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Free Averages MCQs with Answers

90 Averages MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.

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90 questions · page 1 of 5

1. The average of five numbers is 18. What is their sum?

  • A. 72
  • B. 80
  • C. 90
  • D. 95

Explanation: Average = sum ÷ count, so sum = average × count = 18 × 5 = 90. Rearranging this single relation solves nearly every averages question in…

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Correct answer: 90

2. What is the Arithmetic Mean of the following data 3,6,9,12,15.

  • A. 7
  • B. 9
  • C. 12
  • D. 8

Explanation: The arithmetic mean is found by adding the values and dividing by their count: (3 + 6 + 9 + 12 + 15) / 5 = 45 / 5 = 9.

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Correct answer: 9

3. Calculate the Average of 1,2,3,4,5.

  • A. 1
  • B. 2
  • C. 3
  • D. 4

Explanation: The average equals the total divided by the number of observations. Here, (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.

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Correct answer: 3

4. In two successive years, 100 and 75 students of a school appeared at the final examination. Respectively 75 % and 60 % of them passed. The average rate of pass is:_________?

  • A. 68 4/7 %
  • B. 78 %
  • C. 80 %
  • D. 80 4/7 %

Explanation: The first year had 100 students × 75% = 75 passes, and the second had 75 students × 60% = 45 passes.

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Correct answer: 68 4/7 %

5. The temperature at noon in LHR ,Pakistan was 6 deg on Monday ,4deg on Tuesday,2deg below zero on Wednesday,3deg below zero on Thursday, 0 deg on Friday ,3 deg on Saturday ,and 6 deg on Sunday. What was the average temperature at noon for the week ?

  • A. 14 deg
  • B. -2 deg
  • C. 2 deg
  • D. 7 deg

Explanation: The weekly temperatures are 6, 4, -2, -3, 0, 3 and 6 degrees, whose sum is 14 degrees.

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Correct answer: 2 deg

6. A man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man?

  • A. 47.5
  • B. 50
  • C. 45
  • D. 40

Explanation: For equal distances, average speed is total distance divided by total time, not the ordinary average of the speeds.

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Correct answer: 40

7. A man rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. What is his average speed for the entire trip approximately?

  • A. 11.2 kmph
  • B. 10 kmph
  • C. 10.2 kmph
  • D. 10.8 kmph

Explanation: Total distance is 10 km + 12 km = 22 km, while total time is 10/12 h + 12/10 h = 61/30 h.

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Correct answer: 10.8 kmph

8. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is__________?

  • A. 53.33
  • B. 54.68
  • C. 55
  • D. None of these

Explanation: Use total marks divided by total students: (55 x 50 + 60 x 55 + 45 x 60) marks = 8750 marks, and total students = 55 + 60 + 45 = 160.

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Correct answer: 54.68

9. The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.

  • A. 47.55 kg
  • B. 48 kg
  • C. 48.55 kg
  • D. 49.25 kg

Explanation: The total weight of the 16 boys is 16 x 50.25 kg = 804 kg, and that of the 8 remaining boys is 8 x 45.15 kg = 361.2 kg.

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Correct answer: 48.55 kg

10. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is___________?

  • A. 17 kg
  • B. 20 kg
  • C. 26 kg
  • D. 31 kg

Explanation: The combined weight of A, B and C is 3 x 45 kg = 135 kg, while A + B = 2 x 40 kg = 80 kg and B + C = 2 x 43 kg = 86 kg.

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Correct answer: 31 kg

11. The average of 18 observations was calculated and it was 124. Later on it was discovered that two observations 46 and 82 were incorrect. The correct values are 64 and 28. The correct average of 18 observations is___________?

  • A. 123
  • B. 137
  • C. 121
  • D. 122

Explanation: The originally recorded total is 18 x 124 = 2232. Replacing 46 and 82 by 64 and 28 changes the total by (64 + 28) - (46 + 82) = -36, so…

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Correct answer: 122

12. The mean marks of 30 students in a class is 58.5. Later on it was found that 75 was wrongly recorded as 57. Find the correct them.

  • A. 57.4
  • B. 57.5
  • C. 58.9
  • D. 59.1Everyday Science Quiz

Explanation: The recorded total is 30 students x 58.5 marks = 1755 marks. Correcting 57 marks to 75 marks adds 18 marks, so the new average is (1755 +…

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Correct answer: 59.1Everyday Science Quiz

13. The average of women and child workers in a factory was 15%yr. The average age of all the 16 children was 8yr and average age of women workers was 22 yrs if ten women workers were married then the number of unmarried women workers were________?

  • A. 16
  • B. 12
  • C. 8
  • D. 6

Explanation: Interpreting the damaged text as a combined average age of 15 years, let the number of women be w.

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Correct answer: 6

14. The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is___________?

  • A. 1:2
  • B. 2:3
  • C. 3:4
  • D. 3:5

Explanation: The overall average of 15.8 years is 0.4 years above the girls' average of 15.4 years, while the difference between boys and girls is 1…

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Correct answer: 2:3

15. In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?

  • A. 8
  • B. 9
  • C. 10
  • D. 11

Explanation: The two corrections add 20 marks + 2 marks = 22 marks to the total. Since the average rises from 63 marks to 65 marks, the increase is 2…

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Correct answer: 11

16. The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is__________________?

  • A. 20
  • B. 21
  • C. 22
  • D. 23

Explanation: Let the total number of workers be n. The total salary is Rs. 8000n, while the two groups give Rs. 12000 x 7 + Rs. 6000 x (n - 7) = Rs.

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Correct answer: 21

17. The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is___________?

  • A. 45
  • B. 50
  • C. 51.4 approx.
  • D. 54.6 approx.

Explanation: Use a weighted average: the top 20% contribute 0.20 x 80 = 16 points and the bottom 25% contribute 0.25 x 31 = 7.75 points to the overall…

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Correct answer: 51.4 approx.

18. The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is___________?

  • A. 35 years
  • B. 30 years
  • C. 40 years
  • D. None of these

Explanation: Three years ago, the combined age of the three people was 3 x 27 = 81 years, so their present combined age is 81 + 3 x 3 = 90 years.

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Correct answer: 40 years

19. A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 6 runs. His new average is_____________?

  • A. 48 runs
  • B. 52 runs
  • C. 55 runs
  • D. 60 runs

Explanation: Let the original average be x runs, so the total for 10 innings was 10x runs.

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Correct answer: 48 runs

20. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average of the team?

  • A. 23 years
  • B. 24 years
  • C. 25 years
  • D. None of these

Explanation: Let the team's average age be x years, so the total age is 11x years. The captain and wicketkeeper together are 26 + 29 = 55 years, and…

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Correct answer: 23 years
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