Weighted Average Calculation: Finding Hotel Rating from 50%, 30%, 10% Factors

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

Because the categories have different levels of importance! Satisfaction counts for 50% while Service only counts for 10%. A weighted average gives more influence to the more important categories.

Q: How do I convert percentages to decimals?

Simply divide by 100 or move the decimal point two places left. For example: 50% = 50 ÷ 100 = 0.5, and 10% = 10 ÷ 100 = 0.1.

Q: Why do I multiply instead of just using the percentages?

The percentage tells you how much each category contributes to the final rating. Multiplying $ 4.5 \times 0.5 = 2.25 $ means Satisfaction contributes 2.25 points to the overall rating.

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

Yes, but it's trickier! You'd calculate $ (4.5 \times 50 + 4 \times 30 + 5 \times 10 + 3 \times 10) ÷ 100 $. Converting to decimals first is usually easier and less error-prone.

Weighted Averages with Multiple Category Ratings

A hotel's overall rating is determined according to a weighted average of several categories. Each category is given a rating and a weighted factor. Below are the ratings for the "Happy Tourist" hotel:

Determine the hotel's overall rating?

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Understand the problem

Determine the hotel's overall rating?

Step-by-step solution

In order to determine the hotel rating, we must calculate an average.

Below is the weighted average formula:

(value A X weight percentage A)+(value B X weight percentage B)...

First, let's add up all the percentages:

$50\%+30\%+10\%+10\%=100\%$

Now we must multiply each factor by its weight percentage, convert the percentages to decimal numbers, and add them as follows:

$4.5\times0.5+4\times0.3+5\times0.1+3\times0.1=$

We then proceed to solve the multiplication exercises:

$2.25+1.2+0.5+0.3=$

Finally we add them up and obtain the following: 4.25 which is the hotel's overall rating.

Final Answer

4.25

Key Points to Remember

Essential concepts to master this topic

Formula: Multiply each rating by its weight percentage then sum
Technique: Convert percentages to decimals: 50% = 0.5, 30% = 0.3
Check: Verify all weights sum to 100%: 50% + 30% + 10% + 10% = 100% ✓

Common Mistakes

Avoid these frequent errors

Adding ratings without considering weights
Don't just add ratings (4.5 + 4 + 5 + 3) ÷ 4 = 4.125! This treats all categories equally when they have different importance. Always multiply each rating by its decimal weight first, then add the 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 ratings?

Because the categories have different levels of importance! Satisfaction counts for 50% while Service only counts for 10%. A weighted average gives more influence to the more important categories.

How do I convert percentages to decimals?

Simply divide by 100 or move the decimal point two places left. For example: 50% = 50 ÷ 100 = 0.5, and 10% = 10 ÷ 100 = 0.1.

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

Always check that your weights sum to 100% first! If they don't, there might be missing categories or an error in the problem. In this case: 50% + 30% + 10% + 10% = 100% ✓

Why do I multiply instead of just using the percentages?

The percentage tells you how much each category contributes to the final rating. Multiplying $4.5 \times 0.5 = 2.25$ means Satisfaction contributes 2.25 points to the overall rating.

Can I work with percentages directly without converting to decimals?

Yes, but it's trickier! You'd calculate $(4.5 \times 50 + 4 \times 30 + 5 \times 10 + 3 \times 10) ÷ 100$ . Converting to decimals first is usually easier and less error-prone.

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