Data Interpretation

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medium importance~2 Q in Tier 119 formulas⚡ 10 shortcuts5 subtopics

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Pie charts: degrees, shares and totals

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⏱ 4 min read🧩 5 question types🎯 13 practice Q

The idea in one minute

A pie chart splits a total into slices by angle: 360 degrees is the whole, so 1 degree is total ÷ 360.

Two conversions answer everything: degrees to percent ( $360° = 100\%$ ) and degrees to value ( $1° =$ total ÷ $360$ ).

Reading the slices

A family spends ₹72,000 a month:

Head	Food	Rent	Education	Travel	Savings
Angle	108°	90°	72°	54°	36°

The angles must add to 360°: $108+90+72+54+36 = 360$ . Check this before using any slice.

Rule: One slice's value $= \dfrac{\text{angle}}{360} \times \text{total}$ . Food $= \dfrac{108}{360} \times 72000 = ₹21,600$ .

Degrees into percent

$360°$ is the whole, so divide by 36: $108° \rightarrow 3 \rightarrow 30\%$ . Each 3.6° is 1%.

Going the other way, $15\% = 15 \times 3.6 = 54°$ .

Tip: Memorise the pair: $25\% = 90°$ , $50\% = 180°$ . Halving and doubling gets the rest.

Angles as simple fractions

Common slice angles are neat fractions of the whole. Learn the pairs once:

Angle	180°	120°	90°	60°	45°	36°
Fraction	$\dfrac{1}{2}$	$\dfrac{1}{3}$	$\dfrac{1}{4}$	$\dfrac{1}{6}$	$\dfrac{1}{8}$	$\dfrac{1}{10}$

A 90° slice of any total is a quarter of it; 120° is a third. Fractions beat decimal division under time pressure.

Tip: Split odd angles into known pieces: 135° is 90° + 45°, so $\dfrac{1}{4} + \dfrac{1}{8} = \dfrac{3}{8}$ .

Comparing slices

Ratios and differences work directly in degrees.

Rent : Education $= 90 : 72 = 5 : 4$ . Food exceeds Education by $108 - 72 = 36°$ , worth $\dfrac{36}{360} \times 72000 = ₹7,200$ .

Watch: A difference asked in rupees needs the degree gap converted through the total. Answering "36" alone is the planted option.

Two pies side by side

Two pies show two totals. The same angle does not mean the same amount.

Company exports 2020: Asia 120° of ₹80 crore; 2021: Asia 135° of ₹96 crore. Asia's share rose from $33\dfrac{1}{3}\%$ to $37.5\%$ . In value: 2020 gave $\dfrac{120}{360} \times 80 = 26\dfrac{2}{3}$ crore, 2021 gave $\dfrac{135}{360} \times 96 = 36$ crore. That is a $35\%$ rise, not the $12.5\%$ the angles alone suggest.

Note: When only angles are given for both years, compare angles as ratios: Europe $80° : 90° = 8 : 9$ .

Building a pie from data

To draw or check a pie: each slice angle $= \dfrac{\text{part}}{\text{total}} \times 360°$ .

Three items of 150, 250, 100 out of 500 take $108°$ , $180°$ , $72°$ .

Example: Savings at 36° is $\dfrac{36}{360} = 10\%$ of ₹72,000, i.e. ₹7,200.

The one-degree value

Many questions hand you one slice value and ask for the total.

A 40° slice holds 1,600 units, so $1° = 40$ units and the whole pie is $360 \times 40 = 14,400$ .

Tip: Find the per-degree value first; every slice then costs one multiplication.

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common2 practice Q

Value of one slice

How to spot it:

A pie of known total; one slice's angle is given and its value asked.

\text{value} = \frac{\theta}{360} \times \text{total}

Method

Write the total.
Place the angle over 360.
Multiply.

Why it works:

A slice holds its fraction of the total, angle over 360.

Try this

A family's monthly budget of ₹72,000 is shown as a pie:

Head	Food	Rent	Education	Travel	Savings
Angle	108°	90°	72°	54°	36°

The amount spent on Food is:

Show solution

Food angle $= 108°$ .
$\dfrac{108}{360} \times 72000 = 21600$ .

Answer

₹21,600

Type 2common2 practice Q

Percent into angle

How to spot it:

A share is given as a percent and the slice angle is asked (or the reverse).

\theta = \% \times 3.6

Method

Take the percentage.
Multiply by 3.6.
State the answer in degrees.

Why it works:

The full circle, 360 degrees, carries the full 100 percent.

