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Charts and Graphical Data Interpretation Notes for GATE CS

Charts and Graphical Data Interpretation notes for GATE CS: 13 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questio

charts and graphical data interpretation notes

Chapter Roadmap: Charts and Graphical Data Interpretation

.roadmap-step { opacity: 0; animation: fadeInUp 0.6s ease-out forwards; } .roadmap-step:nth-child(1) { animation-delay: 0.1s; } .roadmap-step:nth-child(2) { animation-delay: 0.3s; } @keyframes fadeInUp { from { opacity: 0; transform: translateY(10px); } to { opacity: 1; transform: translateY(0); } } Chapter Roadmap: Charts and Graphical Data Interpretation 1. Pie Chart Interpretation and Percentage Change Current Topic. Master converting degrees to percentages, finding absolute values, and calculating true percentage change versus percentage points. 2. Bar Charts and Ratio Comparison Up next. Learn to extract data from vertical and horizontal bars and solve multi-variable ratio problems efficiently.

Topic Hero: The Essence of Pie Charts

.hero-highlight { animation: pulseHighlight 2s ease-in-out infinite alternate; } @keyframes pulseHighlight { from { opacity: 0.6; } to { opacity: 1; } } Topic Hero: The Essence of Pie Charts 100% A pie chart is a circular statistical graphic divided into sectors, or slices, to illustrate numerical proportion. Core Principles: The entire circle represents the Total Value, which is always 100% or 36 0^{\circ} . The arc length, central angle, and area of each slice are strictly proportional to the quantity it represents. Data is rarely given in absolute numbers directly; you must derive them using the total value and the given percentage or angle.

Calculating Percentage Change in Pie Charts

.anchor-highlight { animation: glow 2s ease-in-out infinite alternate; } @keyframes glow { from { background: transparent; } to { background: color-mix(in srgb, var(--color-primary) 20%, transparent); border-radius: 4px; } } Calculating Percentage Change in Pie Charts When comparing a component across two different pie charts, for example Year 1 versus Year 2, you are often asked for the percentage change in the actual quantity. The Method: Calculate the Absolute Value for the component in the old period: Old Value = Total_{old} \times (Percentage_{old} /100) . Calculate the Absolute Value for the component in the new period: New Value = Total_{new} \times (Percentage_{new} /100) . Apply the standard percentage change formula: Percentage Change = (\frac{New Value - Old Value}{Old Value}) \times 100 Old Value is the critical anchor denominator Crucial Rule: If the total values differ between the two charts, you must calculate the absolute values first. Never just subtract the percentages.

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Question 1

Level 1: Warm-up

A component's share in a pie chart was 20% of a total value of 500 . In the next year, its share became 25% of a total value of 600 . What is the percentage change in the absolute value of this component?

Question 2

Level 1: Warm-up

A pie chart shows the expenses of a department with a total budget of ₹10,00,000. The sectors have central angles of 7 2^{\circ}, 10 8^{\circ}, 5 4^{\circ}, and 12 6^{\circ} . What is the maximum absolute expense (in ₹) among these sectors?

Question 3

Level 1: Warm-up

Assertion (A): If the share of a category in a pie chart increases from 20% to 25%, the actual quantity of that category has increased by 5% . Reason (R): The difference between two percentages is measured in percentage points, not in percent change. Is the assertion correct, and is the reason the correct explanation?

Question 4

Level 1: Warm-up

Assertion (A): In a bar chart, if the Y-axis has grid lines at intervals of 50, and a bar reaches exactly halfway between the 100 and 150 marks, its value is 125. Reason (R): The width of the bar determines the exact value when it falls between grid lines. Is the assertion correct, and is the reason the correct explanation?

Question 5

Level 1: Warm-up

A pie chart represents the distribution of tasks across four servers. The central angles for three servers are 8 0^{\circ}, 10 0^{\circ}, and 12 0^{\circ} . What is the central angle of the fourth server?

Question 6

Level 1: Warm-up

A pie chart represents a total expenditure of ₹8,00,000. Consider the following statements: (I) A sector with a central angle of 4 5^{\circ} represents ₹1,00,000. (II) The ratio of the absolute values of two sectors is equal to the ratio of their central angles. Which of the statements is/are correct?

