Bar and Line Graphs

Prerequisites

Tables — a graph is a table drawn as a picture; the six question types are the same.
Percentages — growth rates and percentage points.
Ratio and Proportion — comparing two series.

The Hook: The Steepest Line Is Not Always the Fastest

Connect

A cooperative society in a Bastar block puts up a chart on its wall: a bar for every year’s maize (मक्का) collection. The tallest jump between two bars is in the last year, and the secretary proudly calls it “our fastest growth ever”.

But a jump of 36 on a base of 180 is 20%, while an earlier, smaller-looking jump of 30 on a base of 120 was 25%. The biggest jump and the fastest growth are different things — and a CSAT option is waiting for whoever confuses them.

The question this page answers: how do you read values off bar and line graphs accurately, and how do you tell absolute change from percentage change at a glance?

Why it matters for CGPSC: bar graphs (दंड आरेख) and line graphs (रेखा आलेख) are the second most common DI format in Prelims Paper II. They add one skill on top of tables — reading values from a scale — and one classic trap: judging growth by the height of a jump.

Types of Bar Graphs

Type	What it shows	Typical question
Simple bar	One series across categories or years	Which year had the highest value / growth?
Grouped (multiple) bar	Two or more series side by side for each year	Ratio of series 1 to series 2 in a year
Stacked bar	Parts stacked into one bar; bar height = total	Share of one part in the total
Percentage (100%) stacked bar	Every bar has the same height (100%)	Change in share — but not in actual amount

Our working dataset

Table 1: Maize and rice production of a hypothetical district (thousand tonnes) — practice figures, not official data

Year	Maize	Rice	Total (stacked bar height)
2019	120	300	420
2020	150	330	480
2021	135	345	480
2022	162	360	522
2023	180	378	558
2024	216	396	612

The maize column drawn as a simple bar graph:

xychart-beta
    title "Maize production, hypothetical district (thousand tonnes)"
    x-axis [2019, 2020, 2021, 2022, 2023, 2024]
    y-axis "Thousand tonnes" 0 --> 250
    bar [120, 150, 135, 162, 180, 216]

In a grouped bar graph, each year would show a maize bar and a rice bar side by side; in a stacked bar graph, the rice segment would sit on top of the maize segment, and the bar’s total height would be the “Total” column above.

Reading a Bar Graph

Check the scale — where the axis starts (0 or not) and the gap between gridlines. A bar graph whose axis starts at 100 exaggerates differences.
Read values to the nearest gridline, then refine. CSAT graphs usually print the value on top of each bar; if not, the options are far enough apart for estimation.
Write the values in a row under the graph once. Every later question then becomes a table question.

Absolute change vs percentage change

Year	Maize change	Maize growth
2020	+30	\( \frac{30}{120} = 25\% \)
2021	−15	\( \frac{-15}{150} = -10\% \)
2022	+27	\( \frac{27}{135} = 20\% \)
2023	+18	\( \frac{18}{162} \approx 11.1\% \)
2024	+36	\( \frac{36}{180} = 20\% \)

Biggest jump vs fastest growth

The largest absolute rise in maize came in 2024 (+36), but the highest percentage growth came in 2020 (25%). In 2020, maize and rice both rose by 30 thousand tonnes — yet maize grew 25% and rice only 10%, because maize started from a smaller base.

Stacked bars: shares inside a bar

Maize’s share of the total in 2019 = \( \frac{120}{420} \approx 28.6\% \); in 2024 = \( \frac{216}{612} \approx 35.3\% \). The maize segment grew faster than the rice segment (maize +80% over 2019–2024, rice +32%), so its share of the bar rose.

Line Graphs

A line graph (रेखा आलेख) joins values over time. It is ideal for trends, and for comparing two series — revenue and expenditure, imports and exports, births and deaths.

