Given the following sale prices: $245,000, $250,000, $255,000, $260,000, and $290,000, what is the median?
Correct Answer
A) $255,000
Why this is correct: The median is the middle number in an ordered list. First, order the values: 245,000, 250,000, 255,000, 260,000, 290,000. With five numbers, the third one (255,000) is the median. Why the other choices are wrong: $260,000 is the fourth value, not the middle. $250,000 is the second value. $290,000 is the fifth (maximum) value. Exam tip: For an odd number of data points, the median is the exact middle value after sorting. For an even number, it's the average of the two middle values.
Why This Is the Correct Answer
Option B ($255,000) is correct because when the five sale prices are arranged in ascending order ($245,000, $250,000, $255,000, $260,000, $290,000), the median is the middle (third) value. With an odd number of data points (5), the median is simply the value that has an equal number of values above and below it. In this case, there are two values below $255,000 and two values above it, making $255,000 the median.
Why the Other Options Are Wrong
Option B: $260,000
$260,000 is the fourth value in the ordered sequence, which means there are three values below it and only one above, so it's not the median.
Option C: $250,000
$250,000 is the second value in the ordered sequence, not the middle value, so it cannot be the median.
Option D: $290,000
$290,000 is the highest value in the dataset and represents the maximum, not the median.
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 numbers are arranged from lowest to highest.
How to use: When you see a median question, immediately think 'middle child' and arrange all values in order from lowest to highest, then find the value that has an equal number of values on each side.
Exam Tip
Always write out the numbers in ascending order first, then count to find the middle position - for odd numbers of values, it's position (n+1)/2, where n is the total count.
Common Mistakes to Avoid
- -Confusing median with mean (average) and adding all values then dividing
- -Forgetting to arrange the data in numerical order before finding the middle value
- -Selecting the middle position number instead of the actual value at that position
Concept Deep Dive
Analysis
This question tests understanding of the median, a fundamental measure of central tendency used extensively in real estate appraisal for analyzing comparable sales data. The median represents the middle value in an ordered dataset and is particularly valuable in real estate because it's less affected by extreme values (outliers) than the arithmetic mean. In appraisal practice, the median helps identify the typical market value when analyzing comparable sales, especially when dealing with properties that may have unusual characteristics or sale conditions. Understanding how to calculate and interpret the median is essential for the sales comparison approach, which is one of the three primary valuation methods in real estate appraisal.
Background Knowledge
The median is a measure of central tendency that identifies 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 of values, the median is the average of the two middle values.
Real-World Application
Appraisers use median sale prices to analyze market trends and identify typical values in a neighborhood, especially when some sales include distressed properties or luxury homes that might skew the average price, providing a more representative picture of the typical market value.
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