Average, Mean, Median & Mode MCQs With Answers
Basic statistics is now a regular part of general ability tests. This page of average, mean, median and mode MCQs covers simple averages, averages of consecutive and natural numbers, replacing or removing a value, a teacher's age added to a class, batsman averages, median and mode of a data set, range, variance, standard deviation, mean deviation, and geometric and harmonic means. It is useful for PPSC, FPSC, NTS, statistics-based interviews and school and college exams.
Take a scored quiz instead →The average of 5, 10, and 15 is:
• Average = (Sum of values) / (Number of values).
• (5 + 10 + 15) / 3 = 30 / 3 = 10.
What is the median of 1, 2, 3, 4, 5?
• The median is the middle value in a sorted list. 3 is the middle.
Average of 10, 20, and 30 is:
(10+20+30)/3 = 20.
The mode of 1, 2, 2, 3, 4 is:
2 appears twice.
The average of 5, 10, 15, 20, 25 is:
(5+10+15+20+25)/5 = 75/5 = 15.
The mode of 2, 3, 3, 4, 5 is:
3 appears most.
What is the average of the first 10 even natural numbers?
The numbers are 2, 4, …, 20, and their sum is 2 × (1 + 2 + … + 10) = 2 × 55 = 110.
Average = 110 ÷ 10 = 11. (The average of the first n even numbers is n + 1.)
Find the median of 7, 3, 9, 1, 5.
Sorted: 1, 3, 5, 7, 9. Median is 5.
Average of 2, 4, 6, 8, 10 is:
30/5 = 6.
The mode of 5, 5, 2, 3, 4 is:
Most frequent is 5.
Average of first 5 prime numbers is:
(2+3+5+7+11)/5 = 28/5 = 5.6.
Average of 4, 8, 12 is:
24/3 = 8.
Average of first 5 odd numbers is:
(1+3+5+7+9)/5 = 25/5 = 5.
The median of 10, 5, 20, 15, 25 is:
Sorted: 5, 10, 15, 20, 25.
Average of 5, 10, 15, 20 is:
50/4 = 12.5.
The average of 4, 6, 8 is:
18/3 = 6.
Average of 10 and 40 is:
50/2 = 25.
The average of five numbers is 18. If one number is removed, the average of the rest becomes 16. What is the removed number?
Sum of the five numbers = 5 × 18 = 90; sum of the remaining four = 4 × 16 = 64.
Removed number = 90 − 64 = 26.
The average of 5 consecutive integers is 12. What is the smallest?
Middle=12. Integers 10, 11, 12, 13, 14. Smallest is 10.
The median of 10, 20, 30, 40, 50 is:
Middle value is 30.
The average of first 5 even numbers is:
(2+4+6+8+10)/5 = 30/5 = 6.
The median of 5, 2, 8, 1, 9 is:
Sorted: 1, 2, 5, 8, 9.
The average of 20, 30, 40 is:
90/3 = 30.
The average weight of 8 students is 45 kg. When a new student joins, the average rises by 1 kg. What is the new student’s weight?
Total weight of 8 students = 8 × 45 = 360 kg; total for 9 students = 9 × 46 = 414 kg.
New student's weight = 414 − 360 = 54 kg.
The average of 5 consecutive odd numbers is 21. What is the smallest number?
Middle is 21. Sequence 17, 19, 21, 23, 25. Smallest is 17.
The range of the data set 12, 15, 8, 10, 20 is:
20 - 8 = 12.
The average age of 8 men is increased by 2 years when one man of 20 years is replaced by a new man. Find the age of the new man.
Increase = 8*2 = 16. New = 20 + 16 = 36.
Mean of first 5 multiples of 3?
3, 6, 9, 12, 15. Sum=45. Mean=9.
The range of data: 1, 9, 4, 7, 5.
9-1=8.
A batsman scores 45, 62, 38 and 75 in four innings. How many runs must he score in the fifth innings to make his average 56?
Required total for 5 innings = 5 × 56 = 280; total so far = 45 + 62 + 38 + 75 = 220.
Runs needed = 280 − 220 = 60.
The average of 10 numbers is 20. If each number is increased by 5, what is the new average?
Adding a constant to each number adds it to the average. 20+5=25.
The average of 5 numbers is 18. If one number is removed, the average becomes 16. What is the removed number?
