The following sale prices were recorded: $285,000, $295,000, $310,000, $295,000, $305,000. What is the median sale price?
Correct Answer
C) $295,000
Why this is correct: Median is the middle value when sorted. Ordered: $285,000, $295,000, $295,000, $305,000, $310,000. The third (middle) value is $295,000. Why the other choices are wrong: '$300,000' is the mean, not median. '$298,000' is an average of the two middle values if incorrectly calculated. '$310,000' is the highest value. Exam tip: For median, sort and pick the middle; for even counts, average the two middle values.
Why This Is the Correct Answer
Option A ($295,000) is correct because when the five sale prices are arranged in ascending order ($285,000, $295,000, $295,000, $305,000, $310,000), the median is the middle value, which is the third value in this five-number sequence. Since there are an odd number of data points (5), the median is simply the value in the exact center position. The fact that $295,000 appears twice in the dataset doesn't change the calculation - we still identify the positional middle value. This demonstrates the median's reliability as a measure of central tendency that represents the typical market value.
Why the Other Options Are Wrong
MIDDLE-MAN Method
M-I-D-D-L-E: 'Make It Deliberately Divided, Line Everything' - Always arrange data in order first, then find the exact middle position. For odd numbers, it's the center value; for even numbers, average the two middle values.
How to use: When you see a median question, immediately think 'MIDDLE-MAN' and remember to first sort the data in ascending order, then count to find the exact middle position. Don't calculate averages unless you have an even number of data points.
Exam Tip
Always write out the numbers in ascending order on your scratch paper before attempting to identify the median - this visual organization prevents errors and makes the middle value obvious.
Common Mistakes to Avoid
- -Confusing median with mean (average) and trying to add and divide
- -Forgetting to arrange the data in numerical order before finding the middle value
- -When there are duplicate values, thinking you need to treat them differently in the calculation
Concept Deep Dive
Analysis
This question tests understanding of the median, a fundamental measure of central tendency used extensively in real estate appraisal for analyzing comparable sales data. The median represents the middle value in an ordered dataset and is particularly valuable in real estate because it's less affected by extreme values (outliers) than the arithmetic mean. In appraisal practice, the median helps appraisers identify the central tendency of market prices without distortion from unusually high or low sales. Understanding how to calculate and interpret the median is essential for the sales comparison approach and market analysis components of appraisal reports.
Background Knowledge
The median is the middle value in an ordered dataset and is one of three primary measures of central tendency (along with mean and mode) used in statistical analysis. In real estate appraisal, the median is particularly useful because it provides a measure of typical market value that isn't skewed by extremely high or low sales prices that might not represent normal market conditions.
Real-World Application
Appraisers use median sale prices when analyzing neighborhood market trends and selecting comparable sales, as the median helps identify typical market values while filtering out the influence of luxury sales or distressed properties that might skew the mean.
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