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Weighted Average

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Weighted Average [#permalink]

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New post 20 Oct 2017, 07:23
Hello All,

I have a question on weighted average for a problem I saw at work and am not sure how to answer it.

Say you there are 5 different sizes of buildings (1500,2500,3500,4500,5500 sqft) and you have 35 total buildings - 7 buildings of each size, so your mix percentage is 20% for each building size. The weighted average size is 3500 sqft.

Each building has a different cost to build. From smallest to largest their respective costs to build are $100,000 ($66.67/sqft), $110,000 ($44/sqft), $120,000 ($34.29/sqft), $130,000 (28.89/sqft), $140,000 ($25.45/sqft). The weighted average of the cost to build is $120,000.

The weighted average sq ft of 3,500 / weighted average cost of $120,000 = $34.29/sqft (makes sense right?)

Now if I take each individual building's price per square foot (i.e $66.67, $44, $34.29, $28.89, $25.45) and calculate the weighted average based on the mix percentage above (20% for each), I am getting $39.86/sqft.

Why does the weighted average of the $/sqft ($39.86/sqft) differ from the calculation of the weighted average size / weighted average cost ($34.29/sqft)?

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Re: Weighted Average [#permalink]

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New post 20 Oct 2017, 08:22
Hi cwilliams1591 ,

Welcome to GMATClub :)

Please note that weighted average or average speed cannot be calculated by taking the average of averages.

Here is the great article written by our expert. Check it out once and let us know in case of any concern. :)

https://gmatclub.com/forum/weighted-ave ... 06999.html
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New post 20 Oct 2017, 09:58
So which part would be the incorrect way to calculate it? Technically, the price per square foot to build would not be an average, for example, $100,000 / 1,500 sqft = $66.67/sqft

The weighted average is a combination of the mix percentage (20% for each building) and the unit cost for each building to build. So, technically this would not be taking an average of averages, correct?

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Re: Weighted Average [#permalink]

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New post 21 Oct 2017, 00:01
cwilliams1591 wrote:
So which part would be the incorrect way to calculate it? Technically, the price per square foot to build would not be an average, for example, $100,000 / 1,500 sqft = $66.67/sqft

The weighted average is a combination of the mix percentage (20% for each building) and the unit cost for each building to build. So, technically this would not be taking an average of averages, correct?


Yes, that's correct. You cannot find average of average. You need to find total/no. of units.

Does that make sense?
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Re: Weighted Average   [#permalink] 21 Oct 2017, 00:01
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