Calculate Weighted Average: 30% of 79 and 70% of 83 in Test Scores

Q: Why can't I just find the regular average of 79 and 83?

A regular average treats both scores equally, but weighted averages give more importance to certain scores. Here, the second exam (83) counts for 70% while the first (79) only counts for 30%.

Q: How do I convert percentages to decimals?

Simply divide by 100! 30% = 30 ÷ 100 = 0.3 and 70% = 70 ÷ 100 = 0.7. This makes the multiplication easier.

Q: Should my weighted average always be between the two exam scores?

Yes! Your weighted average should fall between 79 and 83. Since the higher score (83) has more weight, the result should be closer to 83 than to 79.

Q: Can I use this formula for more than two scores?

Absolutely! Just add more terms: $ (score_1 \times weight_1) + (score_2 \times weight_2) + (score_3 \times weight_3) $ and so on. The weights should still total 100%.

Weighted Average with Percentage Weights

What is Michael's score if he gets 79 on the first exam and 83 on the second, given that the weight of the first test is 30% and that of the second is 70%?

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Step-by-step written solution

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Understand the problem

What is Michael's score if he gets 79 on the first exam and 83 on the second, given that the weight of the first test is 30% and that of the second is 70%?

Step-by-step solution

To solve the weighted average, we will use the following formula:

exam 2 * weight of evaluation 2 + exam 1 * weight of the evaluation 1 = Weighted average

We will place the data in the formula, where the weights will be in decimal numbers:

0.3*79 + 0.7*83 =
23.7+58.1 =

81.8

Final Answer

$81.8$

Key Points to Remember

Essential concepts to master this topic

Formula: Weighted Average = (score1 × weight1) + (score2 × weight2)
Technique: Convert percentages to decimals: 30% = 0.3, 70% = 0.7
Check: Verify weights sum to 100% and final answer is between exam scores ✓

Common Mistakes

Avoid these frequent errors

Adding scores first then applying weights
Don't add 79 + 83 = 162, then multiply by weights = wrong method! This treats both exams equally instead of giving more importance to the weighted exam. Always multiply each score by its individual weight first, then add the results.

Practice Quiz

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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 79 and 83?

A regular average treats both scores equally, but weighted averages give more importance to certain scores. Here, the second exam (83) counts for 70% while the first (79) only counts for 30%.

How do I convert percentages to decimals?

Simply divide by 100! 30% = 30 ÷ 100 = 0.3 and 70% = 70 ÷ 100 = 0.7. This makes the multiplication easier.

Should my weighted average always be between the two exam scores?

Yes! Your weighted average should fall between 79 and 83. Since the higher score (83) has more weight, the result should be closer to 83 than to 79.

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

Check your problem again! In most cases, weights should total 100%. If they don't, you might need to normalize them or ask your teacher for clarification.

Can I use this formula for more than two scores?

Absolutely! Just add more terms: $(score_1 \times weight_1) + (score_2 \times weight_2) + (score_3 \times weight_3)$ and so on. The weights should still total 100%.

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