Table 2: Revenue and expenditure of a hypothetical cooperative society (₹ lakh) — practice figures

Year	2019	2020	2021	2022	2023	2024
Revenue	40	46	52	50	60	75
Expenditure	32	36	40	42	45	54
Profit (gap)	8	10	12	8	15	21

xychart-beta
    title "Revenue and expenditure, hypothetical society (Rs lakh)"
    x-axis [2019, 2020, 2021, 2022, 2023, 2024]
    y-axis "Rs lakh" 0 --> 80
    line [40, 46, 52, 50, 60, 75]
    line [32, 36, 40, 42, 45, 54]

(Upper line: revenue; lower line: expenditure.)

Three rules for line graphs

Slope shows absolute change, not percentage change. Revenue rose by ₹6 lakh in both 2020 and 2021 — the two segments have the same slope — but the growth rates differ: \( \frac{6}{40} = 15\% \) and \( \frac{6}{46} \approx 13\% \). In a rising series, an equal slope later on always means smaller percentage growth.
A falling segment is a decrease. Revenue fell only once, in 2022 (52 → 50, about −3.8%).
The vertical gap between two lines is the difference. Here, gap = profit. The gap is narrowest in 2019 and 2022 (₹8 lakh) and widest in 2024 (₹21 lakh). Where two lines cross, the difference is zero and the order flips.

Worked example

In which year was profit the highest percentage of revenue?

Year	2019	2020	2021	2022	2023	2024
Profit ÷ Revenue	20%	≈21.7%	≈23.1%	16%	25%	28%

Answer: 2024 (\( \frac{21}{75} = 28\% \)).

Memory Tricks

Anchor these

“Slope = rupees, not rate.” A steep segment means a big absolute change; for a rate, divide by the starting value.
“Same jump, later year, smaller rate.” In a rising series, equal absolute jumps give shrinking percentages.
“Gap = difference, cross = swap.” Between two lines, the vertical gap is the difference; where they cross, the larger and smaller swap places.
Write the row once. Convert the graph into a row of numbers before answering anything.

Don’t Confuse

This	vs	That
Largest absolute rise (maize 2024: +36)		Highest growth rate (maize 2020: 25%)
Grouped bar — series side by side		Stacked bar — series piled into one total
100% stacked bar — every bar equal height, shows shares		Ordinary stacked bar — height shows the actual total
Steeper segment of a line		Higher percentage growth (not necessarily)

Common Mistakes

Trap 1: Judging growth by bar height or slope

The tallest jump or steepest segment is the largest absolute change. For the highest percentage growth, divide each jump by the bar before it — the answer often moves to an earlier year with a smaller base.

Trap 2: A y-axis that does not start at zero

If the axis starts at, say, 100, a bar that looks twice as tall may be only slightly larger. Always read the numbers, never the visual proportion.

Trap 3: Reading a share from a 100% stacked bar as an amount

A segment that grows in a 100% stacked bar has a larger share — the actual amount may still have fallen if the total fell.

Practice

All questions use Table 1 (maize and rice) and Table 2 (revenue and expenditure) above. All figures are hypothetical.

Level 1: Foundation

In which year did maize production fall?
What was the society’s profit in 2023?
By how much did rice production increase from 2019 to 2024 (absolute)?
Which type of bar graph shows only shares, with every bar the same height?

Answers

2021 (150 → 135).
\( 60 - 45 = \) ₹15 lakh.
\( 396 - 300 = \) 96 thousand tonnes.
The 100% (percentage) stacked bar graph.

Level 2: Prelims MCQs

Q1. In which year did maize production record the highest percentage increase over the previous year?

Answer: (a) 2020

Growth: 2020 \( \frac{30}{120} = 25\% \); 2022 \( \frac{27}{135} = 20\% \); 2023 \( \frac{18}{162} \approx 11.1\% \); 2024 \( \frac{36}{180} = 20\% \).

Option (d) is the trap: 2024 has the largest absolute jump (+36) but only 20% growth.

Q2. The ratio of rice production to maize production in 2024 is:

(a) 5 : 2 (b) 11 : 6 (c) 9 : 5 (d) 7 : 4

Answer: (b) 11 : 6

\( 396 : 216 \); divide both by 36 to get \( 11 : 6 \). Option (a), 5 : 2, is the 2019 ratio (300 : 120).

