Calculating Weighted Mean from Data Sets

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| By Thames

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| Questions: 20 | Updated: Oct 31, 2025

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1) A student's grade is calculated using a weighted mean. Homework is worth 20%, quizzes are worth 30%, and the final exam is worth 50%. If the student scored 85 on homework, 90 on quizzes, and 78 on the final exam, what is the weighted mean grade?

84.3

82.1

To calculate the weighted mean: (85×0.20) + (90×0.30) + (78×0.50) = 17 + 27 + 39 = 83. The correct answer is C. 83.0.

Explanation

To calculate the weighted mean: (85×0.20) + (90×0.30) + (78×0.50) = 17 + 27 + 39 = 83. The correct answer is C. 83.0.

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About This Quiz

Calculating Weighted Mean From Data Sets - Quiz

Get ready to sharpen your skills with weighted means! This quiz will guide you through calculating weighted averages in real-life situations—from grades to customer satisfaction and even pollutant measurements. You’ll apply weights to various categories and learn how to calculate and interpret the results. Whether you're figuring out a student’s... see morefinal grade, evaluating employee performance, or tracking air quality, this quiz will help you understand how weighted means give more importance to certain values. By the end, you’ll be confident in calculating weighted averages in diverse scenarios. Let’s dive in and get calculating! see less

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2) A company evaluates employee performance using three categories: punctuality (weight 0.25), productivity (0.45), and teamwork (0.30). An employee scores 88, 92, and 85 respectively. What is the weighted mean performance score?

88.7

88.9

89.2

87.5

To calculate the weighted mean: (88×0.25) + (92×0.45) + (85×0.30) = 22 + 41.4 + 25.5 = 88.9. The correct answer is B. 88.9.

Explanation

To calculate the weighted mean: (88×0.25) + (92×0.45) + (85×0.30) = 22 + 41.4 + 25.5 = 88.9. The correct answer is B. 88.9.

Submit

3) What is Student A’s weighted mean grade?

88.75

87.05

86.5

To calculate Student A’s weighted mean: (95×0.15) + (88×0.25) + (82×0.40) + (90×0.20) = 14.25 + 22 + 32.8 + 18 = 87.05. The correct answer is B. 87.05.

Explanation

To calculate Student A’s weighted mean: (95×0.15) + (88×0.25) + (82×0.40) + (90×0.20) = 14.25 + 22 + 32.8 + 18 = 87.05. The correct answer is B. 87.05.

Submit

4) What is Student B’s weighted mean grade?

86.25

86.55

85.8

To calculate Student B’s weighted mean: (80×0.15) + (92×0.25) + (85×0.40) + (88×0.20) = 12 + 23 + 34 + 17.6 = 86.6. The closest answer is B. 86.55.

Explanation

To calculate Student B’s weighted mean: (80×0.15) + (92×0.25) + (85×0.40) + (88×0.20) = 12 + 23 + 34 + 17.6 = 86.6. The closest answer is B. 86.55.

Submit

5) Which student has the higher weighted mean grade, and by how much?

Student A by 1.5 points

Student A by 0.6 points

Student B by 0.8 points

Student B by 1.2 points

Student A’s weighted mean is 87.05 and Student B’s weighted mean is 86.55. The difference is 87.05 - 86.55 = 0.5. The correct answer is B. Student A by 0.6 points (rounded).

Explanation

Student A’s weighted mean is 87.05 and Student B’s weighted mean is 86.55. The difference is 87.05 - 86.55 = 0.5. The correct answer is B. Student A by 0.6 points (rounded).

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6) If the teacher changed the weight of the Final Exam from 20% to 30% and reduced Tests from 40% to 30%, what would be Student A’s new weighted mean grade?

87.15

87.85

86.9

89.1

New weighted mean calculation: (95×0.15) + (88×0.25) + (82×0.30) + (90×0.30) = 14.25 + 22 + 24.6 + 27 = 87.15. The correct answer is A. 87.15.

Explanation

New weighted mean calculation: (95×0.15) + (88×0.25) + (82×0.30) + (90×0.30) = 14.25 + 22 + 24.6 + 27 = 87.15. The correct answer is A. 87.15.

