Descriptive Statistics and Data Normalization Practice Questions for GATE DA: 20+ Solved Questions with Step-by-Step Solutions

Solve 20+ Descriptive Statistics and Data Normalization practice 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 (5 Problems)

Question 1 · Quantitative Aptitude MCQ

For a sorted data set of 7 numbers represented as $x_{1} \leq x_{2} \leq x_{3} \leq x_{4} \leq x_{5} \leq x_{6} \leq x_{7}$ , which position corresponds to the median?

A.
3rd
B.
4th
C.
5th
D.
Average of 3rd and 5th

Correct Answer:

Step-by-Step Solution

Key idea: This is a definition recall question, recognisable because it asks for the position of the median in a sorted list of a specific size.

Step 1: Recall the definition of the median. The median is the middle value of a sorted data set.

Step 2: Determine the middle position for an odd number of elements $n$ . The formula for the middle position is $\frac{n + 1}{2}$ .

Step 3: Substitute $n = 7$ into the formula: $\frac{7 + 1}{2} = \frac{8}{2} = 4$ .

Step 4: The 4th position corresponds to the variable $x_{4}$ .

Answer: B

Question 2 · Quantitative Aptitude MCQ

For a sorted data set of 9 variables $x_{1} \leq x_{2} \leq x_{3} \leq x_{4} \leq x_{5} \leq x_{6} \leq x_{7} \leq x_{8} \leq x_{9}$ , which variable represents the median?

A.
x_3
B.
x_4
C.
x_5
D.
x_6

Correct Answer:

Step-by-Step Solution

Key idea: This is a definition recall question, recognisable because it asks for the position of the median in a sorted list of a specific size.

Step 1: Recall the definition of the median. The median is the middle value of a sorted data set.

Step 2: Determine the middle position for an odd number of elements $n$ . The formula for the middle position is $\frac{n + 1}{2}$ .

Step 3: Substitute $n = 9$ into the formula: $\frac{9 + 1}{2} = \frac{10}{2} = 5$ .

Step 4: The 5th position corresponds to the variable $x_{5}$ .

Answer: C

Question 3 · Quantitative Aptitude MCQ

If a data set is stated to have a "single mode" of 25, what must be true about the frequency of 25?

A.
It is equal to the frequencies of all other values.
B.
It is strictly greater than the frequency of any other value.
C.
It is the only value that appears exactly once.
D.
It appears exactly twice in the data set.

Correct Answer:

Step-by-Step Solution

Key idea: This is a definition question about the unique mode condition, recognisable because it specifies a "single mode".

Step 1: Recall the definition of a mode. The mode is the value that appears most frequently in a data set.

Step 2: Understand the "single mode" constraint. If there is a single mode, it means exactly one value has the highest frequency, and no other value shares this highest frequency.

Step 3: Apply this to the value 25. Since 25 is the single mode, its frequency must be strictly greater than the frequency of any other value in the data set.

Answer: It is strictly greater than the frequency of any other value.

Question 4 · Quantitative Aptitude MCQ

Which measure of central tendency is most influenced by extreme outlier values in a data set?

A.
Mode
B.
Median
C.
Mean
D.
Range

Correct Answer:

Step-by-Step Solution

Key idea: This is a conceptual question about the interplay of central tendencies, recognisable because it asks about the effect of outliers on a specific measure.

Step 1: Recall the properties of the three main measures of central tendency: mean, median, and mode.

Step 2: Understand how each measure is calculated. The mean is the arithmetic average, which includes every value in the sum. The median is the middle value, and the mode is the most frequent value.

Step 3: Determine the effect of an extreme outlier. Since the mean includes every value in its calculation, an extreme outlier will pull the mean towards it. The median and mode are resistant to outliers.

Answer: Mean.

Question 5 · Quantitative Aptitude MCQ

When using the "Fixed Sum and Middle Element" pattern to solve for unknown integers, what is the primary purpose of subtracting the median from the total sum?

A.
To find the sum of the remaining elements.
B.
To find the mode of the data set.
C.
To calculate the mean of the extreme values.
D.
To determine the range of the data set.

Correct Answer:

Step-by-Step Solution

Key idea: This is a pattern recognition question, recognisable because it asks about the specific algebraic step in the "Fixed Sum and Middle Element" method.

Step 1: Recall the "Fixed Sum and Middle Element" pattern. This pattern is used when you know the total sum of a data set and the value of the median (the middle element).

Step 2: Understand the algebraic goal. The total sum includes all elements. By subtracting the median (the middle element), you isolate the sum of all the other elements.

Step 3: Identify the purpose. This isolated sum is then used to solve for the remaining unknown integers.

Answer: To find the sum of the remaining elements.

A question from this chapter

Question 1

For a sorted data set of 7 numbers represented as x_{1} \leq x_{2} \leq x_{3} \leq x_{4} \leq x_{5} \leq x_{6} \leq x_{7}, which position corresponds to the median?

Question 2

For a sorted data set of 9 variables x_{1} \leq x_{2} \leq x_{3} \leq x_{4} \leq x_{5} \leq x_{6} \leq x_{7} \leq x_{8} \leq x_{9}, which variable represents the median?

Question 3

If a data set is stated to have a "single mode" of 25, what must be true about the frequency of 25?

Question 4

Which measure of central tendency is most influenced by extreme outlier values in a data set?

Question 5

When using the "Fixed Sum and Middle Element" pattern to solve for unknown integers, what is the primary purpose of subtracting the median from the total sum?

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Descriptive Statistics and Data Normalization Practice Questions for GATE DA: 20+ 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 (5 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

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A question from this chapter

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Honest progress

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