Calculate Weighted Average: Finding The Swan Inn's Overall Rating with 45% Satisfaction Weight

Q: Why do I need to convert percentages to decimals?

Percentages represent parts of 100, so 45% means 45 out of 100, or 0.45. If you multiply by 45 instead of 0.45, your answer will be 100 times too big!

Q: How do I know if all my weights are included?

Add up all the weight percentages - they should equal 100%. In this problem: 45% + 30% + 10% + 10% + 5% = 100% ✓

Q: Why is satisfaction weighted so heavily at 45%?

In hotel ratings, customer satisfaction is often the most important factor because it reflects the overall guest experience. The higher weight means it has more influence on the final rating.

Weighted Averages with Percentage Conversion

A number of hotels are ranked based on various factors, each with a different weight.

This is the rating and weights for the hotel "The Swan Inn":

What is the hotel's overall rating?

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Understand the problem

A number of hotels are ranked based on various factors, each with a different weight.

This is the rating and weights for the hotel "The Swan Inn":

What is the hotel's overall rating?

Step-by-step solution

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

Let's remember the weighted average formula:

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

First, let's add all the percentages together to make sure we reach 100 percent:

$45\%+30\%+10\%+10\%+5=100\%$

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

$0.45\times3.5+0.3\times4+0.1\times2+0.1\times4.5+0.05\times1=$

Let's solve the multiplication problems first:

$1.575+1.2+0.2+0.45+0.05=$

We'll add them together and get: 3.475 and that's the hotel rating

Final Answer

3.475

Key Points to Remember

Essential concepts to master this topic

Formula: Sum of (rating × weight percentage) for all factors
Technique: Convert percentages to decimals: 45% becomes 0.45 for multiplication
Check: All weights must sum to 100%: 45+30+10+10+5 = 100% ✓

Common Mistakes

Avoid these frequent errors

Forgetting to convert percentages to decimals before multiplying
Don't multiply 3.5 × 45 instead of 3.5 × 0.45 = gives 157.5 instead of 1.575! This makes your answer 50 times too large because you're treating 45% as 45 whole units. Always convert percentages to decimals by dividing by 100.

Practice Quiz

Test your knowledge with interactive questions

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?

FAQ

Everything you need to know about this question

Why do I need to convert percentages to decimals?

Percentages represent parts of 100, so 45% means 45 out of 100, or 0.45. If you multiply by 45 instead of 0.45, your answer will be 100 times too big!

How do I know if all my weights are included?

Add up all the weight percentages - they should equal 100%. In this problem: 45% + 30% + 10% + 10% + 5% = 100% ✓

What if my calculated answer seems too high or low?

Check your decimal conversions! Your weighted average should be between the lowest and highest individual ratings. Here, it should be between 1 and 4.5.

Can I solve this without converting to decimals?

Yes! You can keep percentages and divide your final sum by 100. For example: $\frac{45 \times 3.5 + 30 \times 4 + 10 \times 2 + 10 \times 4.5 + 5 \times 1}{100} = 3.475$

Why is satisfaction weighted so heavily at 45%?

In hotel ratings, customer satisfaction is often the most important factor because it reflects the overall guest experience. The higher weight means it has more influence on the final rating.

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