CUET UG General Test: Quantitative Reasoning - Data Interpretation, Tables, Bar Graphs, Pie Charts, Line Graphs

Must?Know

• In a pie chart, the central angle of a sector = (Value of the component / Total value) × 360°; e.g., if a category is 25% of total, its angle is 90°.
• For bar graphs, if bars are horizontal, the length represents magnitude along the x-axis, while categories are on the y-axis; used when category names are long.
• In line graphs, trends over time are shown with x-axis as time and y-axis as quantity; consecutive points joined by straight lines to show continuity.
• A table in data interpretation must be read row-wise and column-wise to identify totals, percentages, or missing values; always check units in headers.
• When comparing two pie charts, percentage share may remain same but actual values differ if totals are different; e.g., 20% of 500 = 100, 20% of 800 = 160.
• Cumulative frequency in tables helps find median: median class is where cumulative frequency-N/2, N = total frequency.
• In grouped frequency bar graphs, bars touch each other to indicate continuous data, unlike ungrouped categorical data where gaps exist.
• To calculate average from a table: sum of (value × frequency) / total frequency; e.g., marks: 10 (2 students), 20 (3 students)-avg = (10×2 + 20×3)/5 = 16.
• Percentage increase from line graph between two points = [(New – Old)/Old] × 100; e.g., from 40 to 50? (10/40)×100 = 25%.
• In comparative bar graphs (e.g., dual bars per category), each bar represents a different variable (e.g., boys vs girls) for same category (e.g., class).
• Central angle for 1% in a pie chart is 3.6°, since 360°/100 = 3.6°; useful for quick estimation.
• Missing data in tables may be inferred using row or column totals; e.g., if total = 200 and others sum to 170, missing = 30.
• Year-on-year growth rate in line graphs uses previous year as base; e.g., 2022: ?100 cr, 2023: ?120 cr-growth = 20%.
• Pie chart sectors must add to 100% or 360°; if not, either data is approximate or there’s an "others" category.
• Bar graph scale must be checked: broken axis (zigzag line) indicates scale starts above zero; can exaggerate differences.
• In stacked bar graphs, each bar shows total, divided into segments; part-to-whole comparison within each category.
• Mode from frequency table is the value with highest frequency; e.g., values: 5, 7, 7, 8, 7-mode = 7.
• When a line graph shows multiple lines, each represents a different dataset; legend is essential to interpret.
• In population data tables, density = population / area; verify units (e.g., per km²).
• For time-series data, line graphs are preferred over bar graphs because they emphasize trend and continuity.

Difficulty Level

Intermediate — requires interpretation beyond reading values, including calculations and trend analysis, but does not involve multi-layered data integration.

Common CUET Traps

• Trap: Assuming equal percentages in pie charts mean equal values without checking total size. Avoid: Always compare actual values if totals differ across charts.
• Trap: Reading bar graph values from top of bar without checking scale intervals (e.g., scale jumps from 10 to 15). Avoid: Note scale divisions and use ruler method mentally.
• Trap: Confusing cumulative frequency with individual frequency in tables. Avoid: Labelled “Cumulative” or “C.F.” indicates running total; subtract to get individual.

Practice MCQs

Q1. The table shows marks of 5 students:
| Student | Marks |
|---------|-------|
| A | 80 |
| B | 85 |
| C | 90 |
| D | 75 |
| E | 70 |
What is the average mark?
A. 80
B. 82
C. 84
D. 85
Answer: A
Explanation: Sum = 80+85+90+75+70 = 400; average = 400/5 = 80.
Why others fail: Option B (82) may come from incorrect sum (410).

Q2. In a pie chart, a sector has a central angle of 72°. What percentage of the total does it represent?
A. 10%
B. 15%
C. 20%
D. 25%
Answer: C
Explanation: (72/360) × 100 = 20%.
Why others fail: Option A (10%) comes from dividing 72 by 7.2 incorrectly.

Q3. A line graph shows sales (in-lakh): 2020: 50, 2021: 60, 2022: 75, 2023: 90. What is the percentage increase from 2021 to 2022?
A. 15%
B. 20%
C. 25%
D. 30%
Answer: C
Explanation: [(75 – 60)/60] × 100 = 25%.
Why others fail: Option B (20%) comes from using 75 as base instead of 60.

Q4. A bar graph shows production (in tonnes) of wheat in 4 states: UP: 120, MP: 90, Punjab: 100, Haryana: 80. If total production is 400 tonnes, what percentage is contributed by UP?
A. 25%
B. 30%
C. 35%
D. 40%
Answer: B
Explanation: (120/400) × 100 = 30%.
Why others fail: Option A (25%) assumes equal distribution (100 each), ignoring actual values.

Q5. Two companies A and B have revenue pie charts. A’s total revenue is ?500 cr, B’s is ?800 cr. Both show 40% for electronics. How much more does B earn from electronics than A?
A. ?100 cr
B. ?120 cr
C. ?150 cr
D. ?180 cr
Answer: B
Explanation: A: 40% of 500 = ?200 cr; B: 40% of 800 = ?320 cr; difference = ?120 cr.
Why others fail: Option A (?100 cr) comes from 40% of difference in totals (300 × 0.4), which is wrong.

Last?Minute Revision

• Central angle formula: (Component/Total) × 360° — must use actual value, not percentage.
• In bar graphs, width of bars is uniform; only length matters.
• Line graphs show trend; do not assume values between points unless linear.
• Pie chart total must sum to 100% or 360° — if not, check for rounding or "others".
• Average = Total sum / Number of items — apply to table data.
• Percentage change = (Difference / Original) × 100 — base is original value.
• Stacked bar graph: total bar height = sum of parts; read segments carefully.
• Horizontal bar graph: categories on Y-axis, values on X-axis.
• Cumulative frequency-N/2 gives median class — used in grouped data.
• Mode = highest frequency — visible in frequency tables.
• Scale in graphs may be non-linear; check for breaks (zigzag symbol).
• Dual bar graphs compare two variables per category — check legend.
• Year-on-year growth uses previous year as denominator.
• 1% of pie chart = 3.6° — use for fast estimation.
• Density = Population / Area — units matter (e.g., per km²).