Data Interpretation: Tables, Charts and Graphs Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

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

Exam Readiness Checklist

Final Verification Protocol

Base Check: Is the percentage applied to the correct total (e.g., Valid = Total - Invalid)?
Weighting Check: For averages, did I compute $\sum f_{i} x_{i} / \sum f_{i}$ and not just the average of the $x_{i}$ values?
Transformation Check: If $Y = a X + b$ , did I use $\overset{ˉ}{Y} = a \overset{ˉ}{X} + b$ to save time?
Unit Check: Did I carry the correct units (e.g., rupees, degrees, absolute counts) to the final answer?

Quick Counting Checklist

Condition Clarity: Verified inequality type ( $<$ , $\leq$ , $>$ , $\geq$ , $=$ )
Systematic Scan: Used consistent row-wise or column-wise pattern
Logic Accuracy: Applied AND/OR conditions correctly (no double-counting)
Boundary Check: Confirmed edge cases (e.g., $U = 4$ for $U \leq 4$ )
Total Verification: $Count + Non-qualifying = m \times n$

Quick Reference

Condition	Include Boundary?
$U < k$	No
$U \leq k$	Yes
$U > k$	No
$U \geq k$	Yes
$a \leq U \leq b$	Both ends

Accuracy over speed—take 10 extra seconds to verify.

Data Interpretation: Tables, Charts and Graphs: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Quantitative Aptitude MCQ

If the average value of a dataset $X$ is 10, and a new dataset $Y$ is created using the linear transformation $Y = 2 X + 3$ , what is the average value of $Y$ ?

A.
20
B.
13
C.
26
D.
23

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct substitution question, recognisable because it gives the average of a variable and asks for the average after a linear transformation.

Step 1: Recall the property of linear transformation of averages. If $Y = a X + b$ , then the average of $Y$ is $\overset{ˉ}{Y} = a \overset{ˉ}{X} + b$ .

Step 2: Identify the given values. $\overset{ˉ}{X} = 10$ , $a = 2$ , and $b = 3$ .

Step 3: Substitute these values into the formula: $\overset{ˉ}{Y} = 2 (10) + 3$ .

Step 4: Calculate the result: $20 + 3 = 23$ .

Answer: D

Question 2 · Quantitative Aptitude MCQ

When interpreting a pie chart that explicitly shows the "share of valid votes", what is the correct base value to use for percentage calculations?

A.
Total votes cast minus invalid votes
B.
Total votes cast
C.
Total votes cast plus invalid votes
D.
The number of candidates

Correct Answer:

Step-by-Step Solution

Key idea: This is a definition question, recognisable because it asks for the correct baseline (denominator) when a chart specifies "valid" data.

Step 1: Read the chart title carefully. It specifies "share of valid votes".

Step 2: The pie chart represents parts of the "valid votes" whole.

Step 3: Therefore, the correct base value for any percentage calculation from this chart is the total number of valid votes, which is calculated as Total votes cast minus invalid votes.

Answer: A

chapter

Data Interpretation: Tables, Charts and Graphs Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Data Interpretation: Tables, Charts and Graphs short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved pract

A question from this chapter

Question 1

If the average value of a dataset X is 10, and a new dataset Y is created using the linear transformation Y = 2 X + 3, what is the average value of Y ?

Question 2

When interpreting a pie chart that explicitly shows the "share of valid votes", what is the correct base value to use for percentage calculations?

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