IMAT Logical Reasoning · Data Interpretation

Reading Tables, Bar Charts, Line Graphs and Pie Charts

Before calculating, read the title, the units and the headings; then pick out only the rows and columns the question needs.

All Data Interpretation notes

Why this matters

Every item in this chapter starts by reading a table or chart. About a quarter of the past items, all from the Cambridge years, showed a chart or asked which chart matches a table or a story (a pie chart of seats, a distance-time graph of a journey).

Concept 1 of 2: Reading a table: rows, columns, units and totals

A table answers many questions, and each IMAT item asks only one. Read the headings and the units first, so you know what one cell means. Then find the rows and columns the question names, and combine only those. Most errors are a wrong row, a missed unit (thousands, millions, per 100 g) or an answer to a question that was not asked.

Definition

Read the title, the row and column headings and the units (including notes such as "millions" or "per 100 g") before any number.
A row total adds across; a column total adds down. Check a given total if a question depends on it.
When each cell must be weighted (price × quantity, rate × hours), make one small column of products before comparing.
The largest raw count is not always the largest value: compare the quantity the question asks about.

Weighted total from a table

\text{total} = \sum (\text{quantity} \times \text{rate})

$\text{quantity}$ the count in each cell (hours, items, classes)
$\text{rate}$ the value of one unit of that cell (price, pay per hour)

Worked example

A clinic records how many patients each department sees on each weekday:

Department	Mon	Tue	Wed	Thu	Fri
Cardiology	18	22	15	20	25
Dermatology	12	9	14	11	10
Paediatrics	30	26	28	33	31

Which day had the most patients in total, and what percentage of the week's patients were seen in Paediatrics?

Practice this conceptself-check · 3 quick reps

The most items is not the most money

When cells have different prices or rates, the row with the largest count can still have the smallest value. Multiply each count by its rate before comparing.

Concept 2 of 2: Bar charts, line graphs and pie charts

Each kind of chart shows one thing well. A bar chart compares sizes, a line graph shows how something changes over time, and a pie chart shows how a whole is shared out. To match a table to a chart, check the order of the values, any zero or equal values, and the rough ratios, rather than drawing the chart yourself.

Definition

Bar chart: compare bar heights, but read the scale. If the vertical axis does not start at zero, the bars exaggerate the differences.
Line graph: the slope is the rate of change. Steeper means faster change; a flat section means no change.
Distance-time graph: the slope is the speed. A flat section is a stop; a line going back down is the return journey.
Pie chart: each sector's angle is its share of 360°. Equal values give equal sectors; a value twice as big gives an angle twice as big.
Matching a chart to data: check the largest and smallest values, any equal pairs and any zeros first. Usually only one option survives.

Angle of a pie-chart sector

\text{angle} = \frac{\text{value}}{\text{total}} \times 360^\circ

$\text{value}$ the size of one category
$\text{total}$ the sum of all categories

Worked example

In a survey of 72 students about how they get to school, 18 walk, 30 take the bus, 12 come by car and 12 cycle. Find the angles of a pie chart of these results.

Practice this conceptself-check · 4 quick reps

A cut-off axis exaggerates differences

If a bar chart's axis starts at 30, bars for 40 and 50 have heights 10 and 20, so the second looks twice the first. The real values differ by a factor of 1.25. Options claiming "twice as many" from bar lengths are often wrong.

On a distance-time graph, steeper means faster

The slope, not the height, gives the speed. A high but flat section is a stop far from home; a steep section is fast travel, whichever way it slopes.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Reading a table: rows, columns, units and totals
Weighted total from a table
$\text{total} = \sum (\text{quantity} \times \text{rate})$
Bar charts, line graphs and pie charts
Angle of a pie-chart sector
$\text{angle} = \frac{\text{value}}{\text{total}} \times 360^\circ$

Watch out for (3)

The most items is not the most money
→ Reading a table: rows, columns, units and totals
A cut-off axis exaggerates differences
→ Bar charts, line graphs and pie charts
On a distance-time graph, steeper means faster
→ Bar charts, line graphs and pie charts

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