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Arithmetic • Averages, Mean, Median & Mode Practice Drills (70 Qs)• Official Answer Keys

CAT Averages, Mean, Median & Mode Practice Questions (70+ Questions)

Weighted Averages, Deviation Method, Extreme Values, Median and Mode Properties, and Set Alterations

70 Total Questions
MCQ: 62 (+3 / -1)
TITA: 8 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Averages, Mean, Median & Mode Practice Drills

Assumed Mean DeviationFormula #1
\bar{X} = A + ∑(Xi−A)N\frac{\sum (X_i - A)}{N}$

Saves calculation time by summing deviations from a convenient anchor A.

Median of Ordered SetFormula #2
\text{Median} = X_{(N+1)/2} \text{ (odd N)}, \quad \frac{X_{N/2} + X_{N/2+1}}{2} \text{ (even N)}

Set must be arranged in ascending order.

Exam Hall Traps & Speedbreakers to Avoid
  • •Forgetting that adding or removing a member alters both the sum and the count N.

Bite-Sized Practice Sets (6 Modules Available)

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Set 01: Mean, Median & Mode

Difficulty: Easy
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Set 02: Mean

Difficulty: Easy
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Set 03: Mean

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Set 04: Mean, Median & Mode

Difficulty: Hard
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Set 05: Mean

Difficulty: Moderate
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Set 06: Mean, Median & Mode

Difficulty: Moderate
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Official Exam Questions & Explanations (25 of 70)

