Reading a bar graph
Check the scale on the axis and the unit (₹ lakh, thousands, %).
Read each bar's value from the axis; estimate between gridlines when needed.
Note whether bars are simple (one series), grouped (bars side by side for comparison) or stacked (parts piled up to a total).
Example data
Annual sales of a company (₹ lakh), shown as bars:
2019 | ████████ 40
2020 | ██████ 30
2021 | ██████████ 50
2022 | ████████████ 60
2023 | ██████████████ 70Average sales: (40 + 30 + 50 + 60 + 70) ÷ 5 = 50.
Largest increase over the previous year: 2021 (+20).
Percentage increase from 2020 to 2021: 20/30 = 66.7%.
2023 sales as a percentage of 2019: 70/40 = 175%.
Largest increase vs largest percentage increase
They can be different years. An increase of 20 on a base of 30 (66.7%) beats an increase of 20 on a base of 60 (33%). Always check which one the question asks for.
Stacked bars
In a stacked bar, each segment is one part and the full height is the total. Read a segment as the difference between its top and bottom edges.
Shortcuts and tricks
The standard way is to read every bar, write the values down and calculate. Once the values are written, these shortcuts speed up the comparisons.
Average by deviation
Example: bars of 42, 38, 50, 46 and 44.
Standard way: the total is 220, and 220 ÷ 5 = 44.
Shortcut: take 44 as a base. The deviations −2, −6, +6, +2 and 0 cancel, so the average is 44.
Percentage change as a fraction
Example: sales rise from 45 to 60.
Standard way: 15 ÷ 45 × 100 = 33.3%.
Shortcut: 15/45 = 1/3, which is 33.3%.
Largest percentage increase
Example: 40 → 50 or 80 → 96?
Standard way: 10/40 = 25% and 16/80 = 20%, so the first.
Shortcut: compare new ÷ old: 50/40 = 1.25 and 96/80 = 1.2. The larger ratio is the larger percentage increase.
Exam tips
The tallest bar is not always the answer: read the question's exact measure.
If bars start from a non-zero baseline, heights exaggerate differences; use the axis values.
Write down the values you read once, then work from your list.