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Joined: 20 Oct 2017
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Weighted Average
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20 Oct 2017, 08:23
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)?
