CDS Mathematics · Data Interpretation

Pie Charts

A pie chart spreads a total over 360°, so a sector's angle is its share of the total: 1% of the whole is 3.6°.

All Data Interpretation notes CDS Mathematics strategy

Why this matters

Eighteen PYQs, none HARD. Eight convert between angle, percentage and count; the other ten compare two or three charts with DIFFERENT totals, where a share must be turned into a count before anything is compared.

Concept 1 of 2: Angle, share and count

The whole circle is the whole total. A sector's angle out of

360^\circ

is the same fraction as its value out of the total, so any one of angle, percentage or count gives the other two.

Definition

Share $= \dfrac{\theta}{360^\circ}$ ; angle $= \text{percentage} \times 3.6^\circ$ ; count $= \dfrac{\theta}{360^\circ} \times \text{total}$ .
Remove a sector and the rest are redrawn to fill $360^\circ$ : scale each by $\dfrac{360}{360 - \theta_{\text{removed}}}$ .
Adding to one item also adds to the total, so every angle changes.
Slice area and arc length are proportional to the angle; the slice perimeter is not.
Two pies drawn to compare totals: AREA represents the total, so radii go as the square root: $r_1 : r_2 = \sqrt{T_1} : \sqrt{T_2}$ .

Sector angle

\theta = \dfrac{\text{value}}{\text{total}} \times 360^\circ

Worked example

A budget pie gives education

72^\circ

. What percentage of the budget is it?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2016 · CDS (II) 2016 — Elementary Mathematics · Q93Easy

Example 1 · Data Interpretation · Pie Charts

A pie chart depicts the classification of total funds of an organization according to different sources of funds. A particular sector of pie chart for corporate tax has

108^\circ

angle at the centre. What is the percentage of income from corporate tax to total funds ?

The total changes too

Adding

5000

to one item of a

1{,}20{,}000

total makes the new total

1{,}25{,}000

. Keeping the old total in the new angle overstates the change.

Radius is not the total

Pies drawn to compare two totals use AREA. Radii in the ratio

16 : 9

mean totals in the ratio

256 : 81

, not

16 : 9

Drill 8 more on angle, share and count

Concept 2 of 2: Comparing charts with different totals

27\%

share of

4000

and a

27\%

share of

5000

are different numbers of people. Before comparing two charts, turn each share into a count with its own chart's total.

Definition

Count $=$ share $\times$ that chart's total. Compare counts, never percentages, across charts.
Percentage change of an item $= \dfrac{\text{new count} - \text{old count}}{\text{old count}} \times 100$ .
An unchanged share with a total that grew by $k\%$ means the item grew by $k\%$ too.
A chart inside a chart (age groups within States): multiply the two shares.

Share to count

\text{count} = \dfrac{p}{100} \times \text{total}

Worked example

An item is

20\%

3000

staff in one year and

16\%

4500

the next. Find its percentage change.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2021 · CDS (II) 2021 — Elementary Mathematics · Q93Moderate

Example 2 · Data Interpretation · Pie Charts

Consider the following for the items that follow : The following Pie-Charts show the percentage of different categories (

A

B

C

D

E

and

F

) of employees in a company in the year 2019 and 2020. The total number of employees was 4000 in 2019 and 5000 in 2020.

What was the percentage increase of category-

E

employees in 2020 as compared to that in 2019 ?

Same share is not the same size

When the totals differ, an item holding the same percentage in both charts has grown or shrunk with the total. Comparing percentages across the charts answers the wrong question.

Drill 8 more on comparing charts with different totals

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Angle, share and count
Sector angle
$\theta = \dfrac{\text{value}}{\text{total}} \times 360^\circ$
Comparing charts with different totals
Share to count
$\text{count} = \dfrac{p}{100} \times \text{total}$

Watch out for (3)

The total changes too
→ Angle, share and count
Radius is not the total
→ Angle, share and count
Same share is not the same size
→ Comparing charts with different totals

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