Average Price per Sqft Question

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rmrfl

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I am trying to calculate the average price per sqft for my neighborhood. I get two different answers using two different methods, one is obviously wrong. Please assist with the correct method.

House 1 = $200,000 , 1500sqft
House 2 = $225,000 , 1350sqft
House 3 = $250,000 , 2000sqft

Method One:
200,000/1500 = 133.33
225,000/1350 = 166.67
250,000/2000 = 125

133.33+166.67+125 = 425
425/3 = 141.67
Average Price per Sqft = $141.67

Method Two:
200,000+225,000+250,000 = 675,000
675,000/3 = 225,000
1500+1350+2000 = 4850
4850/3 = 1616.67
225,000/1616.67 = 139.17
Average Price per Sqft = $139.17

I am assuming its an order of operations error.
 
rmrfl said:
I am trying to calculate the average price per sqft for my neighborhood. I get two different answers using two different methods, one is obviously wrong. Please assist with the correct method.

House 1 = $200,000 , 1500sqft
House 2 = $225,000 , 1350sqft
House 3 = $250,000 , 2000sqft

Method One:
200,000/1500 = 133.33
225,000/1350 = 166.67
250,000/2000 = 125

133.33+166.67+125 = 425
425/3 = 141.67
Average Price per Sqft = $141.67

Method Two:
200,000+225,000+250,000 = 675,000
675,000/3 = 225,000
1500+1350+2000 = 4850
4850/3 = 1616.67
225,000/1616.67 = 139.17
Average Price per Sqft = $139.17

I am assuming its an order of operations error.
Click to expand...
No, the error is trying apply statistics to a very small sample size. The answers you got are NOT "significantly" different.
 
rmrfl said:
I am trying to calculate the average price per sqft for my neighborhood. I get two different answers using two different methods, one is obviously wrong. Please assist with the correct method.

House 1 = $200,000 , 1500sqft
House 2 = $225,000 , 1350sqft
House 3 = $250,000 , 2000sqft

Method One:
200,000/1500 = 133.33
225,000/1350 = 166.67
250,000/2000 = 125

133.33+166.67+125 = 425
425/3 = 141.67
Average Price per Sqft = $141.67

Method Two:
200,000+225,000+250,000 = 675,000
675,000/3 = 225,000
1500+1350+2000 = 4850
4850/3 = 1616.67
225,000/1616.67 = 139.17
Average Price per Sqft = $139.17

I am assuming its an order of operations error.
Click to expand...
No, you're just calculating two different things, which won't have the same value.

The first method gives the average price-per-square-foot of a house (weighted by the house).

The second gives the average price of a square foot (weighted by area). This counts the largest house more heavily, so its lower price per square foot pulls the average down.

It isn't an order of operations error, so much as an example that the order matters!
 
Your method 1 isn't how we define averages.
Your method 2, with extra step of dividing by 3.
[math]Average=\frac{\text{Total cost}}{\text{Total square footage}}=\frac{675,000}{4850}=\underbrace{\frac{675,000\div3}{4850\div3}}_{\text{extra step}}=139.17\\[/math]What you're doing in method 1:
[math]Average \neq \left(\frac{200,000}{1500}+\frac{225000}{1350}+\frac{250,000}{2000}\right)\cdot \frac{1}{3} = 141.67[/math]
 
Dr.Peterson said:
Actually, it is: https://www.thebalance.com/can-i-use-the-price-per-square-foot-to-figure-home-values-1798754

That article also mentions the median price per square foot, which may be better when comparing one home with others around it.

The important thing is that both methods give averages, but of different things. Both produce skewed results, just with different skews.
Click to expand...
I guess it comes down to whether you're looking to compare houses within the same area or different areas.
 
\(\displaystyle \dfrac{a/c}{b/c} = \dfrac{a}{b}\) meaning that you did not need to divide by 3 as you did in method 2.
 
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