The sale prices of five comparable properties are: $245,000, $252,000, $248,000, $260,000, and $250,000. What is the median sale price?
Correct Answer
C) $250,000
Why this is correct: The median is the middle number in an ordered list. First, order the values: $245,000, $248,000, $250,000, $252,000, $260,000. With five numbers, the third (middle) one is $250,000. Why the other choices are wrong: $248,000 is the second number, not the median. $251,000 is the mean (average), not the median. $252,000 is the fourth number. Exam tip: Median = middle value after sorting. Mean = average. Don't confuse them.
Why This Is the Correct Answer
Option A ($250,000) is correct because when the five sale prices are arranged in ascending order ($245,000, $248,000, $250,000, $252,000, $260,000), the median is the middle (third) value in this odd-numbered dataset. With five data points, the median is always the third value when arranged sequentially. The value $250,000 sits exactly in the middle position, with two values below it and two values above it, making it the true median.
Why the Other Options Are Wrong
Middle Child Method
Think of the median as the 'middle child' in a family lineup by height - just like the middle child stands in the center when siblings line up from shortest to tallest, the median is the value that stands in the middle when all numbers are arranged in order.
How to use: When you see a median question, immediately think 'middle child' and arrange all values in order from lowest to highest, then pick the one standing in the exact center position.
Exam Tip
Always write out the numbers in ascending order first, then count to find the middle position - don't try to identify the median from the original unordered list.
Common Mistakes to Avoid
- -Confusing median with mean (average)
- -Forgetting to arrange values in numerical order first
- -Miscounting the middle position in odd-numbered datasets
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 for analyzing comparable sales data. The median represents the middle value in a dataset when all values are arranged in ascending or descending order, making it particularly valuable in real estate because it's less affected by extreme outliers than the mean. Understanding median is essential for appraisers when evaluating market data, as it provides a more stable representation of typical market values when dealing with sales that may include distressed properties or luxury outliers. This statistical tool helps appraisers identify the most representative market value from a set of comparable sales.
Background Knowledge
The median is a measure of central tendency that identifies the middle value in a dataset when arranged in numerical order, and it's particularly useful in real estate because it's not skewed by extreme high or low values. 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 when analyzing neighborhood comparables to establish market value ranges, especially when some sales include foreclosures or luxury properties that might skew the average, providing clients with a more representative picture of typical market conditions.
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