Weighted & combined averages drills

Compute weighted or combined means across groups or categories.

Free, timed SHSAT practice sets on weighted & combined averages— every question includes a full worked explanation, and there's no account required.

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How to solve weighted average problems

When groups have different sizes or weights, you cannot just average the averages. Work with totals.

Quick check: the answer always lies between the group averages, closer to the bigger (or heavier) group. Common traps: averaging the two numbers evenly, pairing each percent with the wrong score, and stopping at the point total without dividing by the number of students.

Worked examples

Example 1.
On a science test, 30 students in Ms. Ortiz's class averaged 72 points, and 16 students in Mr. Diallo's class averaged 95 points. What is the combined average score of all 46 students?
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Answer:
A

Weighted average = (total points) \(\div\) (total students) = (30 \(\times\) 72 + 16 \(\times\) 95) \(\div\) 46 = 3680 \(\div\) 46 = 80. (Averaging 72 and 95 without the class sizes gives 83.5. Multiplying 72 by 16 and 95 by 30 (the class sizes swapped) gives 87. Stopping at the total points without dividing by 46 gives 3680.)

Example 2.
In a class, tests count for 20% of the grade and homework counts for 80%. A student's test average is 90 and homework average is 60. What is the student's weighted average grade?
Show answer and explanation
Answer:
A

Weighted grade = 20% \(\times\) 90 + 80% \(\times\) 60 = 18 + 48 = 66. (Averaging 90 and 60 evenly gives 75. Swapping the weights (80% of 90 + 20% of 60) gives 84. Dividing the sum of the two weighted parts by 2 gives 33.)