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 8080 (weight 22) and 9090 (weight 11). Compute the weighted sum ∑wixi\sum w_i x_i.

Example 2

hard
A weighted average of two values aa and bb with weights waw_a and wbw_b equals aa exactly. What does that tell you about wbw_b?

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%50\% and 90%90\% to get the overall pass rate of two groups of different sizes?

Example 5

easy
Compute the weighted average of 2020 (weight 0.50.5) and 4040 (weight 0.50.5).

Example 6

medium
A test grade is 7070 (counts 25%25\%), midterm 8080 (counts 35%35\%), final 9090 (counts 40%40\%). Find the weighted average.

Example 7

medium
In a course, homework counts 20%20\%, midterm 30%30\%, final 50%50\%. A student scored 90,75,8290, 75, 82. Compute the final grade.

Example 8

hard
A student needs a course average of 8585. So far: homework 20%20\% at 9090, midterm 30%30\% at 8080. The final exam counts 50%50\%. What score is needed on the final to reach 8585 overall?

Example 9

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

Example 10

easy
Using weighted sum 250250 and total weight 33, find the weighted average.

Example 11

easy
Weights of 0.30.3 and 0.70.7 sum to what?

Example 12

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

Example 13

hard
A teacher wants final grades to weight homework, midterm, and final at 0.2,0.3,0.50.2, 0.3, 0.5. A student got 70,80,x70, 80, x. The teacher wants the final grade to be exactly 8080. What must xx be?

Example 14

medium
A course grade: exam 9090 (weight 0.60.6), homework 8080 (weight 0.40.4). Find the weighted average.

Example 15

challenge
Two schools combined have an average test score of 7777. School A averages 8080 with 120120 students. School B averages 7272. How many students does school B have?

Example 16

medium
A school has 200200 students at grade-level average 7575 and 300300 students at grade-level average 8585. Find the schoolwide (weighted) average.

Example 17

hard
In a survey, 60%60\% of 500500 respondents rated a product 4/54/5 stars, and the rest rated it 3/53/5. What is the average rating?

Example 18

challenge
A blend mixes 33 kg of coffee at $8/kg with 22 kg at $13/kg. Find the price per kg of the blend.

Example 19

medium
A car drives 100100 miles at 4040 mph and 100100 miles at 6060 mph. What is the (time-weighted) average speed for the whole trip?

Example 20

medium
Values 2020 and 4040 have weights ww and 11. For what weight ww does the weighted average equal 2525?
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