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Charts and Graphical Data Interpretation Short Notes for GATE CS

Charts and Graphical Data Interpretation short notes for GATE CS: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice qu

charts and graphical data interpretation short notes

Quick Revision Checklist

.check-item { opacity: 0; animation: checkPop 0.4s cubic-bezier(0.175, 0.885, 0.32, 1.275) forwards; } .check-item:nth-child(1) { animation-delay: 0.1s; } .check-item:nth-child(2) { animation-delay: 0.2s; } .check-item:nth-child(3) { animation-delay: 0.3s; } .check-item:nth-child(4) { animation-delay: 0.4s; } .check-item:nth-child(5) { animation-delay: 0.5s; } @keyframes checkPop { from { opacity: 0; transform: scale(0.9); } to { opacity: 1; transform: scale(1); } } Quick Revision Checklist Total Circle: 100% = 36 0^{\circ} . Absolute Value: Total \times (Percentage /100) . Ratios: Ratio of two slices = Ratio of their percentages (Total value is not needed). Percentage Change: Requires absolute values if the total base has changed between periods. Terminology: A difference in shares is "percentage points", not "percent change".

Quick Revision Checklist

.check-item { opacity: 0; animation: checkPop 0.4s cubic-bezier(0.175, 0.885, 0.32, 1.275) forwards; } .check-item:nth-child(1) { animation-delay: 0.1s; } .check-item:nth-child(2) { animation-delay: 0.2s; } .check-item:nth-child(3) { animation-delay: 0.3s; } .check-item:nth-child(4) { animation-delay: 0.4s; } @keyframes checkPop { from { opacity: 0; transform: scale(0.9); } to { opacity: 1; transform: scale(1); } } Quick Revision Checklist Check the Baseline: Verify if the Y-axis starts at 0 or a higher value before making any visual comparisons. Read, Do Not Estimate: Extract exact numerical values using the grid scale. Visual height ratios are unreliable if the baseline is non-zero. Respect the Order: "Ratio of A to B" means A : B . Reversing this is a common, costly mistake. Simplify: Always reduce the final ratio to its lowest integer terms (e.g., 120 : 150 becomes 4 : 5).

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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 Short Notes for GATE CS

Charts and Graphical Data Interpretation short notes for GATE CS: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Quick Revision Checklist

Total Circle: $100% = 36 0^{\circ}$ .
Absolute Value: $Total \times (Percentage /100)$ .
Ratios: Ratio of two slices = Ratio of their percentages (Total value is not needed).
Percentage Change: Requires absolute values if the total base has changed between periods.
Terminology: A difference in shares is "percentage points", not "percent change".

Quick Revision Checklist

Check the Baseline: Verify if the Y-axis starts at $0$ or a higher value before making any visual comparisons.
Read, Do Not Estimate: Extract exact numerical values using the grid scale. Visual height ratios are unreliable if the baseline is non-zero.
Respect the Order: "Ratio of A to B" means $A : B$ . Reversing this is a common, costly mistake.
Simplify: Always reduce the final ratio to its lowest integer terms (e.g., $120 : 150$ becomes $4 : 5$ ).

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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