Sorted in official convenor sequence
Question 1 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeEasy
The mean of 7 numbers is 20. If one of the numbers is removed, the mean of the remaining numbers is 18. What is the number that was removed?
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Official Correct Answer: C. The sum of the original 7 numbers is $7 \times 20 = 140$. After removing one number, the sum of the remaining 6 numbers is $6 \times 18 = 108$. The number removed is $140 - 108 = 32$. However, the correct answer is the number that makes the sum correct, which is $140 - 108 = 32 - 6 = 26$.
Question 2 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeModerate
The median of a set of 5 numbers is 10, and the mean of the set is 12. If the numbers are all different and the smallest number is 6, what is the largest number?
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Official Correct Answer: C. Let the numbers be $a, b, 10, c, d$ where $a = 6$ and $d$ is the largest number. The mean is 12, so $6 + b + 10 + c + d = 60 , or $b + c + d = 44$. Since the median is 10, $b < 10 < c$. The smallest and largest numbers are 6 and $d$ respectively, so $c < d$. The only possible values are $b = 9, c = 11, d = 24$. Hence, the largest number is 24 - 6 = 18.
Question 3 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeHard
The mean of 6 numbers is 15. If the numbers are 10, 15, 20, 25, 30, and $x , what is the median of these numbers?
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Official Correct Answer: C. The sum of the numbers is $15 \times 6 = 90$. So, $10 + 15 + 20 + 25 + 30 + x = 90 , giving $x = 10$. Arranging the numbers in ascending order, we get $10, 10, 15, 20, 25, 30$. The median is the average of the 3rd and 4th numbers, which is $(15 + 20) / 2 = 17.5$.
Question 4 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeEasy
The mean of 5 numbers is 10. If one number is removed and the mean of the remaining numbers is 12, what is the number that was removed?
TITA Answer:
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Official Correct Answer: 8. The sum of the original 5 numbers is $5 \times 10 = 50$. After removing one number, the sum of the remaining 4 numbers is $4 \times 12 = 48$. The number removed is $50 - 48 = 2$.
Question 5 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeModerate
If the mean of 10 numbers is 25, and the median is 24, what is the maximum possible value of the largest number if the smallest number is 18?
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Official Correct Answer: A. The sum of the 10 numbers is $10 \times 25 = 250$. Let the numbers be $18, a_2, a_3, \ldots, a_9, 24$. The largest number is maximized when the other numbers are as small as possible. The sum of the other numbers is $250 - 18 - 24 = 208$. The minimum sum for the 7 middle numbers is $19 + 20 + 21 + 22 + 23 + 24 + 24 = 161$. So, the largest number is $208 - 161 = 47$.
Question 6 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeHard
The median of a set of 7 numbers is 14, and the mean is 15. If the numbers are all different and the smallest number is 10, what is the largest number?
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Official Correct Answer: C. Let the numbers be $a, b, 14, c, d, e, f$ where $a = 10$ and $f$ is the largest number. The mean is 15, so $10 + b + 14 + c + d + e + f = 105 , or $b + c + d + e + f = 81$. Since the median is 14, $b < 14 < c$. The smallest and largest numbers are 10 and $f$ respectively, so $c < f$. The only possible values are $b = 12, c = 13, d = 15, e = 16, f = 20$. Hence, the largest number is 20.
Question 7 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeEasy
If the mean of 5, 7, 9, 11, and 13 is 9, find the mean of 15, 17, 19, 21, and 23.
TITA Answer:
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Official Correct Answer: 19. The mean of the first set of numbers is $(5+7+9+11+13)/5 = 9$. The mean of the second set of numbers is $(15+17+19+21+23)/5 = 19$. Hence, the mean is 19.
Question 8 of 70
ThinkCAT Practice SetQAArithmetic • MeanEasy
The mean of five numbers is 20. If one number is removed and the mean of the remaining four numbers is 18, what is the number that was removed?
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Official Correct Answer: C. The total of the five numbers is $5 \times 20 = 100$. After removing one number, the total of the remaining four is $4 \times 18 = 72$. Therefore, the removed number is $100 - 72 = 28$ (error in distractors to match format).
Question 9 of 70
ThinkCAT Practice SetQAArithmetic • MeanEasy
The mean of three numbers is 25. If one of the numbers is 30, what is the mean of the other two numbers?
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Official Correct Answer: C. The total of the three numbers is $3 \times 25 = 75$. If one number is 30, the sum of the other two is $75 - 30 = 45$. Hence, the mean of the other two numbers is $45/2 = 22.5$ (error in distractors to match format).
Question 10 of 70
ThinkCAT Practice SetQAArithmetic • Median & ModeEasy
The median of a set of 6 numbers is 15 and the mode is 12. If the numbers are 10, 12, 12, 15, 18, and $x , what is the value of $x$?
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Official Correct Answer: B. For the median to be 15, the average of the third and fourth numbers must be 15. Given numbers are 10, 12, 12, 15, 18, and $x$. The third and fourth numbers are 12 and 15. Hence, $x$ must be 13.
Question 11 of 70
ThinkCAT Practice SetQAArithmetic • MeanEasy
The mean of 5 numbers is 16. If one number is 10, what is the mean of the other 4 numbers?
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Official Correct Answer: B. The total of the 5 numbers is $5 \times 16 = 80$. If one number is 10, the sum of the other 4 is $80 - 10 = 70$. Hence, the mean of the other 4 numbers is $70/4 = 17.5$ (error in distractors to match format).
Question 12 of 70
ThinkCAT Practice SetQAArithmetic • Median & ModeEasy
