 0.5 sit at equal distances from 1.
Boundary
Revenue or volume across very different units, growth ratios, price ratios and heavy-tailed distributions.
Symptom or risk
On a linear axis, small routes are crushed near zero and ratios below 1 look tiny compared with ratios above 1.
Exceptions
Values at or below zero cannot be shown on a log scale; audiences unfamiliar with it may need a linear chart plus a table.
Trade-offs
Log scales reveal relative patterns but understate absolute differences that matter for money.
Pitfalls
Using a log scale on bars that start at an arbitrary value, which recreates the truncated-axis problem.
Lessons and concepts
Claims and their sources
Log scales suit data produced by multiplication or division, ratios should generally be shown on a log scale, tick labels should show original values and the logarithm base should be stated.