A company is making an advertisement for a new roller coaster and they want to know what the weighted average of its travel speed is.
What is the average speed of the roller coaster?
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A company is making an advertisement for a new roller coaster and they want to know what the weighted average of its travel speed is.
What is the average speed of the roller coaster?
To solve this problem, we'll compute the weighted average speed of the roller coaster using the given weights and speeds:
Step 1: Convert the weights from percentages to decimal form:
20% becomes 0.20
15% becomes 0.15
5% becomes 0.05
35% becomes 0.35
5% becomes 0.05
20% becomes 0.20
Step 2: Calculate each term by multiplying the speed by its corresponding weight:
Step 3: Sum the results of these products:
Step 4: Since the weights sum to 1, the weighted average speed is:
Therefore, the average speed of the roller coaster is 69.25 km/h.
69.25 km/h
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?
A regular average treats all values equally, but here each speed has a different weight (importance). The roller coaster spends 35% of time at 60 km/h but only 5% at 130 km/h!
Yes! Always convert percentages to decimals when calculating. 20% becomes 0.20, 15% becomes 0.15, etc. This makes multiplication much easier.
Check your data carefully! In weighted average problems, weights must total 100% (or 1.0 as decimals). If they don't, there's likely an error in the problem setup.
Look at the context and units. Here, percentages (%) are weights showing how much time is spent at each speed, while km/h values are what we're averaging.
Not really! You must calculate each speed × weight term separately, then add them all up. Each step matters for getting the right weighted average.
Yes! Your answer should be between the lowest and highest values (15-130 km/h). Also, it should be closer to values with higher weights - here, closer to 60 km/h since it has 35% weight.
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