The following sale prices were recorded: $425,000, $450,000, $435,000, $425,000, $475,000. What is the median sale price?
Correct Answer
A) $435,000
Why this is correct: First, arrange prices in ascending order: $425,000, $425,000, $435,000, $450,000, $475,000. The median is the middle (third) value: $435,000. Why the other choices are wrong: $450,000 is not the middle value. $425,000 is the mode (most frequent), not the median. $442,000 is the mean (average), calculated as (425,000+450,000+435,000+425,000+475,000)/5 = 442,000. Exam tip: Median = middle after sorting; mean = average; mode = most frequent.
Why This Is the Correct Answer
Option B ($435,000) is correct because when the five sale prices are arranged in ascending order ($425,000, $425,000, $435,000, $450,000, $475,000), the median is the middle (third) value. With an odd number of data points (5), the median is simply the value that falls exactly in the center position. Since there are two values below $435,000 and two values above it, $435,000 is definitively the median.
Why the Other Options Are Wrong
Option B: $450,000
Option B ($450,000) is the fourth value in the ordered sequence, which would be the median if we were looking for the second-highest value, but it's not the middle position in this five-value dataset.
Option C: $425,000
Option C ($425,000) represents the mode (most frequently occurring value) and the minimum value, but not the median. While $425,000 appears twice in the dataset, the median specifically requires finding the middle position value, not the most common value.
Option D: $442,000
Option D ($442,000) appears to be the arithmetic mean (average) of the five values ($2,210,000 ÷ 5 = $442,000), but the question specifically asks for the median, not the mean. This is a common confusion between measures of central tendency.
MIDDLE Method
M-I-D-D-L-E: Make It Descending (or ascending), Determine Length, Extract middle position. Remember: 'Median sounds like Middle' - you're always looking for the middle value after sorting.
How to use: When you see a median question, immediately think 'MIDDLE' and sort the numbers first. Count the total values, add 1, then divide by 2 to find the middle position (for odd numbers of values).
Exam Tip
Always write out the numbers in order before attempting to find the median - don't try to do it mentally as you're likely to make errors under exam pressure.
Common Mistakes to Avoid
- -Confusing median with mean (average)
- -Forgetting to arrange the data in order first
- -Selecting the mode (most frequent value) instead of 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 appraisers understand typical market conditions and identify reasonable price ranges for comparable sales. Understanding how to calculate and interpret median values is essential for the sales comparison approach, which is one of the three primary valuation methods.
Background Knowledge
Median is the middle value in an ordered dataset and is one of three primary measures of central tendency (along with mean and mode). For datasets with an odd number of values, the median is the middle value; for even numbers of values, 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 (foreclosures, luxury upgrades, or distressed sales). The median provides a more stable indicator of market trends than the mean when extreme values are present.
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