Data interpretation
Data interpretation questions give you a table or a graph and ask for a comparison, a total, an average or a percentage. The numbers are always in the data, so the skill is choosing the right numbers and the right base. Read the title, the unit and the labels before you calculate anything.
Formulas and when they apply
- Percentage change = (new value − old value) ÷ old value × 100Applies when: The old (starting) value is always the base.
- Share of a total (%) = part ÷ total × 100
- x is what percent more than y = (x − y) ÷ y × 100Applies when: y is the base, the value you compare against.
- Average = sum of the values ÷ number of values
- Central angle of a pie slice = share (%) × 3.6°Applies when: The pie shows percentages that total 100. A full circle is 360°.
- Amount for a slice = share (%) × total ÷ 100Applies when: The total must be given in the caption or the question.
- Percentage points = difference between two percentagesApplies when: A rise from 20% to 25% is 5 percentage points but a 25% increase.
Worked examples
Example 1. Sales of a stall rose from ₹250 in March to ₹300 in April. By what percentage did sales rise?
Solution. The increase is 300 − 250 = ₹50. Percentage rise = 50 ÷ 250 × 100 = 20%. The base is March, the starting month.
Example 2. A pie chart shows a school budget of ₹2,40,000. Sports takes a 30% slice. What amount goes to sports, and what is the central angle of its slice?
Solution. Amount = 30% of ₹2,40,000 = ₹72,000. Central angle = 30 × 3.6° = 108°. Check: 108 ÷ 360 = 0.3, which is 30%.
Example 3. A table shows that Branch X sold 480 units in January and 600 in February, and Branch Y sold 400 in January and 440 in February. Which branch grew faster in percent, and by how much?
Solution. Branch X rose by 120, so 120 ÷ 480 × 100 = 25%. Branch Y rose by 40, so 40 ÷ 400 × 100 = 10%. Branch X grew faster, at 25%, even though Y started from a lower figure.
Shortcuts and their limits
- Cancel common zeros before you divide, for example 210 ÷ 300 becomes 21 ÷ 30.Does not apply when: Cancel the same number of zeros from both numbers, and only from the end.
- Compare ratios instead of percentages: Q3 ÷ Q1 of 1.6 means a 60% rise.Does not apply when: Works when you only need to rank or compare changes, not when an exact percentage is asked.
- When two amounts are shares of the same total, compare the shares directly and ignore the total.Does not apply when: Only valid when both amounts come from the same pie or the same total.
- Use a round guess for the average and add the deviations.Does not apply when: Pays off only when the values sit close to a round number.
Common mistakes
- Using the new value as the base for a percentage change. The base is the old value, or the value after the words 'than' or 'of'.
- Confusing percentage points with percent. A move from 40% to 50% is 10 points, but a 25% rise.
- Reading the wrong series or the wrong year from a graph with two bars or two lines. Check the legend first.
- Treating the tallest bar as the best rate. A large number can still be a small share of a larger total.
- Converting a pie share to an amount without checking what the total is.
Independent practice made by EduVistaHQ with original questions. It is not an official examination paper, it is not affiliated with or endorsed by any examination body or company, and a practice score does not predict a real result.