Calculate the Weighted Average: Student's Grade from 40%, 20%, 15%, and 25% Scores

Q: Why can't I just find the regular average of the four grades?

A regular average treats all grades equally, but weighted averages give more importance to certain grades. Here, the 40% grade (68) counts much more than the 15% grade (94)!

Q: How do I convert percentages to decimals quickly?

Simply move the decimal point two places left! For example: 40% becomes 0.40, 25% becomes 0.25. You can also divide by 100.

Q: Can I work with percentages directly without converting to decimals?

Yes, but it's trickier! You'd calculate $ (68 \times 40 + 73 \times 20 + 94 \times 15 + 91 \times 25) ÷ 100 $. Converting to decimals first is usually less error-prone.

Q: How do I check if my weighted average makes sense?

Your weighted average should fall between the lowest and highest grades (68 and 94). Also, it should be closer to grades with higher weights - here, closer to 68 since it has 40% weight.

Weighted Average with Percentage Weights

What is the average grade of the student who got the following:

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Understand the problem

What is the average grade of the student who got the following:

Step-by-step solution

To find the weighted average grade, follow these steps:

Step 1: Convert the percentage weights into decimal form:

40% to 0.40
20% to 0.20
15% to 0.15
25% to 0.25

Step 2: Calculate the contribution of each grade by multiplying it by its weight:

Grade 68 with weight 0.40: $68 \times 0.40 = 27.2$
Grade 73 with weight 0.20: $73 \times 0.20 = 14.6$
Grade 94 with weight 0.15: $94 \times 0.15 = 14.1$
Grade 91 with weight 0.25: $91 \times 0.25 = 22.75$

Step 3: Sum the contributions:

27.2 + 14.6 + 14.1 + 22.75 = 78.65

Since the weights sum up to 100%, the weighted average grade is directly this sum.

Therefore, the student's weighted average grade is $78.65$ .

Final Answer

$78.65$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percentages to decimals before multiplying by grades
Technique: Multiply each grade by its decimal weight: $68 \times 0.40 = 27.2$
Check: Weights must sum to 100% or 1.0 in decimal form ✓

Common Mistakes

Avoid these frequent errors

Adding grades first then applying weights
Don't add all grades (68 + 73 + 94 + 91 = 326) then divide by weights = wrong weighted average! This treats all grades equally instead of emphasizing important ones. Always multiply each grade by its individual weight first, then sum those products.

Practice Quiz

Test your knowledge with interactive questions

Norbert buys some new clothes.

When he gets home, he decides to work out how much each outfit cost him on average.

What answer should he come up with?

FAQ

Everything you need to know about this question

Why can't I just find the regular average of the four grades?

A regular average treats all grades equally, but weighted averages give more importance to certain grades. Here, the 40% grade (68) counts much more than the 15% grade (94)!

How do I convert percentages to decimals quickly?

Simply move the decimal point two places left! For example: 40% becomes 0.40, 25% becomes 0.25. You can also divide by 100.

What if my weights don't add up to 100%?

Check your problem again! In most cases, weights should total 100%. If they don't, you may need to normalize them by dividing each weight by the total sum first.

Can I work with percentages directly without converting to decimals?

Yes, but it's trickier! You'd calculate $(68 \times 40 + 73 \times 20 + 94 \times 15 + 91 \times 25) ÷ 100$ . Converting to decimals first is usually less error-prone.

How do I check if my weighted average makes sense?

Your weighted average should fall between the lowest and highest grades (68 and 94). Also, it should be closer to grades with higher weights - here, closer to 68 since it has 40% weight.

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