Q3. Consider the following statements about Table 2:

The society’s revenue increased every year from 2019 to 2024.
The society’s expenditure increased every year from 2019 to 2024.
The society’s profit was the highest in 2024.

Which of the statements given above is/are correct?

(a) 1 and 2 only (b) 3 only (c) 2 and 3 only (d) 1, 2 and 3

Answer: (c) 2 and 3 only

Statement 1 is wrong: revenue fell in 2022 (52 → 50). Statement 2 is correct: 32, 36, 40, 42, 45, 54 rise every year. Statement 3 is correct: profit in 2024 is \( 75 - 54 = 21 \), the largest gap.

Q4. Match the year (List I) with the percentage change in maize production over the previous year (List II):

List I (Year)	List II (Change)
A. 2020	1. −10%
B. 2021	2. About 11%
C. 2023	3. 25%
D. 2024	4. 20%

(a) A-3, B-2, C-1, D-4 (b) A-4, B-1, C-2, D-3 (c) A-3, B-1, C-2, D-4 (d) A-1, B-3, C-4, D-2

Answer: (c) A-3, B-1, C-2, D-4

2020: \( \frac{30}{120} = 25\% \); 2021: \( \frac{-15}{150} = -10\% \); 2023: \( \frac{18}{162} \approx 11.1\% \); 2024: \( \frac{36}{180} = 20\% \).

Q5. Revenue rose by ₹6 lakh in 2020 and again by ₹6 lakh in 2021. Which of the following is correct?

(a) The growth rate was the same in both years. (b) The growth rate was higher in 2021. (c) The growth rate was higher in 2020. (d) Growth rates cannot be compared without expenditure data.

Answer: (c)

2020: \( \frac{6}{40} = 15\% \); 2021: \( \frac{6}{46} \approx 13\% \). Equal absolute rises on a growing base mean a falling growth rate — the two line segments have the same slope, but the rates differ.

Level 3: Speed Drill — Solve in 60 Seconds

Total maize production over the six years.
Maize’s share of total (maize + rice) production in 2024, to one decimal place.
Percentage growth of rice in 2023.
Profit as a percentage of revenue in 2023.
Percentage increase in expenditure from 2019 to 2024.
Average annual profit over the six years.

Answers with the shortcut used

963 thousand tonnes — pair them: \( (120 + 180) + (150 + 135) + (162 + 216) = 300 + 285 + 378 \).
About 35.3% — \( \frac{216}{612} = \frac{6}{17} \) (divide both by 36); \( \frac{1}{17} \approx 5.9\% \), so \( 6 \times 5.88 \approx 35.3 \).
5% — \( \frac{18}{360} = \frac{1}{20} \).
25% — \( \frac{15}{60} = \frac{1}{4} \).
68.75% — \( \frac{22}{32} = \frac{11}{16} \); \( \frac{1}{16} = 6.25\% \), times 11.
About ₹12.3 lakh — \( \frac{8 + 10 + 12 + 8 + 15 + 21}{6} = \frac{74}{6} \).

Quick Revision Table

Idea	Formula / Fact
Bar types	Simple, grouped, stacked, 100% stacked
Stacked bar	Height = total; segment ÷ height = share
Slope of a line	Absolute change per period
Growth rate	Jump ÷ starting value \( \times 100 \)
Two lines	Vertical gap = difference; crossing = order swaps
Equal jumps, rising series	Falling percentage growth
Axis check	Does the y-axis start at zero?

Key Takeaways

Convert the graph into a row of numbers first; then it is a table question.
Bar height and line slope show absolute change. Percentage growth needs a division by the starting value.
A smaller base produces higher growth for the same jump — the “fastest” year is often an early one.
Between two lines, the gap is the difference (profit, trade balance, surplus).
Check whether the y-axis starts at zero before trusting any visual comparison.

What’s Next

Pie Charts — shares of a whole, drawn as a circle.
Tables — revisit the six question types and the 1% block method.
Data Sufficiency — when the chart (or the statements) may not be enough.
Agriculture and Irrigation in Chhattisgarh — real crop data to practise reading, with official sources.
Data Interpretation — Quick Revision — the whole chapter on one page.