The sale prices in a neighborhood are: $180,000, $195,000, $185,000, $200,000, $190,000. What is the range of these prices?
Correct Answer
B) $20,000
The maximum price is $200,000 and the minimum is $180,000, so range = $20,000. The $200,000 option gives only the maximum. The $950,000 option is the sum. The $190,000 option equals both mean and median of these observations, but neither is the requested range.
Why This Is the Correct Answer
Option B is correct because the highest price is $200,000 and the lowest is $180,000, so the range is $200,000 − $180,000 = $20,000. The range measures how far apart the extremes are.
Why the Other Options Are Wrong
Option A: $200,000
Option A, $200,000, is only the maximum price. The range subtracts the minimum from it: $200,000 − $180,000 = $20,000.
Option C: $950,000
Option C, $950,000, is the sum of all five prices ($180,000 + $195,000 + $185,000 + $200,000 + $190,000). The range is the maximum minus the minimum, $20,000.
Option D: $190,000
Option D, $190,000, is both the mean ($950,000 / 5) and the median of these prices, which are measures of center. The range is the spread from $180,000 to $200,000, or $20,000.
Range: top minus bottom
Picture the range as the distance from the top of the price list to the bottom: subtract the lowest from the highest.
How to use: Use this whenever a question asks for the range of a data set.
Exam Tip
Sort the values first so the minimum and maximum are easy to spot, then subtract.
Common Mistakes to Avoid
- -Reporting the maximum value instead of the range
- -Confusing the range with the mean or median
- -Adding the values instead of subtracting the extremes
Concept Deep Dive
Analysis
This question tests the range, the simplest measure of spread. The range is the largest value minus the smallest value. Here $200,000 − $180,000 = $20,000.
Background Knowledge
The range is the maximum value of a sample minus the minimum value. It is easy to compute but depends only on the two extremes, so a single unusual sale can change it greatly. Measures such as the interquartile range and standard deviation describe spread more robustly.
Real-World Application
An appraiser describes a neighborhood where five recent sales ran from $180,000 to $200,000. The $20,000 range shows the sales fall within a narrow price band, though the appraiser still checks the properties' characteristics before treating the market as homogeneous.
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