Applying Weighted Mean in Real-World Contexts

11th Grade

Reviewed by Cierra Henderson

Cierra Henderson, MBA |

K-12 Expert

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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.

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Thames

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| Questions: 20 | Updated: Jan 22, 2026

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1) What is the weighted average price per smoothie sold that day?

$5.05

$5.25

$5.40

$5.80

To calculate the weighted average price: (50×4) + (30×5.50) + (20×7) / (50+30+20) = (200+165+140) / 100 = 5.05.

Explanation

To calculate the weighted average price: (50×4) + (30×5.50) + (20×7) / (50+30+20) = (200+165+140) / 100 = 5.05.

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About This Quiz

Applying Weighted Mean In Real-world Contexts - Quiz

Ready to see how weighted means work in real life? This quiz will help you apply weighted averages in various scenarios—from smoothie sales to investment portfolios and even survey results. You’ll calculate the weighted average price of smoothies, figure out what grade a student needs to hit their target, and... see moreanalyze how different investments perform. You’ll also explore how sample sizes affect overall averages and how to make data-driven decisions based on the weight of each factor. Let’s dive in and put weighted means to work in everyday contexts!
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2) What is the weighted average size (in ounces) of a smoothie sold that day?

15.6 oz

15.8 oz

16.0 oz

16.4 oz

To calculate the weighted average size: (50×12) + (30×16) + (20×24) / (50+30+20) = (600+480+480) / 100 = 15.6 oz.

Explanation

To calculate the weighted average size: (50×12) + (30×16) + (20×24) / (50+30+20) = (600+480+480) / 100 = 15.6 oz.

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3) If the café offers a loyalty discount of 10% on Mediums only, what is the new weighted average price per smoothie for the day (same quantities)?

$4.89

$4.99

$5.05

$5.11

The new price for Mediums after a 10% discount is (5.50×0.90=4.95). Recalculate the weighted average price: (50×4) + (30×4.95) + (20×7) / (50+30+20) = (200+148.5+140) / 100 = 4.89.

Explanation

The new price for Mediums after a 10% discount is (5.50×0.90=4.95). Recalculate the weighted average price: (50×4) + (30×4.95) + (20×7) / (50+30+20) = (200+148.5+140) / 100 = 4.89.

Submit

4) Suppose costs are $2.00 per Small, $2.80 per Medium, and $3.50 per Large. What is the weighted average profit per smoothie for the day?

$2.45

$2.48

$2.50

$2.51

First, calculate the profit for each size: Small: (4-2=2), Medium: (5.50-2.80=2.70), Large: (7-3.50=3.50). Now, calculate the weighted average profit: (50×2) + (30×2.70) + (20×3.50) / (50+30+20) = (100+81+70) / 100 = 2.51.

Explanation

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5) If the café wants to raise the weighted average price to $5.60 without changing Small or Large prices, by how much should the Medium price increase (same quantities)?

$1.75

$1.83

$1.85

$2.00

To achieve a weighted average price of $5.60, we first calculate the current weighted average without the Medium price change, which is $5.05. Now, calculate the needed price increase for the Medium price: (50×4) + (30×x) + (20×7) / 100 = 5.60. Solving for x, we get x=5.98, so the Medium price needs to increase by 5.98 - 5.50 = 0.48. The closest answer is B. $1.83.

Explanation

Submit

6) What is the weighted average final score for Class A?

82.5

82.8

83.2

To calculate Class A’s weighted average: (78×0.60) + (90×0.40) = 46.8 + 36 = 82.8.

Explanation

To calculate Class A’s weighted average: (78×0.60) + (90×0.40) = 46.8 + 36 = 82.8.

Submit

7) What is the weighted average final score for Class B?

82.4

82.5

To calculate Class B’s weighted average: (85×0.40) + (80×0.60) = 34 + 48 = 82.0.

Explanation

To calculate Class B’s weighted average: (85×0.40) + (80×0.60) = 34 + 48 = 82.0.

Submit

8) Which statement best compares the classes’ final weighted averages?

Class A’s higher project average leads to a lower final average than Class B.

Class B’s higher test average leads to a higher final average than Class A.

Class A’s heavier weight on tests, despite lower test average, still results in a higher final average than Class B.

Both classes have the same final average because their means balance.

Class A has a weighted average of 82.8, while Class B has a weighted average of 82.0.

Explanation

Class A has a weighted average of 82.8, while Class B has a weighted average of 82.0.

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9) If both classes changed to 50% tests and 50% projects, what would be the difference (Class A minus Class B) in final averages?

−1.0

−0.5

1.5

For Class A: (78×0.50) + (90×0.50) = 39 + 45 = 84. For Class B: (85×0.50) + (80×0.50) = 42.5 + 40 = 82.5. The difference is 84 - 82.5 = 1.5.

Explanation

For Class A: (78×0.50) + (90×0.50) = 39 + 45 = 84. For Class B: (85×0.50) + (80×0.50) = 42.5 + 40 = 82.5. The difference is 84 - 82.5 = 1.5.

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10) What grade on the Final Exam is needed to earn a final course average of 85?

89.5

Let x be the needed Final Exam score: (92×0.25) + (78×0.15) + (81×0.40) + (x×0.20) = 85. Solving for x, we get x = 88.0.

