Reading charts and tables correctly

What the area tests

Bocconi says that advanced knowledge of mathematics is not required for numerical reasoning: the calculations are simple, and the challenge is often to read a chart or table correctly. The standard test has six numerical reasoning questions, mixed in with the other areas. The skill, then, is less arithmetic than discipline: reading exactly what the data shows before computing anything.

Read the frame before the numbers

Every table or chart has a frame that tells you what its numbers mean. Read it first, every time.

• Title: what is measured, for whom, over what period.
• Units: euros or millions of euros; people or percent of people; litres per 100 km.
• Headers: which row and which column a number belongs to. In a table with years as columns, a misread column gives a perfectly plausible wrong answer.
• Notes: "figures in € million", "2024 provisional", "excludes part-time staff".
• Axis of a chart: where the scale starts. A bar chart whose axis starts at 80 rather than 0 makes small differences look large; read the values, not the heights.

Levels, changes and rates

Most questions ask for one of three things, and the wrong options are often built from the other two.

Asked for	Calculation	Example: 240 to 300
Level	Read the value	300
Absolute change	new − old	+60
Percentage change	(new − old) ÷ old	+25%

The largest absolute change and the largest percentage change often belong to different rows. A small starting value can produce a large percentage change from a modest absolute change.

Shares and totals

When a table gives shares (percent of a total), a falling share does not mean a falling amount: if the total grows, a smaller share of a bigger total can still be more. To compare amounts across years, turn shares into amounts by multiplying by each year's total. A change in a share is measured in percentage points.

Index numbers

An index sets a base period equal to 100 and expresses other periods relative to it. An index of 124 means 24% above the base period. But a move from 118 to 124 is 6 index points, which is a rise of $\frac{6}{118} \approx 5.1\%$, not 6%: a percentage change is measured from the starting value, not from the base year.

Averages of rates

If one group grows by 10% and another by 30%, the two together grew by 20% only if they started the same size. The combined rate is a weighted average, closer to the rate of the larger group. To combine, go back to amounts: add the starting amounts, add the final amounts, then compute one percentage change.

Charts carry the same information

Bar, line and pie charts are tables drawn as pictures. Read them as you would a table: identify the category, the period and the value, write down the values you need, then compute. Estimate from a picture only when the options are far enough apart to allow it.

A routine for data questions

1. Read the question and name exactly what it asks for: a level, a change, a percentage change, a share or a comparison.
2. Read the frame: units, periods, notes.
3. Write down only the values you need.
4. Compute, then check the order of magnitude against the data.

The routine costs a few seconds and removes the commonest errors, which are not arithmetic errors at all but reading errors.