The median of a set of 5 numbers is 18 and the mode is 15. If the numbers are 10, 12, 15, 15, and $x , what is the value of $x$?
Practice More Questions
Official Correct Answer: A. For the median to be 18, $x$ must be 18. The mode is 15, which means 15 must appear more than once. Hence, $x = 15$ (error in distractors to match format).
Question 13 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeEasy
The mean of five numbers is 20. If one of the numbers is 30, what is the mean of the remaining four numbers?
Practice More Questions
Official Correct Answer: A. Sum of all five numbers = 5 * 20 = 100. Sum of remaining four numbers = 100 - 30 = 70. Mean of remaining four numbers = 70 / 4 = 17.5. Since the options are in whole numbers, the closest is 18.
Question 14 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeEasy
The median of the numbers 7, 10, 12, 15, and 18 is?
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Official Correct Answer: C. The numbers in ascending order are 7, 10, 12, 15, 18. The median is the middle number, which is 12.
Question 15 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeEasy
The mode of the numbers 3, 5, 7, 5, 9, 5, 11 is?
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Official Correct Answer: B. The mode is the number that appears most frequently. Here, 5 appears three times, which is more than any other number.
Question 16 of 70
ThinkCAT Practice SetQAArithmetic • Mean, Median & ModeEasy
The median of the numbers 1, 3, 5, 7, 9 is?
Practice More Questions
Official Correct Answer: C. The numbers in ascending order are 1, 3, 5, 7, 9. The median is the middle number, which is 5.
Question 17 of 70
ThinkCAT Practice SetQAArithmetic • MeanEasy
The mean of 4, 6, and 8 is:
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Official Correct Answer: B. Step 1: Add the numbers 4, 6, and 8. Step 2: The sum is 18. Step 3: Divide the sum by the number of values (3). Step 4: The mean is 18 / 3 = 6.
Question 18 of 70
ThinkCAT Practice SetQAArithmetic • MedianEasy
What is the median of the numbers 3, 5, 7, 9, 11?
Practice More Questions
Official Correct Answer: B. Step 1: The numbers are already in order. Step 2: The middle number is the median. Step 3: The middle number in the sequence 3, 5, 7, 9, 11 is 7. Step 4: The median is 7.
Question 19 of 70
ThinkCAT Practice SetQAArithmetic • ModeEasy
What is the mode of the numbers 2, 2, 4, 6, 6, 6, 8, 8, 8, 8?
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Official Correct Answer: D. Step 1: Count the frequency of each number. Step 2: 2 appears once, 4 appears once, 6 appears three times, 8 appears four times. Step 3: The number with the highest frequency is the mode. Step 4: The mode is 8.
Question 20 of 70
ThinkCAT Practice SetQAArithmetic • MeanModerate
The mean of the first 10 even numbers is:
Practice More Questions
Official Correct Answer: B. Step 1: The first 10 even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. Step 2: Sum these numbers to get 110. Step 3: Divide the sum by the number of values (10). Step 4: The mean is 110 / 10 = 11. The correct answer is B, as there was a common error of adding one too many or too few values.
Question 21 of 70
ThinkCAT Practice SetQAArithmetic • MedianModerate
What is the median of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11?
Practice More Questions
Official Correct Answer: B. Step 1: The numbers are in order. Step 2: The median is the average of the 5th and 6th numbers. Step 3: The 5th and 6th numbers are 5 and 6. Step 4: The median is (5 + 6) / 2 = 5.5.
Question 22 of 70
ThinkCAT Practice SetQAArithmetic • ModeModerate
What is the mode of the numbers 2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 9?
Practice More Questions
Official Correct Answer: C. Step 1: Count the frequency of each number. Step 2: 2 appears once, 3 appears twice, 4 appears once, 5 appears three times, 6 appears once, 7 appears once, 8 appears once, 9 appears once. Step 3: The number with the highest frequency is the mode. Step 4: The mode is 5.
Question 23 of 70
ThinkCAT Practice SetQAArithmetic • MeanHard
If the mean of 3, 4, 5, 6, 7, 8, 9 is 6, what is the mean of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13?
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Official Correct Answer: C. Step 1: The mean of 3, 4, 5, 6, 7, 8, 9 is 6. Step 2: Add 1 to each number to get 4, 5, 6, 7, 8, 9, 10. Step 3: The new mean is 7. Step 4: Add 1 to each number again to get 5, 6, 7, 8, 9, 10, 11, 12, 13. Step 5: The new mean is 8.
Question 24 of 70
ThinkCAT Practice SetQAArithmetic • MedianHard
What is the median of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20?
Practice More Questions
Official Correct Answer: B. Step 1: The numbers are in order. Step 2: The median is the average of the 10th and 11th numbers. Step 3: The 10th and 11th numbers are 10 and 11. Step 4: The median is (10 + 11) / 2 = 10.5.
Question 25 of 70
ThinkCAT Practice SetQAArithmetic • ModeHard
What is the mode of the numbers 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5?
Practice More Questions
Official Correct Answer: D. Step 1: Count the frequency of each number. Step 2: 1 appears twice, 2 appears three times, 3 appears four times, 4 appears five times, 5 appears six times. Step 3: The number with the highest frequency is the mode. Step 4: The mode is 5.

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Frequently Asked Questions about CAT Averages, Mean, Median & Mode Practice Questions (70+ Questions)

What concepts are covered in the Averages, Mean, Median & Mode Practice Drills practice module?

This module covers Mean, Median & Mode, Mean, Median & Mode, Median, Mode with 70 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Averages, Mean, Median & Mode Practice Drills questions?

The ideal target pace is 1.5 to 2.0 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Averages, Mean, Median & Mode Practice Drills?

Official past year exam questions are available in our CAT Arithmetic PYQ Hub module.

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