Descriptive Statistics and Data Normalization Previous Year Questions (PYQs) for GATE DA: 2+ Solved Questions with Step-by-Step Solutions

Solve 2+ Descriptive Statistics and Data Normalization previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Descriptive Statistics and Data Normalization

Chapter Roadmap

Descriptive Statistics and Data Normalization

Mean, Median and Mode Constraints

Reconstructing data sets from statistical properties. Solving for unknown integers using mean, median, and mode definitions.

Standardization and Z-Score Normalization

Transforming data to have zero mean and unit variance. Comparing data from different scales using Z-scores.

What You Will Master

Constraint Satisfaction: Finding specific numbers from average, middle, and most frequent values.
Statistical Rigour: Understanding precise definitions governing these measures.
Data Scaling: Converting raw values into standardized scores.

The Interplay of Central Tendencies

In many exam problems, you are not given the data set. You are given its properties. Treat these properties as constraints in a logic puzzle.

Mean

Fixes the sum of the elements.

Median

Fixes the middle element in sorted order.

Mode

Fixes the frequency of the most common element.

The Strategy

Use the Mean to calculate the total sum required.
Use the Median to place a specific value in the center of your sorted list.
Use the Mode to populate the remaining slots with the most frequent value.
Solve for the unknowns using simple arithmetic.

Descriptive Statistics and Data Normalization: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Quantitative Aptitude MCQ

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20.
Ignoring permutations, the number of ways to pick these five integers is _____

A.
0
B.
1
C.
2
D.
3

Correct Answer:

Step-by-Step Solution

Key idea: This is a statistical constraint satisfaction question, recognisable because it asks to reconstruct a specific data set given its mean, median, and mode.

Step 1: Use the mean to find the sum. For 5 integers with a mean of 12, the sum is $5 \times 12 = 60$ .

Step 2: Use the median to fix the middle value. Sorting the 5 integers as $x_{1} \leq x_{2} \leq x_{3} \leq x_{4} \leq x_{5}$ , the median is $x_{3}$ . Thus, $x_{3} = 18$ .

Step 3: Use the mode to fix the highest values. The mode is 20, meaning 20 must appear more frequently than any other number. Since $x_{3} = 18$ , the only way to include 20 is if $x_{4} = 20$ and $x_{5} = 20$ .

Step 4: Find the remaining sum. We have $x_{1} + x_{2} + 18 + 20 + 20 = 60$ , which simplifies to $x_{1} + x_{2} = 2$ .

Step 5: Find integer pairs for $x_{1}$ and $x_{2}$ . Since the integers are from 0 to 20 and $x_{1} \leq x_{2} \leq 18$ , the possible pairs summing to 2 are $(0, 2)$ and $(1, 1)$ .

Step 6: Apply the "single mode" constraint. If the pair is $(1, 1)$ , the set is ${1, 1, 18, 20, 20}$ , which has two modes (1 and 20). This violates the single mode condition. If the pair is $(0, 2)$ , the set is ${0, 2, 18, 20, 20}$ , which has a single mode of 20.

Answer: There is exactly 1 valid way to pick these integers.

Question 2 · Quantitative Aptitude MCQ

Let the minimum, maximum, mean and standard deviation values for the attribute
income of data scientists be ₹46000, ₹170000, ₹96000, and ₹21000, respectively.
The z-score normalized income value of ₹106000 is closest to which ONE of the
following options?

A.
0.217
B.
0.476
C.
0.623
D.
2.304

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct Z-score calculation question, recognisable because it provides the mean, standard deviation, and a specific data point, asking for its normalized value.

Step 1: Identify the given parameters. The raw value $x = 106000$ , the mean $μ = 96000$ , and the standard deviation $σ = 21000$ . (Note: The minimum and maximum values are distractors for Z-score normalization).

Step 2: Recall the Z-score formula, which measures how many standard deviations a value is from the mean: $z = \frac{x - μ}{σ}$ .

Step 3: Substitute the values into the formula: $z = \frac{106000 - 96000}{21000}$ .

Step 4: Simplify the numerator: $106000 - 96000 = 10000$ .

Step 5: Divide by the standard deviation: $z = \frac{10000}{21000} = \frac{10}{21} \approx 0.47619$ .

Answer: The closest option is 0.476.

A question from this chapter

Question 1

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20. Ignoring permutations, the number of ways to pick these five integers is _____

Question 2

Let the minimum, maximum, mean and standard deviation values for the attribute income of data scientists be ₹46000, ₹170000, ₹96000, and ₹21000, respectively. The z-score normalized income value of ₹106000 is closest to which ONE of the following options?

Free preview ends here

Login to view the complete previous-year questions and solutions

Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

Why MastersUp

Personalised first. High quality throughout.

Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

Built around you, not around a syllabus PDF

Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

Revision that hits your weak spots

We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

Questions calibrated to the real exam

Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

Notes written for recall, not for volume

Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

One place for everything

Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

Honest progress

No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

Unlock the whole course

Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

View all plans Start free

Descriptive Statistics and Data Normalization Previous Year Questions (PYQs) for GATE DA: 2+ Solved Questions with Step-by-Step Solutions

Chapter Roadmap: Descriptive Statistics and Data Normalization

Chapter Roadmap

Mean, Median and Mode Constraints

Standardization and Z-Score Normalization

What You Will Master

The Interplay of Central Tendencies

The Interplay of Central Tendencies

Mean

Median

Mode

The Strategy

Descriptive Statistics and Data Normalization: Solved Questions with Step-by-Step Explanations (2 Problems)

Step-by-Step Solution

Step-by-Step Solution

More previous year questions (pyqs) in this unit

A question from this chapter

Login to view the complete previous-year questions and solutions

Personalised first. High quality throughout.

Built around you, not around a syllabus PDF

Revision that hits your weak spots

Questions calibrated to the real exam

Notes written for recall, not for volume

One place for everything

Honest progress

Unlock the whole course