Mixed Graphs & Data Fusion

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Mixed graphs present multiple data representations together — a pie chart alongside a bar chart, a line graph overlaid on a column chart, or a combination of all three within a single DI passage. The skill isn’t reading each chart separately; it’s integrating information across formats to answer questions that require data from more than one source.

What this topic covers in MAT:

• Reading a passage that contains two or more different chart types simultaneously
• Cross-referencing data between a pie chart and a table
• Combining information from a bar chart and a line graph shown together
• Answering questions where no single chart provides the full answer
• Identifying which chart to consult for which type of question

Key techniques:

• Each chart answers different question types: pie charts answer “what share?”, bar charts answer “what value/trend over time?”, line charts answer “how is it changing?”
• When asked for an absolute value, look for a table or a bar chart with a labelled scale
• When asked for a percentage or proportion, look for a pie chart
• When asked for rate of change or trend, look for a line graph

⚡ MAT exam tips:

• Before attempting any question, quickly survey all the charts in the passage. Identify what each chart shows and which ones are related to each other.
• Some questions can be answered from a single chart; others require fusing data from two. Read the question carefully — it will tell you what’s needed.
• In passages with multiple charts showing the same data in different formats, cross-check your answer by reading from a different chart as verification.
• Time target: 6–8 minutes per mixed-graph passage, as the data density is higher than single-chart passages.
• Mixed-graph passages are the most time-intensive in MAT’s DI section. Budget your time accordingly — if you’re spending more than 8 minutes, consider guessing on the harder questions.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Step-by-Step Problem-Solving Approach

Step 1 — Survey all charts in the passage Take 15–20 seconds to look at every chart before reading any questions. Note: (a) what each chart shows, (b) what the total or baseline is, (c) whether any charts share data series (e.g., the same company appears in both a pie chart and a bar chart).

Step 2 — Map relationships between charts Identify which charts are linked. Often the pie chart shows market share (percentages) and the bar chart shows absolute revenue for the same companies. The table might provide the exact numbers that the pie chart and bar chart approximate.

Step 3 — Match each question to the appropriate chart(s)

• “What is the share of X?” → Pie chart
• “What is the value of X in Year 2?” → Bar chart or table
• “How much did X grow from Year 1 to Year 2?” → Line graph or bar chart (compare two bars)
• “What is the ratio of X to Y?” → Either chart, using whichever gives you both values
• “If Z doubles, what happens to X’s share?” → Usually requires calculation from the pie chart

Step 4 — Extract and combine data Write down values from multiple charts as needed. Show your working on rough paper; don’t try to combine data mentally across different charts.

Worked Example — Mixed Chart Passage

Passage contents:

Chart 1 (Pie Chart): Market share of five telecom operators in India in 2023.

• Jio: 36%, Airtel: 32%, Vi: 15%, BSNL: 10%, Others: 7%

Chart 2 (Bar Chart): Revenue (in ₹ thousand crore) of the same five operators in 2023.

• Jio: 82, Airtel: 74, Vi: 38, BSNL: 22, Others: 14

Chart 3 (Line Graph): Year-on-year revenue growth rate (%) for Jio and Airtel from 2020 to 2023.

• Jio: 2020: 15%, 2021: 22%, 2022: 18%, 2023: 12%
• Airtel: 2020: 8%, 2021: 14%, 2022: 16%, 2023: 15%

Question 1: What was the total revenue of the Indian telecom sector in 2023?

• From bar chart: 82 + 74 + 38 + 22 + 14 = ₹230 thousand crore

Question 2: If Jio’s revenue is ₹82 thousand crore and it holds 36% market share, what was the total sector revenue?

• 36% = 82; Total = 82 × (100/36) = 82 × 2.78 ≈ ₹228 thousand crore (close to bar chart total of 230, minor rounding difference)

Question 3: Which operator had the highest revenue per percentage point of market share?

• Revenue per percentage point = Revenue (₹ thousand crore) / Market share (%)
  • Jio: 82/36 = 2.28
  • Airtel: 74/32 = 2.31
  • Vi: 38/15 = 2.53
  • BSNL: 22/10 = 2.20
  • Others: 14/7 = 2.00
• Answer: Vi (2.53) — it generates the most revenue per percentage point of market share.

Question 4: In which year did Airtel’s growth rate overtake Jio’s?

• Compare year by year: 2020: Jio 15% > Airtel 8%; 2021: Jio 22% > Airtel 14%; 2022: Jio 18% < Airtel 16% → Jio still ahead; 2023: Jio 12% < Airtel 15%
• Airtel overtook Jio in 2023 (first year Airtel’s growth exceeded Jio’s)

Question 5: If Jio’s revenue grew by 12% in 2023 to reach ₹82 thousand crore, what was Jio’s revenue in 2022?