Question 7

Level 1: Warm-up

A pie chart shows the distribution of 500 students across four streams. The central angles for Science, Arts, and Commerce are 10 8^{\circ}, 7 2^{\circ}, and 9 0^{\circ} respectively. How many students are in the fourth stream?

Question 8

Level 1: Warm-up

A bar chart has a Y-axis that starts at 100. The bars for products P and Q reach the 150 and 200 marks respectively. Consider the following statements: (I) The ratio of the actual values of P and Q is 3:4. (II) The ratio of the visual heights of the bars (from the baseline) is 3:4. Which of the statements is/are correct?

Question 9

Level 1: Warm-up

In a pie chart representing the annual expenditure of a university, the sector for 'Library Maintenance' subtends a central angle of 5 4^{\circ} . What percentage of the total annual expenditure is spent on Library Maintenance?

Question 10

Level 1: Warm-up

In a pie chart representing the annual budget of an organization, the 'Research' category accounts for 15% of the total budget. What is the central angle subtended by the 'Research' sector?

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Charts and Graphical Data Interpretation Notes for GATE CS

Charts and Graphical Data Interpretation notes for GATE CS: 13 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Chapter Roadmap: Charts and Graphical Data Interpretation

1. Pie Chart Interpretation and Percentage Change

Current Topic. Master converting degrees to percentages, finding absolute values, and calculating true percentage change versus percentage points.

2. Bar Charts and Ratio Comparison

Up next. Learn to extract data from vertical and horizontal bars and solve multi-variable ratio problems efficiently.

Topic Hero: The Essence of Pie Charts

A pie chart is a circular statistical graphic divided into sectors, or slices, to illustrate numerical proportion.

Core Principles:

The entire circle represents the Total Value, which is always $100%$ or $36 0^{\circ}$ .
The arc length, central angle, and area of each slice are strictly proportional to the quantity it represents.
Data is rarely given in absolute numbers directly; you must derive them using the total value and the given percentage or angle.

Calculating Percentage Change in Pie Charts

When comparing a component across two different pie charts, for example Year 1 versus Year 2, you are often asked for the percentage change in the actual quantity.

The Method:

Calculate the Absolute Value for the component in the old period: $Old Value = Total_{old} \times (Percentage_{old} /100)$ .
Calculate the Absolute Value for the component in the new period: $New Value = Total_{new} \times (Percentage_{new} /100)$ .
Apply the standard percentage change formula:

Percentage Change = (\frac{New Value - Old Value}{Old Value}) \times 100

Old Value is the critical anchor denominator

Crucial Rule: If the total values differ between the two charts, you must calculate the absolute values first. Never just subtract the percentages.

Step-by-Step: Finding Absolute Values and Change

Scenario:
- Total budget in 2023 is

500, 000

. Marketing share is

20%

.
- Total budget in 2024 is

600, 000

. Marketing share is

25%

.
- Find the percentage change in the marketing budget.

Step 1: Find 2023 Absolute Value

Value_{2023} = 500, 000 \times \frac{20}{100} = 100, 000

Step 2: Find 2024 Absolute Value

Value_{2024} = 600, 000 \times \frac{25}{100} = 150, 000

Step 3: Calculate Percentage Change

Change = (\frac{150 , 000 - 100 , 000}{100 , 000}) \times 100 = (\frac{50 , 000}{100 , 000}) \times 100 = 50% increase

Charts and Graphical Data Interpretation: Solved Questions with Step-by-Step Explanations (10 Problems)

Question 1 · Quantitative Aptitude MCQ

A component's share in a pie chart was $20%$ of a total value of $500$ . In the next year, its share became $25%$ of a total value of $600$ . What is the percentage change in the absolute value of this component?

A.
25%
B.
50%
C.
75%
D.
100%

Correct Answer:

Step-by-Step Solution

Key idea: calculate absolute values for both years first, then apply the percentage change formula.

Step 1: Old absolute value = $20%$ of $500 = 100$ .

