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CDS Mathematics · Formula sheet

Data Interpretation formulas

6 formulas and 8 common traps for CDS Mathematics Data Interpretation, grouped by subtopic.

Full notes with worked examples

Reading Tables

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Percentages and percentage change

Percentage change

new−oldold×100\dfrac{\text{new} - \text{old}}{\text{old}} \times 100

Totals, averages and closest-to-average

Average

xˉ=totaln\bar x = \dfrac{\text{total}}{n}

Common traps

Divide by the OLD figure

A change is measured against where it started. From 125125 to 100100 is a 20%20\% fall; dividing by the new figure gives 25%25\%.

'More than' versus 'more than or equal to'

When a value lands exactly on the threshold, the wording decides. 'Greater than 20%20\%' excludes 20%20\%; 'at least 5%5\%' includes 5%5\%.

Which average?

'Close to its own average over the years' and 'close to the average of all newspapers that year' are different numbers. Read which one the question asks for.

Pie Charts

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Angle, share and count

Sector angle

θ=valuetotal×360∘\theta = \dfrac{\text{value}}{\text{total}} \times 360^\circ

Comparing charts with different totals

Share to count

count=p100×total\text{count} = \dfrac{p}{100} \times \text{total}

Common traps

The total changes too

Adding 50005000 to one item of a 1,20,0001{,}20{,}000 total makes the new total 1,25,0001{,}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 16:916 : 9 mean totals in the ratio 256:81256 : 81, not 16:916 : 9.

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.

Bar and Line Graphs

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Year-on-year change and percentage bars

Segment of a percentage bar

length=xT×H\text{length} = \dfrac{x}{T} \times H

Common traps

A doubling is 100%, not 200%

Going from 10001000 to 20002000 is an INCREASE of 100%100\%. The new value is 200%200\% of the old one; the options often include both.

Caselets: Data Given in Words

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Build the table first

Missing cell

cell=row total−known cells\text{cell} = \text{row total} - \text{known cells}

Common traps

A percentage of which total?

'60%60\% of students studying Physics are boys' is 60%60\% of the Physics row, not of the whole university. Using the grand total is the usual slip.

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