Sale-price observations are $395,000, $415,000, $425,000, $445,000. Compute the arithmetic mean. Report to the nearest dollar.
Correct Answer
B) $420,000
Sum=1680000; n=4; mean=1680000/4=420000. Common errors: taking the lower middle observation gives $415,000; reporting the highest observation gives $445,000; dividing the sum by 3 instead of 4 gives $560,000.
Why This Is the Correct Answer
Option B is correct because the four prices sum to $1,680,000 ($395,000 + $415,000 + $425,000 + $445,000), and $1,680,000 divided by 4 equals $420,000. The arithmetic mean uses every observation and divides by the full count.
Why the Other Options Are Wrong
Option A: $415,000
Option A, $415,000, is the lower of the two middle observations, a value read off the ordered list rather than an average. The arithmetic mean adds all four prices and divides by 4: $1,680,000 / 4 = $420,000.
Option C: $445,000
Option C, $445,000, is simply the highest observation, not an average. The correct mean is $1,680,000 / 4 = $420,000.
Option D: $560,000
Option D, $560,000, results from dividing the sum by 3 instead of 4: $1,680,000 / 3 = $560,000. There are four observations, so the mean is $1,680,000 / 4 = $420,000.
Sum, then count
Add every value, then divide by how many values you added. Count the values before dividing.
How to use: Use this check on any mean calculation to avoid dividing by the wrong number.
Exam Tip
Count the observations in the stem before dividing; a wrong divisor is a common trap answer.
Common Mistakes to Avoid
- -Dividing the sum by fewer than the number of observations
- -Reporting the highest price as the average
- -Reading a middle observation off the list instead of averaging all of them
Concept Deep Dive
Analysis
This question tests the basic arithmetic mean: add all observations and divide by the number of observations. With four prices, the divisor must be 4. The distractors come from picking a single observation from the list or using the wrong divisor.
Background Knowledge
The arithmetic mean is the sum of the observations divided by their number. It uses every value, which makes it sensitive to extreme observations, unlike the median. It is a descriptive calculation and does not by itself determine a final value opinion.
Real-World Application
An appraiser summarizing four recent neighborhood sales reports their mean price in the market conditions section. She adds the four prices and divides by 4 to get $420,000, and notes that the summary describes the sales rather than setting the subject's value.
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