Step 2: New absolute value = $25%$ of $600 = 150$ .

Step 3: Percentage change = $\frac{150 - 100}{100} \times 100 = 50%$ .

Answer: 50%.

Question 2 · Quantitative Aptitude MCQ

A pie chart shows the expenses of a department with a total budget of ₹10,00,000. The sectors have central angles of $7 2^{\circ}$ , $10 8^{\circ}$ , $5 4^{\circ}$ , and $12 6^{\circ}$ . What is the maximum absolute expense (in ₹) among these sectors?

A.
₹2,00,000
B.
₹2,50,000
C.
₹3,00,000
D.
₹3,50,000

Correct Answer:

Step-by-Step Solution

Key idea: the sector with the maximum central angle represents the maximum absolute value.

Step 1: Identify the maximum angle: $12 6^{\circ}$ .

Step 2: $Maximum value = (\frac{126}{360}) \times 1000000 = 0.35 \times 1000000 = 350000$ .

Answer: ₹3,50,000.

Question 3 · Quantitative Aptitude MCQ

Assertion (A): If the share of a category in a pie chart increases from $20%$ to $25%$ , the actual quantity of that category has increased by $5%$ .

Reason (R): The difference between two percentages is measured in percentage points, not in percent change.

Is the assertion correct, and is the reason the correct explanation?

A.
Both A and R are correct and R is the correct explanation of A
B.
Both A and R are correct but R is not the correct explanation of A
C.
A is correct but R is incorrect
D.
A is incorrect but R is correct

Correct Answer:

Step-by-Step Solution

Key idea: distinguish between percentage points and percent change.

Step 1: Assertion (A) claims the quantity increased by $5%$ . However, $25% - 20% = 5$ percentage points, not $5%$ increase. The actual percent change depends on the total base. So (A) is incorrect.

Step 2: Reason (R) correctly states that the difference between two percentages is in percentage points. This is correct terminology.

Answer: A is incorrect but R is correct.

Question 4 · Quantitative Aptitude MCQ

Assertion (A): In a bar chart, if the Y-axis has grid lines at intervals of 50, and a bar reaches exactly halfway between the 100 and 150 marks, its value is 125.

Reason (R): The width of the bar determines the exact value when it falls between grid lines.

Is the assertion correct, and is the reason the correct explanation?

A.
Both A and R are correct and R is the correct explanation of A
B.
Both A and R are correct but R is not the correct explanation of A
C.
A is incorrect but R is correct
D.
A is correct but R is incorrect

Correct Answer:

Step-by-Step Solution

Key idea: distinguish between reading the scale (height) and the meaningless visual property (width).

Step 1: Assertion (A) states the value is 125. Halfway between 100 and 150 is indeed $\frac{100 + 150}{2} = 125$ . So (A) is correct.

Step 2: Reason (R) claims the width determines the value. In a standard bar chart, width is uniform and carries no quantitative meaning; only the height determines the value. So (R) is incorrect.

Answer: A is correct but R is incorrect.

Question 5 · Quantitative Aptitude MCQ

A pie chart represents the distribution of tasks across four servers. The central angles for three servers are $8 0^{\circ}$ , $10 0^{\circ}$ , and $12 0^{\circ}$ . What is the central angle of the fourth server?

A.
$4 0^{\circ}$
B.
$6 0^{\circ}$
C.
$8 0^{\circ}$
D.
$10 0^{\circ}$

Correct Answer:

Step-by-Step Solution

Key idea: total central angle in a pie chart is always $36 0^{\circ}$ .

Step 1: Sum of given angles = $8 0^{\circ} + 10 0^{\circ} + 12 0^{\circ} = 30 0^{\circ}$ .

Step 2: Missing angle = $36 0^{\circ} - 30 0^{\circ} = 6 0^{\circ}$ .

Answer: $6 0^{\circ}$ .

Question 6 · Quantitative Aptitude MCQ

A pie chart represents a total expenditure of ₹8,00,000. Consider the following statements:

(I) A sector with a central angle of $4 5^{\circ}$ represents ₹1,00,000.

(II) The ratio of the absolute values of two sectors is equal to the ratio of their central angles.