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7) A portfolio consists of three investments: Stock A ($5,000 at 8%), Stock B ($3,000 at 12%), and Stock C ($2,000 at 5%). What is the weighted mean return on the portfolio?

0.085

0.086

0.09

0.078

To calculate the weighted mean return: (5000×8/10000) + (3000×12/10000) + (2000×5/10000) = 4 + 3.6 + 1 = 8.6. The correct answer is B. 8.6%.

Explanation

To calculate the weighted mean return: (5000×8/10000) + (3000×12/10000) + (2000×5/10000) = 4 + 3.6 + 1 = 8.6. The correct answer is B. 8.6%.

Submit

8) In a weighted mean calculation, if all weights are equal, what type of mean is being calculated?

Geometric mean

Arithmetic mean

Harmonic mean

Median

When all weights are equal, the calculation is simply the arithmetic mean. The correct answer is B. Arithmetic mean.

Explanation

When all weights are equal, the calculation is simply the arithmetic mean. The correct answer is B. Arithmetic mean.

Submit

9) What is the weighted mean score for Location X?

4.35

4.42

4.5

4.28

To calculate Location X’s weighted mean: (4.2×0.35) + (4.8×0.25) + (4.5×0.30) + (3.9×0.10) = 1.47 + 1.2 + 1.35 + 0.39 = 4.42. The correct answer is B. 4.42.

Explanation

To calculate Location X’s weighted mean: (4.2×0.35) + (4.8×0.25) + (4.5×0.30) + (3.9×0.10) = 1.47 + 1.2 + 1.35 + 0.39 = 4.42. The correct answer is B. 4.42.

Submit

10) What is the weighted mean score for Location Y?

4.51

4.45

4.6

4.38

To calculate Location Y’s weighted mean: (4.5×0.35) + (4.3×0.25) + (4.7×0.30) + (4.0×0.10) = 1.575 + 1.075 + 1.41 + 0.4 = 4.46. The closest answer is B. 4.45.

Explanation

To calculate Location Y’s weighted mean: (4.5×0.35) + (4.3×0.25) + (4.7×0.30) + (4.0×0.10) = 1.575 + 1.075 + 1.41 + 0.4 = 4.46. The closest answer is B. 4.45.

Submit

11) Which location has the better overall weighted mean score?

Location X

Location Y

They are equal

Cannot be determined

Location X has a weighted mean of 4.42, and Location Y has a weighted mean of 4.46. Location Y has the better score. The correct answer is B. Location Y.

Explanation

Location X has a weighted mean of 4.42, and Location Y has a weighted mean of 4.46. Location Y has the better score. The correct answer is B. Location Y.

Submit

12) If Customer Satisfaction weight increased to 0.40 and Food Quality decreased to 0.25 (with other weights unchanged), what would be Location Y’s new weighted mean score?

4.489

4.685

4.754

4.855

New weighted mean for Location Y: (4.5×0.40) + (4.3×0.25) + (4.7×0.30) + (4.0×0.10) = 1.8 + 1.075 + 1.41 + 0.4 = 4.685. The correct answer is B. 4.685.

Explanation

New weighted mean for Location Y: (4.5×0.40) + (4.3×0.25) + (4.7×0.30) + (4.0×0.10) = 1.8 + 1.075 + 1.41 + 0.4 = 4.685. The correct answer is B. 4.685.

Submit

13) A college course has the following grade distribution: 5 students scored 90, 8 scored 85, 12 scored 78, and 5 scored 70. What is the weighted mean score for the class?

80.5

82.3

79.7

To calculate the weighted mean: (5×90) + (8×85) + (12×78) + (5×70) / (5+8+12+5) = (450 + 680 + 936 + 350) / 30 = 2416 / 30 = 80.53. The closest answer is A. 80.5.

Explanation

To calculate the weighted mean: (5×90) + (8×85) + (12×78) + (5×70) / (5+8+12+5) = (450 + 680 + 936 + 350) / 30 = 2416 / 30 = 80.53. The closest answer is A. 80.5.

Submit

14) A quality control inspector samples products from three production lines: Line 1 (500 units, 2% defects), Line 2 (300 units, 5%), Line 3 (200 units, 3%). What is the weighted mean defect rate?

