Given the following sale prices: $245,000, $252,000, $248,000, $255,000, $248,000. What is the median sale price?
Correct Answer
B) $248,000
Why this is correct: The median is the middle number in an ordered list. First, arrange the prices in ascending order: $245,000, $248,000, $248,000, $252,000, $255,000. With five data points, the third (middle) value is $248,000. Why the other choices are wrong: "$255,000" is the highest value (maximum), not the median. "$252,000" is the fourth value. "$249,600" is the mean (average), calculated as ($245k+$252k+$248k+$255k+$248k)/5. Exam tip: Median is resistant to outliers. To find it, always sort the data first. For an odd number of points, it's the central one; for an even number, it's the average of the two central values.
Why This Is the Correct Answer
Option A ($248,000) is correct because when the five sale prices are arranged in ascending order ($245,000, $248,000, $248,000, $252,000, $255,000), the median is the middle (3rd) value. With an odd number of data points (5 sales), the median is simply the value that falls exactly in the center position. Even though $248,000 appears twice in the dataset, the middle position still contains $248,000, making it the median value.
Why the Other Options Are Wrong
MIDDLE Method
M-I-D-D-L-E: Make It Descending (or ascending), Determine Length, Locate Exact center. Remember 'median strip' runs down the MIDDLE of the highway, just like median value sits in the MIDDLE of your ordered data.
How to use: When you see a median question, immediately think 'MIDDLE of the highway' and arrange your numbers in order first, then count to find the exact center position. For odd numbers of data points, it's the center value; for even numbers, average the two center values.
Exam Tip
Always write out the numbers in ascending order first, then count positions carefully. Circle or mark the middle position(s) to avoid counting errors, especially under exam pressure.
Common Mistakes to Avoid
- -Calculating the mean (average) instead of the median
- -Not arranging the data in numerical order before finding the middle value
- -Miscounting positions in the ordered dataset, especially with repeated values
Concept Deep Dive
Analysis
This question tests understanding of median calculation, a fundamental statistical concept used extensively in real estate appraisal for analyzing comparable sales data. The median represents the middle value in a dataset when arranged in ascending or descending order, making it less sensitive to extreme values than the mean. In appraisal practice, median values help identify typical market prices and can reveal market trends more reliably than averages when dealing with outliers. Understanding how to calculate median is essential for the sales comparison approach and market analysis components of appraisal reports.
Background Knowledge
Median is a measure of central tendency that represents the middle value in an ordered dataset, making it particularly useful in real estate analysis because it's not skewed by extremely high or low sale prices. When there's an odd number of values, the median is the middle value; when there's an even number, it's the average of the two middle values.
Real-World Application
Appraisers use median sale prices when analyzing comparable sales to determine typical market values for a property type in a specific area. The median helps identify the central market tendency while minimizing the impact of unusually high or low sales that might skew the average, providing a more reliable indicator of market value.
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