Which of the statements is/are correct?

A.
(I) only
B.
(II) only
C.
Both (I) and (II)
D.
Neither (I) nor (II)

Correct Answer:

Step-by-Step Solution

Key idea: verify each statement using the conversion formula and properties of ratios.

Step 1: For (I), $Value = (\frac{45}{360}) \times 800000 = 0.125 \times 800000 = 100000$ . Statement (I) is correct.

Step 2: For (II), $\frac{Value _{1}}{Value _{2}} = \frac{( Angle _{1} /360 ) \times Total}{( Angle _{2} /360 ) \times Total} = \frac{Angle _{1}}{Angle _{2}}$ . Statement (II) is correct.

Answer: Both (I) and (II).

Question 7 · Quantitative Aptitude MCQ

A pie chart shows the distribution of 500 students across four streams. The central angles for Science, Arts, and Commerce are $10 8^{\circ}$ , $7 2^{\circ}$ , and $9 0^{\circ}$ respectively. How many students are in the fourth stream?

A.
150
B.
250
C.
125
D.
100

Correct Answer:

Step-by-Step Solution

Key idea: the sum of all central angles in a pie chart is $36 0^{\circ}$ . Find the missing angle, then convert it to the number of students.

Step 1: Sum of given angles = $10 8^{\circ} + 7 2^{\circ} + 9 0^{\circ} = 27 0^{\circ}$ .

Step 2: Missing angle = $36 0^{\circ} - 27 0^{\circ} = 9 0^{\circ}$ .

Step 3: Number of students in the fourth stream = $(\frac{90}{360}) \times 500 = \frac{1}{4} \times 500 = 125$ .

Answer: 125.

Question 8 · Quantitative Aptitude MCQ

A bar chart has a Y-axis that starts at 100. The bars for products P and Q reach the 150 and 200 marks respectively.

Consider the following statements:

(I) The ratio of the actual values of P and Q is 3:4.

(II) The ratio of the visual heights of the bars (from the baseline) is 3:4.

Which of the statements is/are correct?

A.
(I) only
B.
(II) only
C.
Both (I) and (II)
D.
Neither (I) nor (II)

Correct Answer:

Step-by-Step Solution

Key idea: distinguish between actual values and visual heights when the Y-axis does not start at zero.

Step 1: The actual values are 150 and 200. The ratio is $150 : 200 = 3 : 4$ . Statement (I) is correct.

Step 2: The baseline is 100. The visual heights are $150 - 100 = 50$ and $200 - 100 = 100$ . The ratio of visual heights is $50 : 100 = 1 : 2$ . Statement (II) is incorrect.

Answer: (I) only.

Question 9 · Quantitative Aptitude MCQ

In a pie chart representing the annual expenditure of a university, the sector for 'Library Maintenance' subtends a central angle of $5 4^{\circ}$ . What percentage of the total annual expenditure is spent on Library Maintenance?

A.
10%
B.
15%
C.
18%
D.
20%

Correct Answer:

Step-by-Step Solution

Key idea: use the formula $Percentage = (\frac{Central Angle}{36 0 ^{\circ}}) \times 100$ .

Step 1: $Percentage = (\frac{54}{360}) \times 100 = 0.15 \times 100 = 15%$ .

Answer: 15%.

Question 10 · Quantitative Aptitude MCQ

In a pie chart representing the annual budget of an organization, the 'Research' category accounts for $15%$ of the total budget. What is the central angle subtended by the 'Research' sector?

A.
$4 5^{\circ}$
B.
$5 4^{\circ}$
C.
$2 4^{\circ}$
D.
$1 5^{\circ}$

Correct Answer:

Step-by-Step Solution

Key idea: use the formula $Central Angle = (\frac{Percentage}{100}) \times 36 0^{\circ}$ .

Step 1: Substitute the given percentage into the formula: $Angle = (\frac{15}{100}) \times 36 0^{\circ}$ .

Step 2: Calculate the result: $0.15 \times 36 0^{\circ} = 5 4^{\circ}$ .

Answer: $5 4^{\circ}$ .

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