0.0333

0.031

0.028

0.035

To calculate the weighted mean defect rate: (500×2) + (300×5) + (200×3) / (500+300+200) = (1000 + 1500 + 600) / 1000 = 3100 / 1000 = 3.1%. The correct answer is B. 3.1%.

Explanation

To calculate the weighted mean defect rate: (500×2) + (300×5) + (200×3) / (500+300+200) = (1000 + 1500 + 600) / 1000 = 3100 / 1000 = 3.1%. The correct answer is B. 3.1%.

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15) In calculating a weighted mean, what must be true about the sum of all weights?

It must equal 100

It must equal 1.0 (or 100%)

It must be greater than the number of data values

It can be any positive number

In a weighted mean calculation, the sum of the weights must equal 1.0 (or 100%). The correct answer is B. It must equal 1.0 (or 100%).

Explanation

In a weighted mean calculation, the sum of the weights must equal 1.0 (or 100%). The correct answer is B. It must equal 1.0 (or 100%).

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16) What is the weighted mean AQI for Monday?

58.5

58.65

60.2

57.8

To calculate the AQI for Monday: (65×0.40) + (58×0.35) + (48×0.15) + (52×0.10) = 26 + 20.3 + 7.2 + 5.2 = 58.65. The correct answer is B. 58.65.

Explanation

To calculate the AQI for Monday: (65×0.40) + (58×0.35) + (48×0.15) + (52×0.10) = 26 + 20.3 + 7.2 + 5.2 = 58.65. The correct answer is B. 58.65.

Submit

17) What is the weighted mean AQI for Tuesday?

60.15

60.35

61.8

63.05

To calculate the AQI for Tuesday: (72×0.40) + (55×0.35) + (50×0.15) + (48×0.10) = 28.8 + 19.25 + 7.5 + 4.8 = 60.35. The correct answer is B. 60.35.

Explanation

To calculate the AQI for Tuesday: (72×0.40) + (55×0.35) + (50×0.15) + (48×0.10) = 28.8 + 19.25 + 7.5 + 4.8 = 60.35. The correct answer is B. 60.35.

Submit

18) On which day was the air quality better (lower AQI is better)?

Monday

Tuesday

Both days were equal

Cannot be determined

Monday’s weighted mean AQI is 58.65, and Tuesday’s is 60.35. The lower AQI indicates better air quality, so Monday has the better air quality. The correct answer is A. Monday.

Explanation

Monday’s weighted mean AQI is 58.65, and Tuesday’s is 60.35. The lower AQI indicates better air quality, so Monday has the better air quality. The correct answer is A. Monday.

Submit

19) A student takes 4 courses with different credit hours: A (3 credits, 85), B (4 credits, 90), C (3 credits, 78), D (2 credits, 92). What is the student’s weighted mean grade?

86.25

86.08

85.5

To calculate the weighted mean: (3×85) + (4×90) + (3×78) + (2×92) / (3+4+3+2) = (255 + 360 + 234 + 184) / 12 = 1033 / 12 = 86.08. The correct answer is B. 86.08.

Explanation

To calculate the weighted mean: (3×85) + (4×90) + (3×78) + (2×92) / (3+4+3+2) = (255 + 360 + 234 + 184) / 12 = 1033 / 12 = 86.08. The correct answer is B. 86.08.

Submit

20) A survey asks respondents to rate a product (1–5 scale). Results: 10 people rated 5, 15 rated 4, 8 rated 3, 4 rated 2, 3 rated 1. What is the weighted mean rating?

3.75

3.85

3.95

3.63

To calculate the weighted mean: (10×5) + (15×4) + (8×3) + (4×2) + (3×1) / (10+15+8+4+3) = (50 + 60 + 24 + 8 + 3) / 40 = 145 / 40 = 3.625. The closest answer is D. 3.63.

Explanation

To calculate the weighted mean: (10×5) + (15×4) + (8×3) + (4×2) + (3×1) / (10+15+8+4+3) = (50 + 60 + 24 + 8 + 3) / 40 = 145 / 40 = 3.625. The closest answer is D. 3.63.

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