Total = 5 * 18 = 90. New total = 4 * 16 = 64. Removed number = 90 - 64 = 26.
Mean of first 10 natural numbers?
11/2 = 5.5.
Median of: 5, 2, 9, 1, 7.
Sorted: 1, 2, 5, 7, 9. Median=5.
Mode of: 2, 2, 4, 5, 2?
2 appears 3 times.
Range of: 10, 5, 20, 15?
20-5=15.
Mode of 3, 3, 4, 5?
3.
The average of 5 consecutive odd numbers is 13. Find the largest number.
Average of consecutive odd numbers is the middle one. Middle = 13. Sequence: 9, 11, 13, 15, 17. Largest is 17.
The mean of 5 observations is 10. If the sum of the first 4 is 30, what is the 5th?
Total = 5*10 = 50. 5th = 50 - 30 = 20.
Find the median of: 10, 2, 8, 4, 6.
Sorted: 2, 4, 6, 8, 10. Median is 6.
What is the mode of 1, 2, 2, 3, 3, 3, 4?
3 appears 3 times.
Find the range of: 15, 20, 25, 30, 35.
35 - 15 = 20.
Mode of: 5, 5, 6, 7, 5?
5 repeats 3 times.
Average of first 50 natural numbers?
n+1 / 2 = 51 / 2 = 25.5.
Average of 10, 20, 30, 40, 50?
Sum=150, Mean=30.
Range of 3, 7, 2, 9?
9-2=7.
Mode of 2, 2, 3, 4?
2 appears twice.
The average of the first 5 multiples of 4 is:
Multiples: 4, 8, 12, 16, 20. Average = (4+8+12+16+20) / 5 = 60 / 5 = 12.
The mean of 5 numbers is 20. If one number 20 is excluded, what is the new mean of the remaining 4?
Total = 5 * 20 = 100. New total = 100 - 20 = 80. New mean = 80 / 4 = 20.
The average of 5 consecutive odd numbers is 15. What is the middle number?
In consecutive series, average is the middle number.
Mode of 1, 1, 1, 2, 3?
1 repeats 3 times.
The average age of 5 members in a family is 25 years. If the youngest member is 5 years old, what was the average age of the family at the time of their birth?
Sum now = 125. 5 years ago, sum = 125 - (5 * 5) = 100. Average at that time (of 4 members) = 100 / 4 = 25.
The mean of 5 observations is 10. If each observation is increased by 2, what is the new mean?
New mean = Old mean + 2 = 12.
The average age of 10 students is 15. If the teacher is included, the average becomes 16. Find the teacher’s age.
Sum(students)=150. Sum(with teacher)=11*16=176. Teacher=26.
Find the median of the data: 10, 7, 5, 12, 15.
Sorted: 5, 7, 10, 12, 15. Median = 10.
Find range: 2, 8, 4, 10, 6.
10 - 2 = 8.
Mode of 3, 3, 4, 5, 3?
3 appears 3 times.
The average of 5 consecutive even numbers is 20. Find the largest number.
Let numbers be x, x+2, x+4, x+6, x+8. Average = x+4 = 20 => x = 16. Largest = 16+8 = 24.
The mean of 10 numbers is 15. If each number is multiplied by 2, what is the new mean?
- Multiplying every value by 2 multiplies the mean by 2, so the new mean is 15 × 2 = 30.
- The reason is that the total rises from 150 to 300 while the count stays at 10, and 300 ÷ 10 = 30.
- Adding 2 to every number instead would shift the mean only to 17.
- The count of 10 numbers does not affect the answer, because it appears on both sides of the division.
- The standard deviation would also double, while the variance would become four times as large.
Average age of 3 men is 25. If their ages are in ratio 3:5:7, find the age of the youngest.
Total age = 75. Ratio = 3x+5x+7x = 15x. 15x = 75 => x=5. Youngest = 3*5 = 15.
Range of 10, 2, 15, 8?
- Range is the largest value minus the smallest value: 15 − 2 = 13.
- Sorting the data as 2, 8, 10, 15 makes both extremes easy to spot.
- Only the two extreme values matter, so the middle numbers 8 and 10 do not change the range.
- Option D 15 is just the highest number, not the difference between the highest and lowest.
- Because it depends on the extremes alone, the range is easily distorted by one unusually large or small reading.
