CDS Mathematics · Data Interpretation

Bar and Line Graphs

Read each bar's value, total across companies where asked, then compare year with year as a percentage of the earlier year.

All Data Interpretation notes CDS Mathematics strategy

Why this matters

Five PYQs, one of them HARD. Four come from one bar chart of car production and ask for year-on-year percentage rises; the fifth asks how long each segment of a percentage bar diagram should be.

Concept 1 of 1: Year-on-year change and percentage bars

A bar chart is a table drawn as heights. Read the heights into a small table first; then every question is a table question, usually 'which year rose least, as a percentage of the year before'.

Definition

Read the bars into a table: one row per year, one column per company, plus a total column.
Year-on-year rise $= \dfrac{\text{this year} - \text{last year}}{\text{last year}} \times 100$ .
Equal rises in a growing series are SMALLER percentages each year.
Percentage bar diagram of height $H$ : a part worth $x$ of total $T$ gets length $\dfrac xT \times H$ .
'Greater than $20\%$ ' excludes a rise of exactly $20\%$ .

Segment of a percentage bar

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

Worked example

Total production was

800

1000

1200

and

1300

. In which year was the percentage rise smallest?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2021 · CDS (II) 2021 — Elementary Mathematics · Q97Moderate

Example 1 · Data Interpretation · Bar and Line Graphs

Consider the following for the items that follow : The following Bar-Chart gives the production of cars by three different companies

X

Y

and

Z

in different years :

In which year was the percentage increase in production of cars minimum as compared to its previous year ?

A doubling is 100%, not 200%

Going from

1000

2000

is an INCREASE of

100\%

. The new value is

200\%

of the old one; the options often include both.

Drill 4 more on year-on-year change and percentage bars

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 (1)

Year-on-year change and percentage bars
Segment of a percentage bar
$\text{length} = \dfrac{x}{T} \times H$

Watch out for (1)

A doubling is 100%, not 200%
→ Year-on-year change and percentage bars

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