Data Interpretation

Why percentages rule DI

Raw numbers are hard to compare. A shop that grows from ₹100 to ₹150 and a factory that grows from ₹1,000 to ₹1,100 both "increased", but by very different amounts relative to their size. Percentages put everything on a scale of 100, so that fair comparison is possible. Almost every DI set has at least one percentage question.

Percentage change — the base is the OLD value

$\%\ \text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100$

• Sales go from 160 to 200: change $= 40$, base $= 160$, so $\frac{40}{160} \times 100 = 25\%$.
• Sales go from 260 to 250: change $= -10$, base $= 260$, so a fall of $\frac{10}{260} \times 100 \approx 3.85\%$. The "old" value is the earlier year or the value the question says "over" or "compared with". Dividing by the new value is the number-one trap, and its result is always among the options.

"X is what percent of Y"

$\frac{X}{Y} \times 100$ The value after "of" is the base. ₹200 as a percent of ₹320 is $\frac{200}{320} = 62.5\%$.

"X is what percent more than Y"

$\frac{X - Y}{Y} \times 100$ ₹320 is $\frac{120}{200} = 60\%$ more than ₹200. But ₹200 is $\frac{120}{320} = 37.5\%$ less than ₹320. The same gap gives different percentages because the base changes.

Share of a total

A part as a percent of the whole: $\frac{\text{part}}{\text{total}} \times 100$. If a family spends ₹12,000 of ₹36,000 on food, the food share is $33\tfrac{1}{3}\%$. Add parts first when two items are asked together.

Percentage points versus percent

If a school's pass rate rises from 60% to 72%:

• The rise is 12 percentage points (simple subtraction of two percentages).
• The rise is 20 percent in relative terms ($\frac{12}{60} \times 100$). Read which one is asked. "By how many percentage points" means subtract; "by what percent" means divide by the old rate.

Largest percentage rise — do not trust the biggest jump

In a series 160, 200, 260, 250, 320 the biggest absolute rise is 2023 (+70), but the biggest percentage rise is 2021 ($\frac{60}{200} = 30\%$ against $\frac{70}{250} = 28\%$). A small base makes a small jump look big in percent terms.

Useful fraction table

Fraction	%	Fraction	%
$\frac{1}{8}$	12.5	$\frac{1}{3}$	33.33
$\frac{1}{6}$	16.67	$\frac{3}{8}$	37.5
$\frac{1}{5}$	20	$\frac{5}{8}$	62.5
$\frac{1}{4}$	25	$\frac{2}{3}$	66.67

Quick revision

• % change $= \frac{\text{new} - \text{old}}{\text{old}} \times 100$ — base is the earlier value.
• "What percent of Y" → base Y. "More than Y" → base Y.
• Same gap, different base: 60% more ≠ 37.5% less.
• Percentage points = subtract rates; percent change of a rate = divide by old rate.
• Biggest absolute jump is not always the biggest % jump.