The average age of 24 students and their teacher is 15 years. If the teacher’s age is excluded, the average age decreases by 1 year. What is the teacher’s age?
Total age of 25 people = 25 * 15 = 375 years. Total age of 24 students = 24 * 14 = 336 years. Teacher's age = 375 - 336 = 39 years.
Find the mean of the first 10 prime numbers.
First 10 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Sum = 129. Mean = 129 / 10 = 12.9.
The average age of a family of 5 members is 20 years. The age of the youngest member is 4 years. What was the average age of the family at the birth of the youngest member?
Sum of the ages now = 5 × 20 = 100 years. Excluding the youngest (4 years), the other four members total 96 years.
Four years ago, when the youngest was born, those four totalled 96 − 4 × 4 = 80 years and the family had 4 members, so the average age was 80 ÷ 4 = 20 years.
Find the range of the following set of data: 12, 25, 7, 34, 19, 42, 15.
Range = Maximum value - Minimum value = 42 - 7 = 35.
Find the geometric mean of 3, 9, and 27.
Geometric Mean GM = (3 * 9 * 27)^(1/3) = (729)^(1/3) = 9.
Find the mode of the given distribution: 12, 15, 12, 18, 14, 12, 15, 19, 12.
The number 12 appears most frequently (4 times). Mode = 12.
The average score of 40 students is 65. If the highest and lowest scores (which differ by 50) are excluded, the average of the remaining 38 students is 64. What is the highest score?
Sum of 40 students = 40 * 65 = 2600. Sum of 38 students = 38 * 64 = 2432. Sum of highest (H) and lowest (L) = 2600 - 2432 = 168. Given H - L = 50. Adding both equations gives 2H = 218 => H = 109.
The median of observations 11, 12, 14, 18, x+2, x+4, 30, 32, 35, 41 arranged in ascending order is 24. Find x.
Number of terms n = 10. Median is average of 5th and 6th terms: [(x+2) + (x+4)] / 2 = 24 => (2x + 6) / 2 = 24 => x + 3 = 24 => x = 21.
Find the mean deviation about mean for numbers: 3, 6, 9, 12, 15.
Mean = 45 / 5 = 9. Absolute deviations: |3-9|=6, |6-9|=3, |9-9|=0, |12-9|=3, |15-9|=6. Sum = 18. Mean deviation = 18 / 5 = 3.6.
Find the harmonic mean of 4 and 6.
Harmonic Mean HM = 2ab / (a + b) = 2(4)(6) / (4 + 6) = 48 / 10 = 4.8.
Find the mode of the following data: 4, 7, 5, 4, 8, 4, 9, 7, 5, 4.
The number 4 appears most frequently (4 times). Mode = 4.
The average score of 50 students in a class test was 70. Later it was found that a score of 45 was misread as 95. What is the correct mean?
Incorrect total = 50 * 70 = 3500. Difference = 45 - 95 = -50. Correct total = 3500 - 50 = 3450. Correct mean = 3450 / 50 = 69.
If the mean of x, x+3, x+6, x+9, and x+12 is 15, what is the value of x?
Mean of AP is middle term (x+6). x + 6 = 15 => x = 9.
Find the population standard deviation of the numbers: 2, 4, 6, 8, 10.
Mean = 30 ÷ 5 = 6. Squared deviations: 16, 4, 0, 4, 16, total 40. Population variance = 40 ÷ 5 = 8, so the standard deviation = √8 ≈ 2.83.
Dividing by n − 1 = 4 instead gives the sample standard deviation, √10 ≈ 3.16.
Find the geometric mean of 2, 4, 8, and 16.
- The geometric mean of n numbers is the nth root of their product, so here it is (2 × 4 × 8 × 16)^(1/4).
- The product is 1024, and 1024 = 2¹⁰, so the fourth root is 2^(10/4) = 2^2.5 = 4√2.
- As a decimal 4√2 is about 5.66, which correctly lies between the smallest term 2 and the largest term 16.
- Using the arithmetic mean by mistake gives (2 + 4 + 8 + 16) ÷ 4 = 7.5, which is not even listed as an option.
- These four numbers form a geometric progression, so the geometric mean also equals √(first × last) = √(2 × 16) = √32 = 4√2.
The median of 10 observations arranged in ascending order is 24. If two middle terms are (2x + 1) and (2x + 3), find x.
