Practice Weighted Average in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A weighted average is an average in which different values contribute unequally based on their assigned weights, reflecting the relative importance or frequency of each value. Unlike a simple average where all values count equally, a weighted average gives more influence to values with larger weights.

Your final grade: exams count 60%, homework 40% — not every assignment counts equally.

Showing a random 20 of 50 problems.

Example 1

easy
A grade is 80 (weight 2) and 90 (weight 1). Compute the weighted sum ∑wixi.

Example 2

hard
A weighted average of two values a and b with weights wa and wb equals a exactly. What does that tell you about wb?

Example 3

challenge
Show that if all weights are doubled, the weighted average is unchanged. Give the key reason.

Example 4

medium
Why can't you just average 50% and 90% to get the overall pass rate of two groups of different sizes?

Example 5

easy
Compute the weighted average of 20 (weight 0.5) and 40 (weight 0.5).

Example 6

medium
A test grade is 70 (counts 25%), midterm 80 (counts 35%), final 90 (counts 40%). Find the weighted average.

Example 7

medium
In a course, homework counts 20%, midterm 30%, final 50%. A student scored 90,75,82. Compute the final grade.

Example 8

hard
A student needs a course average of 85. So far: homework 20% at 90, midterm 30% at 80. The final exam counts 50%. What score is needed on the final to reach 85 overall?

Example 9

medium
If you double every weight in a weighted average, what happens to the result?

Example 10

easy
Using weighted sum 250 and total weight 3, find the weighted average.

Example 11

easy
Weights of 0.3 and 0.7 sum to what?

Example 12

easy
Compute the weighted sum ∑wixi for x=(8,10) with w=(3,2).

Example 13

hard
A teacher wants final grades to weight homework, midterm, and final at 0.2,0.3,0.5. A student got 70,80,x. The teacher wants the final grade to be exactly 80. What must x be?

Example 14

medium
A course grade: exam 90 (weight 0.6), homework 80 (weight 0.4). Find the weighted average.

Example 15

challenge
Two schools combined have an average test score of 77. School A averages 80 with 120 students. School B averages 72. How many students does school B have?

Example 16

medium
A school has 200 students at grade-level average 75 and 300 students at grade-level average 85. Find the schoolwide (weighted) average.

Example 17

hard
In a survey, 60% of 500 respondents rated a product 4/5 stars, and the rest rated it 3/5. What is the average rating?

Example 18

challenge
A blend mixes 3 kg of coffee at $8/kg with 2 kg at $13/kg. Find the price per kg of the blend.

Example 19

medium
A car drives 100 miles at 40 mph and 100 miles at 60 mph. What is the (time-weighted) average speed for the whole trip?

Example 20

medium
Values 20 and 40 have weights w and 1. For what weight w does the weighted average equal 25?
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