Understanding Weighted Mean Concepts

9th Grade

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Cierra Henderson, MBA |

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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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| Attempts: 14 | Questions: 20 | Updated: Jan 21, 2026

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1) Which statement best explains the difference between the weighted and simple average in this scenario?

Weighted averages are always lower than simple averages.

The weighted average is lower because the lowest category (tests) has the highest weight.

They are the same because weights always sum to 1.

The weighted average is higher because homework has the highest score and highest weight.

The weighted average is lower because the category with the lowest score (tests, 70) has the highest weight (50%).

Explanation

The weighted average is lower because the category with the lowest score (tests, 70) has the highest weight (50%).

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About This Quiz

Understanding Weighted Mean Concepts - Quiz

Ever wondered why some things count more than others? In this quiz, you'll discover how weighted averages let us give more importance to certain values. From calculating your course grade to combining data from two stores, you’ll learn how to apply weights to get a more accurate overall result. We’ll... see morealso look at how small changes in the weights can shift the average, helping you make smarter decisions based on real-world scenarios. Ready to unlock the magic of weighted means? Let’s get started!
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2) If the test weight increased to 60% (and quizzes decreased to 20%; homework remains 20%), what happens to the weighted average?

It decreases.

It increases.

It stays the same.

It becomes the simple mean.

Increasing the weight of the test (which is 70) will pull the weighted average down, as the test score is the lowest category.

Explanation

Increasing the weight of the test (which is 70) will pull the weighted average down, as the test score is the lowest category.

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3) If the student raises the test average from 70 to 76 while weights remain 20%, 30%, 50%, what is the new weighted average?

With the new test average of 76, the weighted average calculation is: Homework: (95×0.20=19), Quizzes: (80×0.30=24), Tests: (76×0.50=38). The new weighted average is 81.

Explanation

With the new test average of 76, the weighted average calculation is: Homework: (95×0.20=19), Quizzes: (80×0.30=24), Tests: (76×0.50=38). The new weighted average is 81.

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4) What is the combined average price per apple across both stores?

1.07

1.05

1.1

1.15

To calculate the combined average price, use a weighted average: (50×1.20) + (150×1.00) / (50+150) = 1.05.

Explanation

To calculate the combined average price, use a weighted average: (50×1.20) + (150×1.00) / (50+150) = 1.05.

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5) Which scenario requires a weighted mean rather than a simple mean?

Computing a course grade where categories have different weights.

Averaging daily temperatures across a week.

Averaging shoe sizes in a class.

Averaging five test scores with equal importance.

A weighted mean is needed when categories have different weights, such as in a course grade calculation.

Explanation

A weighted mean is needed when categories have different weights, such as in a course grade calculation.

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6) A student has quiz scores 90, 85, 95. The teacher says the most recent quiz counts double. What is the weighted mean?

91.25

93.5

The most recent quiz counts double, so the weights are 1 for the first two quizzes and 2 for the last one. The weighted mean is 91.25.

Explanation

The most recent quiz counts double, so the weights are 1 for the first two quizzes and 2 for the last one. The weighted mean is 91.25.

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7) In a survey, average satisfaction was 4.2 (n=20) for Group X and 3.8 (n=80) for Group Y on a 5-point scale. What is the combined average?

3.88

3.96

3.9

To find the combined average, use a weighted average: (20×4.2)+(80×3.8) / (20+80) = 3.88.

Explanation

To find the combined average, use a weighted average: (20×4.2)+(80×3.8) / (20+80) = 3.88.

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8) Which example misuses a simple mean where a weighted mean is needed?

Averaging heights of students in a class.

Averaging lengths of pencils from one box.

Averaging store prices where stores sell different quantities.

Averaging rainfall measured daily at one location.

When averaging store prices with different quantities sold, a weighted mean is needed because the quantities should be accounted for.

Explanation

When averaging store prices with different quantities sold, a weighted mean is needed because the quantities should be accounted for.

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9) You compute a weighted average with weights that do not sum to 1. What is the best practice?

Normalize the weights so they sum to 1; the result is unchanged in value.

Double the largest weight.

Convert to a median.

It will always be incorrect.

To correctly calculate a weighted average, the weights should sum to 1. If they do not, normalize the weights by dividing each by the total sum of the weights.

Explanation

To correctly calculate a weighted average, the weights should sum to 1. If they do not, normalize the weights by dividing each by the total sum of the weights.

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10) If all categories were weighted equally (simple mean of the three category averages), what would the average be?

83.33

81.67

If the categories were weighted equally, the simple mean of the averages would be: (95+80+70)/3 = 81.67.

Explanation

If the categories were weighted equally, the simple mean of the averages would be: (95+80+70)/3 = 81.67.

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11) If both stores doubled their number of apples at the same average price, what happens to the combined weighted average?

It halves.

It stays the same.

It doubles.

It moves toward the lower average.

Doubling the number of apples at the same average price would not affect the combined weighted average, as the proportions remain the same.

Explanation

Doubling the number of apples at the same average price would not affect the combined weighted average, as the proportions remain the same.