• Let 2022 revenue = X; X × 1.12 = 82; X = 82 / 1.12 = ₹73.2 thousand crore ≈ ₹73 thousand crore

Cross-Referencing Strategy

The most efficient strategy in mixed-graph passages:

1. Use the pie chart to answer percentage/share questions
2. Use the bar chart to answer absolute value questions
3. Use the line graph to answer trend/rate questions
4. Use the table (if present) to verify or get exact values when the charts are ambiguous
5. If two charts provide the same information in different formats, use the one that requires fewer steps

Common Traps in Mixed Graphs

• Assuming charts are independent: In a well-designed passage, every chart relates to the others in some way. If a question seems to come from nowhere, re-examine whether you’ve missed a connection.
• Reading from the wrong chart: A pie chart shows percentages; a bar chart shows absolute values. Using the pie chart when the bar chart is needed leads to wrong answers.
• Ignoring the legend: In mixed charts, each colour or pattern may represent a different metric in each chart. Don’t assume a colour means the same thing across charts.
• Missing the scale on dual-axis charts: When a line graph is overlaid on a bar chart with a dual Y-axis, the left axis applies to the bars and the right axis applies to the line. Mixing these up is a common trap.
• Aggregation errors: When combining data from multiple charts (e.g., summing revenues from a bar chart across years to get a total), ensure you’re adding the right values and units.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Advanced Mixed Graph Problem Types

1. Multiple charts with shared data but different bases For example, a pie chart shows percentage market share in 2023, a bar chart shows 2023 revenues, and a line graph shows growth rates over 5 years. Questions may ask: “If Company X’s revenue was ₹50 crore in 2022 and it grew at 20% in 2023, and it held 15% market share in 2023, what was the total industry revenue in 2023?” This requires chaining data across all three charts.

2. Chart where one variable acts as the linking key Two charts that don’t share any direct values but are linked by a common variable. For example, Chart A shows the population of five cities, and Chart B shows the per-capita income in the same five cities. The linking key is the city name. A question might ask for the total income across all five cities: you need population × per-capita income for each city.

3. Inconsistent time periods across charts Chart 1 might cover 2020–2023; Chart 2 might cover 2021–2024. Questions about overlapping periods require pulling data from the relevant chart for the relevant year.

4. Compound growth questions Given a pie chart for 2023 and a growth rate for a specific company, you may be asked to estimate that company’s share in 2025. This requires applying compound growth to the absolute value, then recalculating the new percentage share.

Time-Saving Calculation Techniques

• Pie + Bar cross-check: When you have both a pie chart (percentages) and a bar chart (absolute values), you can verify quickly. If the percentages don’t match the bar heights proportionally, one of the charts may use a different total. Note any discrepancy before answering.
• Using ratios from the pie chart: If you need the ratio of two companies’ revenues and the pie chart gives their shares, the ratio of shares equals the ratio of revenues (if the total is the same for both charts). This saves reading from two different bar chart scales.
• Shortcut for compound share change: If Company X grows at 20% and the overall market grows at 10%, X’s share increases by approximately (20−10) = 10 percentage points on a base share. Exact change is slightly different due to the denominator shift: new share = old share × (1+0.20)/(1+0.10) = old share × 1.091.

Cross-Topic Integration

Mixed graphs test your ability to recognise which chart type is best suited for each question. This is essentially a meta-skill: it requires knowing the strengths and weaknesses of pie charts, bar charts, and line graphs individually (covered in other topics) and applying that knowledge in combination.

MAT-specific patterns: mixed-graph passages appear in approximately 30–40% of MAT DI sets. They are the hardest type and carry the most questions (5–8 per passage). MAT examinees who skip mixed-graph practice lose significant marks, as these passages often appear as the final DI set where time pressure is highest.

Practice with Realistic Data Set

Chart 1 (Pie Chart): City-wise distribution of 3,600 students who appeared for a competitive exam.

• Delhi: 25%, Mumbai: 20%, Bangalore: 18%, Chennai: 15%, Hyderabad: 12%, Others: 10%

Chart 2 (Bar Chart): Average score (out of 300) for students from each city.

• Delhi: 185, Mumbai: 192, Bangalore: 178, Chennai: 205, Hyderabad: 198, Others: 165

Chart 3 (Line Graph): Pass rate (%) for each city over four years.

• Delhi: 62% → 65% → 58% → 68%
• Mumbai: 70% → 72% → 75% → 78%
• Bangalore: 55% → 58% → 62% → 65%
• Chennai: 75% → 78% → 80% → 82%
• Hyderabad: 68% → 65% → 70% → 72%
• Others: 45% → 48% → 50% → 52%

Advanced questions to attempt:

1. How many students from Mumbai appeared for the exam?
2. What was the average score of all students from Delhi?
3. If the passing score is 160, how many students from Chennai passed?
4. Which city showed the highest improvement in pass rate from Year 1 to Year 4?
5. The total number of students who passed from Bangalore in Year 3 is what percent of the total students who passed from Mumbai in Year 4?
6. If Delhi’s student count grows by 10% next year and its average score grows by 5%, what will be Delhi’s new average score?

Work through each, using the appropriate chart(s) for each question.

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