The following data set represents property values: $450,000, $475,000, $450,000, $500,000, $525,000. What is the range?
Correct Answer
A) $75,000
Why this is correct: The range in a data set is the difference between the highest and lowest values. Here, the highest value is $525,000 and the lowest is $450,000. Therefore, Range = $525,000 - $450,000 = $75,000. Why the other choices are wrong: $480,000 is close to the mean (average), not the range. $525,000 is just the highest value, not the difference. $450,000 is just the lowest value, not the difference. Exam tip: Range = Max - Min. It measures spread, not central tendency.
Why This Is the Correct Answer
Option A ($75,000) is correct because range is calculated by subtracting the lowest value from the highest value in the data set. From the given property values ($450,000, $475,000, $450,000, $500,000, $525,000), the highest value is $525,000 and the lowest is $450,000. Therefore, the range equals $525,000 - $450,000 = $75,000. This calculation follows the standard statistical formula for range.
Why the Other Options Are Wrong
Option B: $480,000
Option B ($480,000) appears to be the mean (average) of the data set, not the range. This represents a common confusion between measures of central tendency (mean, median, mode) and measures of dispersion (range, standard deviation).
Option C: $525,000
Option C ($525,000) is the highest value in the data set, not the range. While this value is used in the range calculation, it represents only one component of the formula rather than the final calculated result.
Option D: $450,000
Option D ($450,000) is the lowest value in the data set, not the range. This shows confusion between identifying individual data points versus calculating the spread between the highest and lowest values.
High-Low Highway
Remember 'Range = Road trip from LOW to HIGH' - imagine driving from the lowest point to the highest point, and the range is the distance you traveled (highest minus lowest).
How to use: When you see a range question, immediately identify the highest and lowest values in the data set, then visualize the 'road trip distance' between them by subtracting low from high.
Exam Tip
Always organize the data in ascending or descending order first to easily identify the highest and lowest values, then double-check your subtraction calculation.
Common Mistakes to Avoid
- -Confusing range with mean or median
- -Subtracting in wrong order (low minus high instead of high minus low)
- -Including the actual high/low values as the answer instead of their difference
Concept Deep Dive
Analysis
This question tests understanding of range, a fundamental measure of dispersion in statistical analysis used throughout real estate appraisal. Range quantifies the spread or variability in a data set by measuring the difference between the highest and lowest values. In appraisal work, understanding range helps appraisers assess the consistency of comparable sales data and identify potential outliers. A smaller range indicates more consistent data, while a larger range suggests greater variability that may require further investigation or adjustment.
Background Knowledge
Range is the simplest measure of variability in statistics, calculated as the difference between the maximum and minimum values in a data set. In real estate appraisal, statistical measures like range help appraisers evaluate the reliability and consistency of comparable sales data when determining property values.
Real-World Application
When analyzing comparable sales for a residential appraisal, if you have sales ranging from $450,000 to $525,000, the $75,000 range helps you understand the market variability and determine if additional adjustments or different comparables might be needed for a more accurate valuation.
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