Applying Weighted Mean in Real-World Contexts

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| Questions: 20 | Updated: Oct 31, 2025
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1) What is the weighted average price per smoothie sold that day?

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! see less

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2) What is the weighted average size (in ounces) of a smoothie sold that day?

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)?

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.

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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?

Explanation

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.

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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)?

Explanation

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.

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

Explanation

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

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

Explanation

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

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

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?

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?

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?

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.

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

Explanation

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

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13) What is the weighted return of Portfolio X?

Explanation

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

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14) What is the weighted return of Portfolio Y?

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

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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