The range of a data set containing the values $450,000, $475,000, $425,000, $500,000, $440,000 is:
Correct Answer
B) $75,000
Why this is correct: The range is the difference between the highest and lowest values. First, identify the highest value: 500,000. Then, identify the lowest value: 425,000. Subtract: 500,000 minus 425,000 equals 75,000. Why the other choices are wrong: '$458,000' is close to the mean, not the range. '$25,000' and '$50,000' are incorrect differences between various pairs in the data set but not the correct highest-lowest calculation. Exam tip: Range = Max - Min. Always sort the numbers first to avoid mistakes.
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 dataset. First, we identify the highest value ($500,000) and the lowest value ($425,000) from the given data points. Then we perform the subtraction: $500,000 - $425,000 = $75,000. This represents the total spread of values in this comparable sales dataset.
Why the Other Options Are Wrong
Option A: $458,000
Option A ($458,000) is incorrect because this appears to be close to the mean or average of the dataset rather than the range, demonstrating confusion between measures of central tendency and measures of dispersion.
Option C: $25,000
Option C ($25,000) is incorrect as this appears to be the difference between some middle values in the dataset, such as $450,000 and $425,000, rather than the complete range from the absolute highest to lowest values.
Option D: $50,000
Option D ($50,000) is incorrect because this represents the difference between $500,000 and $450,000, which would only account for part of the data spread rather than the full range from highest to lowest values.
High-Low Highway
Remember 'Range = Road from High to Low' - imagine driving on a highway from the highest mountain (maximum value) down to the lowest valley (minimum value), and the range is the total distance traveled.
How to use: When you see a range question, immediately scan the data for the 'highest mountain peak' and 'lowest valley' numbers, then calculate the 'highway distance' between them by subtracting low from high.
Exam Tip
Always organize the data values in ascending or descending order first to quickly identify the highest and lowest values, reducing the chance of calculation errors.
Common Mistakes to Avoid
- -Calculating mean instead of range
- -Using middle values instead of absolute highest and lowest
- -Adding values instead of subtracting
- -Forgetting to identify all values in the dataset before calculating
Concept Deep Dive
Analysis
This question tests understanding of the statistical concept of range, which is a fundamental measure of data dispersion used in real estate appraisal. Range represents the spread between the highest and lowest values in a dataset, providing appraisers with a quick assessment of price variability in comparable sales. In appraisal practice, understanding range helps evaluate the consistency of market data and identify potential outliers that might affect valuation accuracy. The calculation is straightforward but critical for statistical analysis of comparable properties.
Background Knowledge
Range is the simplest measure of variability in statistics, calculated as the difference between the maximum and minimum values in a dataset. In real estate appraisal, range helps assess the consistency and reliability of comparable sales data, with smaller ranges generally indicating more uniform market conditions.
Real-World Application
When analyzing comparable sales for a residential appraisal, an appraiser might find sale prices of $425,000 to $500,000 with a range of $75,000, indicating moderate price variation that suggests either diverse property conditions or a transitioning market requiring careful adjustment analysis.
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