Given the following sale prices: $285,000, $295,000, $310,000, $290,000, and $320,000, what is the median sale price?
Correct Answer
D) $295,000
Why this is correct: First, order the prices: $285,000, $290,000, $295,000, $310,000, $320,000. The median is the middle value in an ordered list, which is $295,000. Why the other choices are wrong: $290,000 is the second value, not the middle. $300,000 is the mean (average), not the median. $310,000 is the fourth value, not the middle. Exam tip: Median = middle value after sorting. It's not affected by extreme values like the mean.
Why This Is the Correct Answer
Option B ($295,000) is correct because when the five sale prices are arranged in ascending order ($285,000, $290,000, $295,000, $310,000, $320,000), the median is the middle (third) value. With an odd number of data points (5 sales), the median is simply the value that falls exactly in the center position. This makes $295,000 the median sale price, as there are two values below it and two values above it.
Why the Other Options Are Wrong
Option A: $290,000
Option A ($290,000) is incorrect because while it appears in the ordered dataset, it occupies the second position, not the middle position. This value would only be part of the median calculation if we had an even number of data points.
Option B: $300,000
Option B ($300,000) is incorrect because this value doesn't even appear in the original dataset. This might represent a mean calculation error or confusion with interpolation methods used when calculating median with even numbers of data points.
Option C: $310,000
Option C ($310,000) is incorrect because although it's in the dataset, it occupies the fourth position in the ordered sequence, not the middle position. This would be above the median value.
Middle Child Method
Think of the median as the 'middle child' - just like the middle child is in the center of siblings by age, the median sits in the center of ordered numbers. Remember: 'Line them up, find the middle pup!'
How to use: When you see a median question, immediately think 'middle child' and arrange all numbers in order from smallest to largest, then count to find the exact center position.
Exam Tip
Always write out the numbers in ascending order on your scratch paper before identifying the median - this visual organization prevents errors and makes the middle value obvious.
Common Mistakes to Avoid
- -Forgetting to arrange numbers in order before finding the middle
- -Confusing median with mean (average)
- -Miscounting the position when identifying the middle value
Concept Deep Dive
Analysis
This question tests the fundamental statistical concept of median, which is a critical measure of central tendency used extensively in real estate appraisal. The median represents the middle value in a dataset when arranged in ascending or descending order, making it particularly valuable in real estate because it's less affected by extreme values (outliers) than the mean. In appraisal practice, median values help establish market trends and typical price ranges, especially when dealing with comparable sales data. Understanding how to calculate median is essential for the sales comparison approach and market analysis components of appraisal reports.
Background Knowledge
Median is the middle value in an ordered dataset and differs from mean (average) in that it's not affected by extreme values. For odd numbers of data points, the median is the middle value; for even numbers, it's the average of the two middle values.
Real-World Application
Appraisers use median sale prices to establish typical market values in neighborhoods, especially when some sales might be outliers (distressed sales, luxury upgrades, etc.). The median provides a more stable indicator of market trends than the mean when extreme values are present.
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