For 10 terms, median is average of 5th and 6th terms: [(2x + 1) + (2x + 3)] / 2 = 24 => (4x + 4) / 2 = 24 => 2x + 2 = 24 => 2x = 22 => x = 11.
The average age of 30 students in a class is 15 years. If the teacher’s age is included, the average increases by 1 year. What is the teacher’s age?
Total age of 30 students = 30 * 15 = 450. Total age of 31 people = 31 * 16 = 496. Teacher's age = 496 - 450 = 46 years.
Find the population variance of the first 5 natural numbers (1, 2, 3, 4, 5).
Mean = (1 + 2 + 3 + 4 + 5) ÷ 5 = 3. Squared deviations: 4, 1, 0, 1, 4, total 10. Population variance = 10 ÷ 5 = 2.
Dividing by n − 1 = 4 instead gives the sample variance, 2.5.
Find the median of the data set: 12, 7, 19, 25, 15, 8, 21.
Arrange in ascending order: 7, 8, 12, 15, 19, 21, 25. Number of items n = 7 (odd). Median is the 4th term = 15.
Find the geometric mean of 4 and 16.
- For two numbers the geometric mean is √(a × b), so it is √(4 × 16) = √64 = 8.
- The geometric mean multiplies the numbers, while the arithmetic mean of 4 and 16 would be (4 + 16) ÷ 2 = 10.
- Option C 10 is that arithmetic mean, and it is the most common slip in this question.
- Useful check: 4, 8 and 16 form a geometric progression with common ratio 2, so 8 sits correctly in the middle.
- The geometric mean is never greater than the arithmetic mean, so an answer below 10 is expected here.
The average of 5 consecutive odd numbers is 27. What is the highest number?
In consecutive AP, average is the middle (3rd) term = 27. The 5 numbers are 23, 25, 27, 29, 31. Highest number is 31.
The average score of 8 numbers is 18. If one number is excluded, the average becomes 16. What is the excluded number?
Sum of 8 numbers = 8 * 18 = 144. Sum of remaining 7 numbers = 7 * 16 = 112. Excluded number = 144 - 112 = 32.
Find the standard deviation of the numbers: 3, 5, 7, 9, 11.
Mean = 7. Squared deviations: 16, 4, 0, 4, 16. Variance = 40 / 5 = 8. Standard Deviation = Sqrt(8) ≈ 2.83.
The mean of 5 observations is 12. If a new observation of value 18 is added, what is the new mean?
Sum of 5 observations = 5 * 12 = 60. New sum = 60 + 18 = 78. New mean = 78 / 6 = 13.
What is the mean proportional between 9 and 25?
Mean proportional = Sqrt(a * b) = Sqrt(9 * 25) = Sqrt(225) = 15.
Find the mode of the following data: 5, 8, 12, 8, 15, 8, 12, 10.
The value 8 appears 3 times, which is the highest frequency in the dataset.
Find the population variance of the numbers: 2, 4, 6, 8, 10.
Mean = 6. Deviations: −4, −2, 0, 2, 4; squared: 16, 4, 0, 4, 16, total 40. Population variance = 40 ÷ 5 = 8.
Dividing by n − 1 = 4 instead gives the sample variance, 10.
The mean of 100 observations was calculated as 40. It was later found that an observation 53 was misread as 83. Find the correct mean.
Total error = 83 - 53 = 30 (excess). Correct sum = (100 * 40) - 30 = 4000 - 30 = 3970. Correct mean = 3970 / 100 = 39.7.
Find the range of the dataset: 12, 25, 8, 42, 31, 17.
Range = Maximum value - Minimum value = 42 - 8 = 34.
Find the average of the first 15 natural numbers.
Average of first n natural numbers = (n + 1) / 2 = (15 + 1) / 2 = 16 / 2 = 8.0.
What is the mode of the dataset: 3, 7, 3, 5, 9, 3, 8, 7, 5?
The mode is the value that appears most frequently. 3 appears 3 times, which is the highest frequency.
What is the geometric mean of 3 and 27?
Geometric Mean = Sqrt(3 * 27) = Sqrt(81) = 9.
Find the mean deviation of the numbers: 2, 4, 6, 8, 10 about their mean.
