Four sales have prices and consistently measured comparison areas of $250,000/1,250 sqft; $312,000/1,600 sqft; $348,000/1,740 sqft; and $410,000/2,000 sqft. Calculate the equal-observation arithmetic mean of their four individual prices per square foot.
Correct Answer
A) $200 per sq ft
Individual unit prices are 200,195,200 and 205 dollars per square foot. Their equal-observation arithmetic mean=(200+195+200+205)/4=$200 per square foot. Dividing pooled total price by pooled area would be an area-weighted mean, a different calculation. Neither summary alone is a marginal adjustment rate for additional subject area.
Why This Is the Correct Answer
Option A is correct because the individual unit prices are $200 ($250,000/1,250), $195 ($312,000/1,600), $200 ($348,000/1,740) and $205 ($410,000/2,000). Their equal-observation mean is (200 + 195 + 200 + 205) / 4 = $200 per square foot.
Why the Other Options Are Wrong
Option B: $195 per sq ft
Option B, $195 per sq ft, is only the lowest individual unit price ($312,000 / 1,600), not the mean of all four. The mean is (200 + 195 + 200 + 205) / 4 = $200.
Option C: $205 per sq ft
Option C, $205 per sq ft, is only the highest individual unit price ($410,000 / 2,000), not the mean of all four. The mean is (200 + 195 + 200 + 205) / 4 = $200.
Option D: $1,320,000 per sq ft
Option D, $1,320,000 per sq ft, is the sum of the four sale prices ($250,000 + $312,000 + $348,000 + $410,000) mislabeled as a unit price; nothing was divided by area. The correct mean of the unit prices is $200 per square foot.
Divide first, then average
For an equal-observation unit-price mean, convert each sale to price per square foot first, then average those results.
How to use: Use this order whenever a question asks for the mean of individual unit prices.
Exam Tip
Check that your answer's units make sense; a price per square foot in the millions signals a missed division.
Common Mistakes to Avoid
- -Reporting a single comparable's unit price as the average
- -Summing prices without dividing by area
- -Treating the average unit price as the size adjustment rate
Concept Deep Dive
Analysis
This question tests the difference between averaging individual unit prices and other calculations. The candidate must first compute each sale's price per square foot, then take the simple mean of those four figures, giving each sale equal weight. Pooled totals, single extremes or unconverted sums are different quantities.
Background Knowledge
An equal-observation mean gives each sale the same weight, while dividing total price by total area gives an area-weighted mean that lets larger sales count more. The two can differ, though here they happen to be close. Neither average by itself is a supported adjustment rate for differences in the subject's size.
Real-World Application
An appraiser lists four comparables' prices per square foot as $195 to $205 and reports their simple mean of $200. She notes that this summary describes the comparables and does not by itself set the size adjustment for the subject.
More Statistics Questions
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Assessment-to-sale ratios are 0.94, 0.96, 0.98, 1, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
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