60-second revision
- Percentage change = (new − old)/old × 100; the base is always the earlier or reference value.
- Pie chart: 100% = 360°, so 1% = 3.6°.
- Value from a pie sector = (angle/360) × total.
- Biggest absolute change is not always the biggest percentage change.
- A rise from 20% to 25% is 5 percentage points but a 25% increase.
- Compare fractions by cross-multiplying instead of dividing.
- Turn every caselet into a small table before answering.
Read before you calculate
Spend the first 30 seconds on the chart, not the questions: the units (thousands, lakhs, crores, tonnes), what each bar or line represents, whether values are absolute or percentages, and the total if one is given. Most DI errors are reading errors, not arithmetic errors.
| Asked for | Formula |
|---|---|
| Percentage change | (new − old)/old × 100 |
| A as a percentage of B | A/B × 100 |
| A is what % more than B | (A − B)/B × 100 |
| Share of a part in the total | part/total × 100 |
| Average | sum of values ÷ number of values |
| Pie: angle of a sector | (value/total) × 360°, or % × 3.6 |
| Pie: value of a sector | (angle/360) × total |
Tables
Worked example: a dealer sold cars on five days: Mon 12, Tue 15, Wed 9, Thu 18, Fri 21. Total = 75, average = 15 a day. Wednesday to Thursday is a rise of 9 on a base of 9, i.e. 100%. Thursday to Friday is a rise of 3 on 18, i.e. 16.7%.
Bar graphs
Simple bars show one value per category; grouped bars put two or more series side by side; stacked bars pile parts into a total. In a stacked bar, the total is the full height, and each part is the length of its own segment, not the height at which it ends.
Worked example: a stacked bar for a shop shows Shirts from 0 to 40 and Trousers from 40 to 70 (in units). Shirts = 40, Trousers = 70 − 40 = 30, total = 70.
Line graphs
A line graph shows a trend over time. The steepest segment is the largest absolute change, but percentage change depends on the base.
Worked example: output rises from 80 to 100 (20 units, 25%) and later from 200 to 230 (30 units, 15%). The second rise is larger in units but smaller in percentage.
Pie charts
A pie chart shows parts of a whole, either as percentages or as angles. 100% = 360°, so 1% = 3.6° and 10% = 36°.
Worked example: a budget of Rs 80,000 has a 72° sector for travel. 72/360 = 1/5 = 20%, so travel gets Rs 16,000.
Histograms
A histogram shows frequencies of class intervals (for example marks 0–10, 10–20) as bars with no gaps between them. With equal class widths, bar heights are the frequencies, and the modal class is the tallest bar.
Caselets
A caselet hides the data in a paragraph. Turn it into a table first, then answer.
Worked example: a school has 800 students, 45% of them girls. 30% of the girls and 20% of the boys play chess. Girls = 360, boys = 440; chess players = 108 girls + 88 boys = 196.
Fast arithmetic
- Compare fractions by cross-multiplying: 17/43 vs 21/52 gives 17 × 52 = 884 and 21 × 43 = 903, so 21/52 is larger.
- Use fraction-percentages: 1/8 = 12.5%, 1/6 = 16.67%, 1/12 = 8.33%, 7/12 = 58.33%.
- When options are far apart, round to two significant figures and estimate.
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