Three sales closed at $200,000 each and one at $280,000. Each sale has equal weight. What is the mean sale price, to the nearest dollar?
Correct Answer
C) $220,000
(3×200000+1×280000)/4=220000. Equal observation weights differ from assigning equal weight to each distinct price.
Why This Is the Correct Answer
Option C is correct because the mean is the sum of the observations divided by their count: (3 × $200,000 + $280,000) / 4 = $880,000 / 4 = $220,000. Each of the four sales carries equal weight, so the three $200,000 sales pull the mean toward $200,000.
Why the Other Options Are Wrong
Option A: $240,000
Option A, $240,000, comes from averaging the two distinct prices, ($200,000 + $280,000) / 2. That gives equal weight to each distinct price rather than to each sale; the correct calculation is $880,000 / 4 = $220,000.
Option B: $200,000
Option B, $200,000, is the most frequent price (the mode) and also the median, not the mean. Adding the $280,000 sale raises the mean to $880,000 / 4 = $220,000.
Option D: $280,000
Option D, $280,000, is simply the highest single sale price. The mean of all four sales is ($600,000 + $280,000) / 4 = $220,000.
Count each sale, not each price
Write out each sale before adding: 200 + 200 + 200 + 280, then divide by the number of sales you wrote.
How to use: Use this whenever a mean question says several sales closed at the same price.
Exam Tip
When a question says several sales closed at the same price, multiply that price by the number of sales before adding. Check that your divisor equals the total number of sales.
Common Mistakes to Avoid
- -Averaging only the distinct prices and ignoring how many sales occurred at each
- -Reporting the mode or median when the mean is asked for
- -Dividing by the number of distinct prices instead of the number of sales
Concept Deep Dive
Analysis
This question tests the arithmetic mean when the same value appears more than once. Each sale counts as one observation, so the repeated $200,000 price must be counted three times. Sum all four prices and divide by four.
Background Knowledge
The arithmetic mean is the sum of the data points divided by the number of data points. When values repeat, each occurrence is a separate observation and must be included in both the sum and the count. Weighting each distinct value equally produces a different, incorrect result for an equally weighted sample.
Real-World Application
An appraiser finds three resales of the same condo floor plan at $200,000 and one upgraded unit at $280,000. Computing the average sale price correctly shows a typical figure of $220,000, not the $240,000 midpoint between the two price levels.
More Statistics Questions
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