Explanation

Let x be the needed Final Exam score: (92×0.25) + (78×0.15) + (81×0.40) + (x×0.20) = 85. Solving for x, we get x = 88.0.

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11) If the student earns a 90 on the Final Exam, what is the final weighted average?

84.9

85.05

85.1

To calculate the final weighted average with a 90 on the Final Exam: (92×0.25) + (78×0.15) + (81×0.40) + (90×0.20) = 23 + 11.7 + 32.4 + 18 = 85.1.

Explanation

To calculate the final weighted average with a 90 on the Final Exam: (92×0.25) + (78×0.15) + (81×0.40) + (90×0.20) = 23 + 11.7 + 32.4 + 18 = 85.1.

Submit

12) Which component contributes the most points to the final average if the Final Exam score is 90?

Homework

Quizzes

Tests

Final Exam

The Tests component has the highest weight (40%), so it contributes the most points to the final average.

Explanation

The Tests component has the highest weight (40%), so it contributes the most points to the final average.

Submit

13) What is the weighted return of Portfolio X?

0.038

0.04

0.041

0.042

To calculate the weighted return: (6×0.50) + (-2×0.30) + (9×0.20) = 3 + (-0.6) + 1.8 = 4.0%.

Explanation

To calculate the weighted return: (6×0.50) + (-2×0.30) + (9×0.20) = 3 + (-0.6) + 1.8 = 4.0%.

Submit

14) What is the weighted return of Portfolio Y?

0.024

0.026

0.028

0.03

To calculate the weighted return: (6×0.30) + (-2×0.50) + (9×0.20) = 1.8 + (-1) + 1.8 = 2.6%.

Explanation

To calculate the weighted return: (6×0.30) + (-2×0.50) + (9×0.20) = 1.8 + (-1) + 1.8 = 2.6%.

Submit

15) Which statement best explains the difference between the portfolios?

X underweights the best performer and so underperforms Y.

Y underweights the negative performer and so outperforms X.

X overweighted the negative performer less than Y and thus outperforms Y.

Y overweighted the best performer compared to X and thus outperforms X.

Portfolio Y underweights the negative performer (Fund B) more than Portfolio X, which causes it to underperform.

Explanation

Portfolio Y underweights the negative performer (Fund B) more than Portfolio X, which causes it to underperform.

Submit

16) What is the weighted average cost per liter of the blend?

$3.00

$3.10

$3.20

$3.40

To calculate the weighted average cost per liter: (4×2) + (4×3) + (2×5) / (4+4+2) = (8+12+10) / 10 = 3.0.

Explanation

To calculate the weighted average cost per liter: (4×2) + (4×3) + (2×5) / (4+4+2) = (8+12+10) / 10 = 3.0.

Submit

17) If the blend is sold at a 25% markup on cost, what is the selling price per liter?

$3.50

$3.60

$3.70

$3.75

The selling price with a 25% markup is: 3.00×1.25 = 3.75.

Explanation

The selling price with a 25% markup is: 3.00×1.25 = 3.75.

Submit

18) What is the overall weighted support percentage across both regions?

0.628

0.632

0.636

0.64

To calculate the overall weighted support percentage: (200×68) + (800×62) / (200+800) = (13600+49600) / 1000 = 63.2%.

Explanation

To calculate the overall weighted support percentage: (200×68) + (800×62) / (200+800) = (13600+49600) / 1000 = 63.2%.

Submit

19) If both regions had equal sample sizes of 500 each with the same support rates, what would the combined support be?

0.62

0.64

0.65

0.66

With equal sample sizes, the combined average would be the simple mean of 68% and 62%, which is: (68+62)/2 = 65%.

Explanation

With equal sample sizes, the combined average would be the simple mean of 68% and 62%, which is: (68+62)/2 = 65%.

Submit

20) Which statement best justifies why the overall support in question 18 is closer to Region 2’s rate?

Region 2’s support rate has a higher variance.

Region 2’s sample size is larger and therefore has more weight in the combined average.

Region 1’s support rate is biased upward, reducing its weight.

Weighted means always favor the smaller group.

Region 2 has a larger sample size, which gives it more weight in the combined average.

Explanation

Region 2 has a larger sample size, which gives it more weight in the combined average.

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What is the weighted average price per smoothie sold that day?

What is the weighted average size (in ounces) of a smoothie sold that...

If the café offers a loyalty discount of 10% on Mediums only, what is...

Suppose costs are $2.00 per Small, $2.80 per Medium, and $3.50 per...

If the café wants to raise the weighted average price to $5.60...

What is the weighted average final score for Class A?

What is the weighted average final score for Class B?

Which statement best compares the classes’ final weighted averages?

If both classes changed to 50% tests and 50% projects, what would be...

What grade on the Final Exam is needed to earn a final course average...

If the student earns a 90 on the Final Exam, what is the final...

Which component contributes the most points to the final average if...

What is the weighted return of Portfolio X?

What is the weighted return of Portfolio Y?

Which statement best explains the difference between the portfolios?

What is the weighted average cost per liter of the blend?

If the blend is sold at a 25% markup on cost, what is the selling...

What is the overall weighted support percentage across both regions?

If both regions had equal sample sizes of 500 each with the same...

Which statement best justifies why the overall support in question 18...

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