Data interpretation and probability
Separate what the data directly shows from conclusions that require calculation or assumptions.
Read before calculating#
Inspect the title, axes, units, scale, categories, time period, and any notes. A truncated vertical axis can make a small difference look dramatic. A percentage and a percentage-point change are not the same.
Comparisons#
Absolute change is new value minus original value. Percentage change is that difference divided by the original value, multiplied by 100.
If a value rises from 80 to 100, the increase is 20 and the percentage increase is 25%.
Tables and charts#
Use the displayed scale rather than visual size alone. In a pie chart, a category's angle equals its proportion × 360°. In a bar chart, compare bars only when the axis uses a consistent scale.
Basic probability#
For equally likely outcomes:
probability = favorable outcomes ÷ total outcomes.
For a fair six-sided die, the probability of rolling an even number is 3/6 = 1/2.
The complement of an event is “not that event.” If P(A) = 0.3, then P(not A) = 0.7.
Common mistakes#
Do not assume outcomes are equally likely unless the model supports it. Avoid adding probabilities for events that can overlap without correcting for the overlap. Do not divide percentage change by the new value.
Final check#
A probability cannot be below 0 or above 1. A chart calculation should reproduce the displayed total or a sensible portion of it.
Key points
- Read titles, labels, scales, units, and sources before calculating.
- Percentage change compares the change with the original value.
- For equally likely outcomes, probability is favorable outcomes divided by total outcomes.
- Probabilities range from zero to one and complementary probabilities add to one.