CDS Mathematics · Data Interpretation

Reading Tables

A table question asks for a percentage, a change or an average built from a few cells; the work is picking the right cells and the right base.

All Data Interpretation notes CDS Mathematics strategy

Why this matters

Twenty-four PYQs, none HARD, almost all in sets of two to four on one table. Two skills cover them: percentages and percentage change (always divide by the base the question names), and totals and averages (add a row or a column, then compare).

Concept 1 of 2: Percentages and percentage change

Every percentage has a base, the thing you divide by. 'X is what per cent of Y' divides by

Y

; 'change over last year' divides by last year. Most wrong options use the right difference over the wrong base.

Definition

$X$ as a percentage of $Y$ : $\dfrac XY \times 100$ .
$X$ is what per cent MORE than $Y$ : $\dfrac{X - Y}{Y} \times 100$ .
Change from one year to the next: $\dfrac{\text{new} - \text{old}}{\text{old}} \times 100$ . The same rise is a bigger percentage on a smaller base.
Two percentage changes from the SAME base compare as the raw changes.
A table given in percentages of a total: multiply by the total to get counts before subtracting across rows.

Percentage change

\dfrac{\text{new} - \text{old}}{\text{old}} \times 100

Worked example

Sales were

40

50

and

60

units in three years. In which year was the percentage rise larger?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2021 · CDS (I) 2021 — Elementary Mathematics · Q91Moderate

Example 1 · Data Interpretation · Tables

Consider the following data with regard to production of cars (in lakhs) :

	Year 2015	Year 2016
Country $A$	35	38
Country $B$	45	47
Country $C$	88	93
Country $D$	75	79
Country $E$	58	60.9

In which of the countries, the production of cars has increased by more than or equal to 5% in 2016 over 2015?

Divide by the OLD figure

A change is measured against where it started. From

125

100

is a

20\%

fall; dividing by the new figure gives

25\%

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

When a value lands exactly on the threshold, the wording decides. 'Greater than

20\%

' excludes

20\%

; 'at least

5\%

' includes

5\%

Drill 13 more on percentages and percentage change

Concept 2 of 2: Totals, averages and closest-to-average

An average question wants a row or column total divided by how many entries it has. 'Closest to the average' then means the smallest distance from that average, found by subtracting.

Definition

Average of a row or column $=$ its total $\div$ the number of entries.
A yearly figure per day: divide by $365$ .
'Closest to the average': compute the average, then the distance $|x - \bar x|$ for each option.
Least or most over several years: compare column totals, not single years.
Count the cases only among the options or years the question names.

Average

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

Worked example

A newspaper's circulation over four years was

9

13

10

and

16

thousand. In which year was it closest to its average?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2025 · CDS (I) 2025 — Elementary Mathematics · Q93Moderate

Example 2 · Data Interpretation · Tables

Consider the following for the items that follow : Circulation figures (in thousands) of different newspapers (A, B, C, D, E) for five years are given below :

Year	A	B	C	D	E
2019	20	10	15	8	20
2020	12	12	18	12	12
2021	24	14	17	14	15
2022	26	10	16	15	9
2023	22	16	14	16	11

In which of the given years was the circulation of the newspaper D close to its average circulation over all the years ?

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.

Drill 9 more on totals, averages and closest-to-average

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)

Percentages and percentage change
Percentage change
$\dfrac{\text{new} - \text{old}}{\text{old}} \times 100$
Totals, averages and closest-to-average
Average
$\bar x = \dfrac{\text{total}}{n}$

Watch out for (3)

Divide by the OLD figure
→ Percentages and percentage change
'More than' versus 'more than or equal to'
→ Percentages and percentage change
Which average?
→ Totals, averages and closest-to-average

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