Try this

In a pie chart of monthly expenses, Travel takes 15% of the budget. The central angle of the Travel slice is:

Show solution

$15\%$ of $360°$ .
$0.15 \times 360 = 54°$ .

Answer

54°

Type 3common2 practice Q

Ratio and difference of slices

How to spot it:

Two slices are compared as a ratio, or their value gap is asked.

\frac{\theta_1}{\theta_2} : \text{ratio}; \quad \frac{\theta_1-\theta_2}{360}\times T : \text{gap}

Method

Write both angles.
Ratio: reduce the angles.
Gap: convert the degree difference through the total.

Why it works:

Angles carry both comparisons without touching the other slices.

Try this

A family's monthly budget of ₹72,000 is shown as a pie:

Head	Food	Rent	Education	Travel	Savings
Angle	108°	90°	72°	54°	36°

The ratio of Rent to Education, and by how much amount Food exceeds Education, are:

Show solution

Rent : Education $= 90 : 72 = 5 : 4$ .
Degree gap $= 108 - 72 = 36°$ .
Amount gap $= \dfrac{36}{360} \times 72000 = ₹7,200$ .

Answer

5 : 4 and ₹7,200

Type 4occasional2 practice Q

Two pies compared

How to spot it:

The same category appears in two pies (two years, two companies).

\text{share} = \frac{\theta}{360}; \quad \text{value} = \text{share} \times \text{total}

Method

Read each pie's total.
Convert the slice to a share or value within its own pie.
Compare the two results.

Why it works:

The same angle of a bigger pie is more money; totals must enter.

Try this

Angles of a company's export pie:

Region	2020	2021
Asia	120°	135°
Europe	80°	90°

For Europe, the ratio of the 2020 angle to the 2021 angle is:

Show solution

2020 angle $= 80°$ ; 2021 angle $= 90°$ .
$80 : 90 = 8 : 9$ .

Answer

8 : 9

Type 5common2 practice Q

Total from one slice

How to spot it:

One slice's value is known; the whole pie (or another slice) is asked.

\text{total} = \frac{\text{slice value} \times 360}{\theta}

Method

Find the per-degree value: slice value ÷ angle.
Multiply by 360 for the total.
Multiply by any other angle for its slice.

Why it works:

One slice prices one degree, and one degree prices the pie.

Try this

In a pie chart of production, a 40° sector represents 1,600 units. The total production of all sectors together is:

Show solution

$1° = 1600 \div 40 = 40$ units.
Total $= 40 \times 360 = 14400$ units.

Answer

14,400 units

Formula sheet

Slice value

\text{value} = \frac{\theta}{360} \times \text{total}

theta is the slice angle in degrees.

Angle to percent

\% = \frac{\theta}{3.6}

Percent to angle

\theta = \% \times 3.6

Part to angle

\theta = \frac{\text{part}}{\text{total}} \times 360

Per-degree value

1° = \frac{\text{total}}{360}

Shortcuts that save time

⚡ Divide by 36 for percent

Angle over 3.6 gives percent; angle over 36 gives percent over 10. 108° -> 30%, 54° -> 15%, 90° -> 25%.

Example

A slice of 72° is what percent of the pie?

Show solution

$72 \div 3.6 = 20$ .
So $72° = 20\%$ .

Answer

20%

⚡ Per-degree shortcut

Given one slice's value, find the value of 1 degree once, then price every other slice (and the whole pie) with one multiplication each.

Example

A 40° slice of a pie is worth 1,600 units. Find the whole pie.

Show solution

$1° = 1600 \div 40 = 40$ units.
Whole $= 360 \times 40 = 14400$ .

Answer

14,400

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Treating angles as values across two different pies.

Convert through each pie's own total first.

Mistake 02

Answering a rupee-difference question with the degree gap.

Convert the degree gap through total ÷ 360.

Mistake 03

Using 100° = 25% style conversions.

25% is 90°; 3.6° is 1%. Keep the pair exact.

Mistake 04

Forgetting to check that the angles add to 360°.

Add them first; a misprint or trap shows up immediately.

Mistake 05

Computing percent change in angles as percent change in value.

Growth in share (angle) and growth in value are different questions.

Quick revision

Read this the night before the exam.

Slice value $= \dfrac{\theta}{360} \times$ total.
$\theta \to \%$ : divide by 3.6. $\% \to \theta$ : multiply by 3.6.
25% = 90°, 50% = 180°, 10% = 36°.
Compare slices in degrees; convert to money through the total.
Two pies: same angle, different total, different value.
One slice value gives the per-degree value for everything.

Practice: 13 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 13 questions

Suggested time 8 min · wrong answers go to your mistake notebook automatically.

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