The following sale prices were recorded: $185,000, $192,000, $188,000, $195,000, $190,000. What is the median sale price?
Correct Answer
A) $190,000
Why this is correct: The median is the middle number in an ordered list. First, arrange the prices in ascending order: $185,000, $188,000, $190,000, $192,000, $195,000. With five numbers, the third (middle) value is $190,000. Why the other choices are wrong: $188,000 is the second value in the ordered list, not the middle. $185,000 is the first (lowest) value. $192,000 is the fourth value. Exam tip: Always sort the data first. For an odd count of numbers, the median is the exact middle one.
Why This Is the Correct Answer
Option B ($190,000) is correct because when the five sale prices are arranged in ascending order ($185,000, $188,000, $190,000, $192,000, $195,000), 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. This makes $190,000 the median sale price, as it has two values below it and two values above it.
Why the Other Options Are Wrong
Option B: $188,000
Option B ($188,000) is incorrect because it represents the second value in the ordered sequence, not the middle value. While $188,000 is part of the dataset, it falls below the true median position.
Option C: $185,000
Option C ($185,000) is incorrect because it represents the lowest value in the dataset, not the median. This is the minimum value, which is at the first position when arranged in ascending order.
Option D: $192,000
Option D ($192,000) is incorrect because it represents the fourth value in the ordered sequence, not the middle value. This value falls above the median position and would only be considered if we were looking for the upper quartile.
Middle Child Method
Think of the median as the 'middle child' - just like a middle child sits between siblings, the median sits in the middle of ordered data. Remember: 'Line them up, find the middle pup!'
How to use: When you see a median question, immediately think 'middle child' and arrange all values in order from smallest to largest, then count to find the exact center position.
Exam Tip
Always write down the numbers in ascending order first - don't try to find the median from unordered data as this leads to errors.
Common Mistakes to Avoid
- -Confusing median with mean (average)
- -Forgetting to arrange data in order before finding the middle
- -Miscounting the position when there are multiple data points
Concept Deep Dive
Analysis
This question tests understanding of median calculation, a fundamental statistical concept in real estate appraisal. 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, median values are crucial for market analysis and establishing typical price ranges in comparable sales analysis. Understanding how to calculate median helps appraisers identify representative market values and detect outliers in their data sets.
Background Knowledge
The median is a measure of central tendency that divides a dataset into two equal halves when values are arranged in order. For odd-numbered datasets, the median is the middle value; for even-numbered datasets, it's the average of the two middle values. This concept is essential in real estate appraisal for analyzing comparable sales and market trends.
Real-World Application
Appraisers use median sale prices to establish typical market values in neighborhood analysis, helping to identify the most representative price point while minimizing the impact of unusually high or low sales that might skew the average.
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