Data Interpretation

What a pie chart shows

A pie chart is a circle cut into slices (sectors). The whole circle stands for the total — the whole budget, all students, all sales. Each slice is one part. A bigger slice means a bigger share. Since a circle has $360^\circ$ at its centre, the total is spread over $360^\circ$.

In competitive exams the pie is often printed as a list of angles or percentages — read it exactly like a table.

The three conversions

$\text{value} = \frac{\text{angle}}{360^\circ} \times \text{total}$ $\text{angle} = \frac{\text{percent}}{100} \times 360^\circ = \text{percent} \times 3.6^\circ$ $\text{percent} = \frac{\text{angle}}{360^\circ} \times 100 = \frac{\text{angle}}{3.6}$ Remember: 1% = 3.6° and 1° = total ÷ 360.

Worked example: value of one degree

Budget ₹72,000, so $1^\circ = \frac{72000}{360} = ₹200$. Rent at $72^\circ$ is $72 \times 200 = ₹14{,}400$. Food at $108^\circ$ is $108 \times 200 = ₹21{,}600$. Finding "one degree" once turns every later question into one multiplication.

Difference and ratio of two slices

• Difference: subtract the angles first, then convert once. Food − Education $= 108^\circ - 54^\circ = 54^\circ = 54 \times 200 = ₹10{,}800$.
• Ratio: the ratio of values equals the ratio of angles — the total cancels. Savings : Transport $= 45 : 36 = 5 : 4$.

When the total is not given

If one slice's value is known, use proportion. Transport ($36^\circ$) is ₹9,000, so Food ($108^\circ$) is $\frac{108}{36} \times 9000 = ₹27{,}000$, and the total is $\frac{360}{36} \times 9000 = ₹90{,}000$.

Two pie charts

Two years (or two companies) each with its own total. The same slice size does not mean the same value if the totals differ. Export share of Asia 30% of ₹400 crore = ₹120 crore; 27% of ₹500 crore = ₹135 crore. The share fell but the amount rose by 12.5%. Always convert each pie to values before comparing.

Common mistakes

• Adding the angles of two sectors and expecting the percent of the sum to equal the sum of the percents — that one is true, but only because both share the same total of $360^\circ$.
• Using 100 instead of 360 when converting an angle to a value.
• Forgetting that two $45^\circ$ sectors of different pies can be different amounts.
• Reporting the angle when the value was asked (the question says "amount" or "degrees" — underline which).

Handy angle table

Percent	Angle	Percent	Angle
5%	18°	25%	90°
10%	36°	30%	108°
12.5%	45°	50%	180°
20%	72°	75%	270°

Quick revision

• Whole circle $= 360^\circ =$ total $= 100\%$.
• value $= \frac{\theta}{360} \times$ total; angle $= \% \times 3.6$.
• Find the value of $1^\circ$ once and reuse it.
• Differences and ratios: work with angles, convert at the end.
• Two pies: convert each to values; shares alone mislead.