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12) A factory makes two batches of bolts: Batch 1: 1,000 bolts with 2% defects, Batch 2: 500 bolts with 4% defects. What is the overall defect rate?

0.025

0.03

0.0267

0.0333

To find the overall defect rate, use a weighted average: (1000×2%)+(500×4%) / (1000+500) = 2.67%.

Explanation

To find the overall defect rate, use a weighted average: (1000×2%)+(500×4%) / (1000+500) = 2.67%.

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13) Which statement is true about weighted means?

Weighted means ignore outliers.

Weighted means are always larger than simple means.

Weighted means account for differing importance or frequency of values.

Weighted means are the same as medians.

Weighted means account for differing importance or frequency of values by assigning different weights to different data points.

Explanation

Weighted means account for differing importance or frequency of values by assigning different weights to different data points.

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14) A runner averages 6 min/mile for 2 miles and 8 min/mile for 1 mile. What is the overall average pace?

7.00 min/mile

6.67 min/mile

7.33 min/mile

6.50 min/mile

To calculate the weighted average pace, use the total time and total distance: Total time = (6×2)+(8×1)=12+8=20, Total distance = 2+1=3. The average pace is 6.67 minutes per mile.

Explanation

To calculate the weighted average pace, use the total time and total distance: Total time = (6×2)+(8×1)=12+8=20, Total distance = 2+1=3. The average pace is 6.67 minutes per mile.

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15) What is the student’s overall weighted average?

82.5

To calculate the weighted average, multiply each category's average by its weight and sum the results. Homework: (95×0.20=19), Quizzes: (80×0.30=24), Tests: (70×0.50=35). The sum is 78.

Explanation

To calculate the weighted average, multiply each category's average by its weight and sum the results. Homework: (95×0.20=19), Quizzes: (80×0.30=24), Tests: (70×0.50=35). The sum is 78.

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16) Which category change would most increase the weighted average?

Increase quiz average by 5 points.

Increase homework average by 10 points.

Decrease quiz weight by 5% and increase homework weight by 5%.

Increase test average by 5 points.

Increasing the homework average by 10 points (from 95 to 105) would have the largest impact on the weighted average, as homework has a 20% weight.

Explanation

Increasing the homework average by 10 points (from 95 to 105) would have the largest impact on the weighted average, as homework has a 20% weight.

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17) Which method correctly computes the combined average?

Average the two averages: (1.20 + 1.00)/2

Take the higher average because more apples were sold there.

Compute a weighted average using quantities as weights.

Use the median of the two averages.

The correct method to compute the combined average is to use a weighted average, where the quantities of apples sold are used as weights.

Explanation

The correct method to compute the combined average is to use a weighted average, where the quantities of apples sold are used as weights.

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18) If Store B had sold fewer apples, which direction would the combined average move?

It would move toward Store B’s average.

It would not change.

It would become the simple mean of 1.10.

It would move toward Store A’s average.

If Store B sold fewer apples, the combined average would be closer to Store A’s average, as Store A’s price would carry more weight.

Explanation

If Store B sold fewer apples, the combined average would be closer to Store A’s average, as Store A’s price would carry more weight.

Submit

19) A project grade is made of: Proposal 10%, Draft 20%, Presentation 30%, Final Report 40%. Scores are 100, 80, 90, 85 respectively. What is the weighted mean?

87.5

To calculate the weighted mean, multiply each score by its respective weight: (100×0.10)+(80×0.20)+(90×0.30)+(85×0.40) = 87.

Explanation

To calculate the weighted mean, multiply each score by its respective weight: (100×0.10)+(80×0.20)+(90×0.30)+(85×0.40) = 87.

Submit

20) A teacher drops the lowest homework score before averaging. How does this relate to weighting?

It gives the dropped score a negative weight.

It gives all remaining scores a weight of zero.

It doubles the weights of the highest scores automatically.

It gives the dropped score a weight of zero.

When a score is dropped, it effectively has a weight of zero, meaning it is excluded from the final calculation.

Explanation

When a score is dropped, it effectively has a weight of zero, meaning it is excluded from the final calculation.

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Answered ()

Which statement best explains the difference between the weighted and...

If the test weight increased to 60% (and quizzes decreased to 20%;...

If the student raises the test average from 70 to 76 while weights...

What is the combined average price per apple across both stores?

Which scenario requires a weighted mean rather than a simple mean?

A student has quiz scores 90, 85, 95. The teacher says the most recent...

In a survey, average satisfaction was 4.2 (n=20) for Group X and 3.8...

Which example misuses a simple mean where a weighted mean is needed?

You compute a weighted average with weights that do not sum to 1. What...

If all categories were weighted equally (simple mean of the three...

If both stores doubled their number of apples at the same average...

A factory makes two batches of bolts: ...

Which statement is true about weighted means?

A runner averages 6 min/mile for 2 miles and 8 min/mile for 1 mile....

What is the student’s overall weighted average?

Which category change would most increase the weighted average?

Which method correctly computes the combined average?

If Store B had sold fewer apples, which direction would the combined...

A project grade is made of: Proposal 10%, Draft 20%, Presentation 30%,...

A teacher drops the lowest homework score before averaging. How does...

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