The following sale prices were recorded: $285,000, $295,000, $285,000, $305,000, $275,000. What is the median sale price?
Correct Answer
D) $285,000
Why this is correct: The median is the middle value in an ordered list. Ordered prices: $275,000, $285,000, $285,000, $295,000, $305,000. The third value (middle) is $285,000. Why the other choices are wrong: '$290,000' is the mean (average), not the median. '$289,000' is not a value in the dataset. '$295,000' is the fourth value, not the middle. Exam tip: For an odd number of data points, the median is the middle one after sorting. For an even number, it's the average of the two middle values.
Why This Is the Correct Answer
Option A ($285,000) is correct because when the five sale prices are arranged in ascending order ($275,000, $285,000, $285,000, $295,000, $305,000), 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. Even though $285,000 appears twice in the dataset, the middle position still contains this value, making it the median.
Why the Other Options Are Wrong
Option A: $290,000
Option A ($290,000) is incorrect because this value does not even appear in the original dataset and seems to be an arbitrary calculation. The median must be an actual value from the dataset when there is an odd number of data points, and $290,000 was never one of the recorded sale prices.
Option B: $289,000
Option B ($289,000) is incorrect because it appears to be an attempt to calculate the mean (average) rather than the median, though even that calculation would be wrong (the actual mean would be $289,000). The median is not calculated by averaging values but by finding the middle position in an ordered dataset.
Option C: $295,000
Option C ($295,000) is incorrect because while this value does appear in the dataset, it occupies the fourth position when the data is arranged in order, not the middle (third) position. This represents a common error of selecting a value from the dataset without properly identifying the middle position.
Middle Child Method
Think of the median as the 'middle child' - just like the middle child sits in the center of siblings arranged by age, the median sits in the center of data arranged by value. Use the phrase 'Line them up, pick the middle pup' to remember to first arrange the data in order, then select the center value.
How to use: When you see a median question, immediately think 'middle child' and follow these steps: 1) Line up the values from smallest to largest (or largest to smallest), 2) Count to find the exact middle position, 3) Pick that middle value as your answer.
Exam Tip
Always write out the numbers in order on your scratch paper before identifying the median - this visual arrangement prevents errors and makes the middle value obvious to spot.
Common Mistakes to Avoid
- -Calculating the mean (average) instead of finding the middle value
- -Forgetting to arrange the data in numerical order before finding the median
- -Selecting a value that appears most frequently (mode) rather than the middle positioned value
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, providing a measure of central tendency that is less affected by extreme values than the mean. In appraisal practice, the median is particularly valuable because it helps identify the typical market value without being skewed by unusually high or low sales prices. Understanding how to calculate and interpret the median is essential for the sales comparison approach and market analysis.
Background Knowledge
The median is a measure of central tendency that represents the middle value in an ordered dataset, used extensively in real estate appraisal to analyze comparable sales and determine typical market 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 market trends because it eliminates the distortion caused by extremely high-end or distressed sales, providing a more accurate picture of what typical buyers are paying for similar properties.
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