Data Interpretation

1A pie sector is a fraction of 360°

The full circle is the whole — 100\% or 360^\circ — and a sector's central angle is its share written in degrees: \theta = \frac{\text{value}}{\text{total}}\times 360^\circ. Working the other way, a value is \frac{\theta}{360^\circ}\times\text{total}. Nothing else about a pie chart is content; every pie question is this fraction.

The conversion worth knowing cold is 1\% = 3.6^\circ, so a 90^\circ sector is instantly 25\%, a 120^\circ sector is one-third, and a 180^\circ sector is half. Learn those three angles and most pie arithmetic collapses before the calculator comes out.

How it works

1. Name the wholeThe pie's total — rupees, units, or 100% — is the denominator for every sector.
2. Turn the angle into a fractionDivide the sector angle by 360^\circ, or convert with 1\% = 3.6^\circ when the question asks for a percent.
3. Multiply by the totalFraction times total is the component value; value over total times 100 is the percentage share.

2Read the scale before you read the bars

Every bar and line graph question begins with the same two checks: what the axes measure, and what one unit of length is worth. Misreading a scale mark of 10 as 1, or treating a broken axis as starting at zero, produces an answer that looks exact and is wrong by a factor.

Bar graphs compare discrete categories — years, products, regions — so the height (or length) of each bar is a value you can read off and then ratio or average. Line graphs emphasise trend and growth over a continuous axis, usually time; the slope between two points is the change, and a steeper segment is a faster rise, not a larger absolute value unless the scale says so.

How to read a chart

1. Name the axesWrite down the unit on each axis — ₹ crore, thousands of units, percent — before touching a bar.
2. Fix the scaleOne grid step is a fixed amount; count steps, then multiply. A broken axis does not change the step size above the break.
3. Choose bar or slopeA category comparison reads bar heights; a growth question on a line graph reads the change between two years, not a single point.

3Percentage change, always on the earlier value

Growth between two periods on a chart is \frac{\text{later}-\text{earlier}}{\text{earlier}}\times 100. The numerator is the rise or fall you can see; the denominator is the year you are changing from — never the later year, and never whichever bar looks larger.

That single choice is the DI trap with the highest yield. Dividing by the later value understates a rise and overstates a fall, and the wrong answer is almost always sitting among the options as the distractor.

Figure. Two vertical bars labelled 2023 and 2024 with values 250 and 300, so the later bar is taller by the growth of 50 that percentage change measures against the earlier bar.

How it works

1. Read both valuesTake the earlier-period reading and the later-period reading off the chart, with units.
2. SubtractLater minus earlier; a negative result is a decrease, not a sign error.
3. Divide by the earlier valueThen multiply by 100. The base is the period named as the starting point.

4"A more than B" anchors the denominator on B

When a DI set asks "by what percent is A more than B", the wording has already named the base: B. The percent is \frac{A-B}{B}\times 100. Swapping the denominator to A answers a different question — how much percent B is less than A — and the two numbers are not equal.

The same sentence with "less than" still anchors on the word after than. Underline that word before you divide; it is the whole mark.

Figure. Two vertical bars B = 400 and A = 480 with a dashed reference rule at 400 marking B as the base for the percent-more reading of the gap of 80.

How it works

1. Underline the baseThe noun after "more than" or "less than" is the denominator.
2. Take A − BThe gap is the same either way; only the base changes which percent you report.
3. Divide by the underlined valueThen × 100. Check the options for the swapped-base distractor.

5Compute shared totals once, then answer by division

A DI set is several questions on one table. The expensive work is adding each category across years and adding each year across categories — do that once, write the totals in the margin, and every ratio, average and percentage share after that is a single division off those parked numbers.

An average across n periods is \frac{\text{sum of values}}{n}. A ratio of two categories is their two totals. Recomputing a column sum inside every sub-question is how time runs out with the arithmetic still correct.

Figure. Add each row once — P totals 150, Q totals 225 — and write those margin totals before touching any question. Every later share, ratio or average is one division off a parked total.

How it works

1. Total each seriesSum every category across the years (or every year across the categories) and write the results beside the table.
2. Park the grand totalAdd the category totals; this is the denominator for every share-of-whole question.
3. Answer by divisionRatios divide two parked totals; averages divide a parked total by the count of periods.

6Approximate only when the options are far apart

DI options are often well separated — 20%, 25%, 33% — so treating 498 as 500 or 997 as 1000 is legitimate time-saving, not sloppiness. The arithmetic becomes mental, and the nearest option is still unambiguous.

The discipline is checking the gap between options before you round. If two options sit 1% apart, an approximation that moves the answer by 0.5% can pick the wrong one; compute exactly. Rounding is a tool for separated options, not a default.

Figure. Options at 20%, 25% and 33% are far apart, so rounding 498/1550 toward 500/1550 still lands unambiguously on 33%. When two options sit within a rounding error of each other, do the exact division instead.

When to round

1. Scan the optionsIf neighbouring choices differ by more than your expected rounding error, approximation is safe.
2. Round both sides the same way498/997 ≈ 500/1000; rounding only the numerator (or only the denominator) biases the fraction.
3. Fall back to exactClose options, or an answer that lands halfway between two choices, means compute without rounding.