Mean = (2+4+6+8+10)/5 = 30/5 = 6. Absolute deviations: |2-6|=4, |4-6|=2, |6-6|=0, |8-6|=2, |10-6|=4. Sum = 12. Mean deviation = 12 / 5 = 2.4.
What is the median of the first 6 prime numbers?
First 6 prime numbers: 2, 3, 5, 7, 11, 13. Since n = 6 (even), median = average of 3rd and 4th terms = (5 + 7) / 2 = 6.0.
Find the median of: 4, 8, 1, 9, 3, 7, 6.
Arranging in order: 1, 3, 4, 6, 7, 8, 9. The middle value (4th term) is 6.
What is the average of the prime numbers between 10 and 20?
Prime numbers between 10 and 20 are 11, 13, 17, and 19. Sum = 11 + 13 + 17 + 19 = 60. Average = 60 / 4 = 15.
Find the median of the data set: 12, 7, 15, 9, 21, 18, 11.
Arrange data in ascending order: 7, 9, 11, 12, 15, 18, 21. Total elements n = 7. Median is the 4th element, which is 12.
A batsman scores 80 runs in his 10th innings and increases his average by 4 runs. What is his new average?
Let previous average be A. Total after 10 innings = 9A + 80 = 10(A + 4) => 9A + 80 = 10A + 40 => A = 40. New average = 40 + 4 = 44.
If standard deviation of a dataset is 4, what is its variance?
Variance is the square of the standard deviation. Variance = 4^2 = 16.
The average age of 3 boys is 15 years. If their ages are in ratio 3:5:7, what is the age of the youngest boy?
Sum of ages = 3 * 15 = 45 years. Let ages be 3x, 5x, 7x => 15x = 45 => x = 3. Youngest boy = 3x = 3 * 3 = 9 years.
The average of 8 numbers is 20. If each number is multiplied by 2, what is the new average?
When every observation in a dataset is multiplied by a constant k, the mean is also multiplied by k. New average = 20 * 2 = 40.
The mean of 5 observations is 12. If one observation 20 is deleted, what is the new mean?
Sum of 5 observations = 5 * 12 = 60. New sum after removing 20 = 60 - 20 = 40. New mean = 40 / 4 = 10.
The average of five consecutive odd numbers is 27. What is the largest of these numbers?
In consecutive odd numbers, the average represents the middle (3rd) term. Thus, the 3rd number is 27. The 4th number is 29 and the 5th (largest) is 31.
Find the median of the following set of numbers: 14, 21, 7, 9, 28, 18, 30.
Arrange in ascending order: 7, 9, 14, 18, 21, 28, 30. Total terms = 7. Median is the 4th term, which is 18.
The average score of 4 tests is 85. What score is needed on the 5th test to raise the average to 87?
Total score for 4 tests = 4 * 85 = 340. Required total for 5 tests = 5 * 87 = 435. Score needed = 435 - 340 = 95.
The average age of a group of 5 friends is 22 years. If a new friend joins them, the average age becomes 24 years. What is the age of the new friend?
Total age of 5 friends = 5 × 22 = 110 years. Total age of 6 friends = 6 × 24 = 144 years. Age of the new friend = 144 − 110 = 34 years.
The mean of five numbers is 20. If one number is excluded, the mean becomes 18. What is the excluded number?
Sum of 5 numbers = 5 * 20 = 100. Sum of remaining 4 numbers = 4 * 18 = 72. Excluded number = 100 - 72 = 28.
What is the standard deviation if the variance of a dataset is 49?
Standard Deviation = sqrt(Variance) = sqrt(49) = 7.
A student scored 35, 45, 55, 65, and 75 marks in five subjects. What is the mean score?
Arithmetic Mean = Sum of all values / Total number of values = (35 + 45 + 55 + 65 + 75) / 5 = 275 / 5 = 55.
Find the median of the following set of numbers: 12, 7, 3, 18, 25, 10, 14.
Sort in ascending order: 3, 7, 10, 12, 14, 18, 25. The middle (4th) number is 12.
Find the mode of the dataset: 4, 2, 7, 4, 8, 4, 9, 2, 1.
Mode is the most frequent value. Frequency of 4 is 3 (highest), so mode = 4.
What is the range of the following data points: 15, 22, 8, 31, 40, 19?
Range = Maximum - Minimum = 40 - 8 = 32.