The following sale prices were recorded: $245,000, $250,000, $255,000, $260,000, $310,000. What is the median sale price?
Correct Answer
A) $255,000
Why this is correct: The median is the middle value in an ordered dataset. Arrange the prices: $245,000, $250,000, $255,000, $260,000, $310,000. With five values, the third (middle) is $255,000. Why the other choices are wrong: "$250,000" is the second value. "$264,000" is the mean (average), not the median. "$260,000" is the fourth value. Exam tip: Median is resistant to outliers (like the $310,000 sale). Always order the data first.
Why This Is the Correct Answer
Option A ($255,000) is correct because when the five sale prices are arranged in ascending order ($245,000, $250,000, $255,000, $260,000, $310,000), the median is the middle (third) value. With an odd number of data points (5), the median is simply the value in the center position. This demonstrates the median's resistance to the influence of the outlier value of $310,000, making it a more representative measure of central tendency for this dataset.
Why the Other Options Are Wrong
Option B: $250,000
Option B ($250,000) is the second value in the ordered dataset, not the middle value. This would only be correct if we were looking for the first quartile or if there was confusion about the position of the median in the ordered sequence.
Option C: $264,000
Option C ($264,000) represents the arithmetic mean (average) of the five sale prices, not the median. The mean is calculated by adding all values ($245,000 + $250,000 + $255,000 + $260,000 + $310,000 = $1,320,000) and dividing by the number of values (5), which equals $264,000. The mean is influenced by the high outlier of $310,000, making it higher than the median.
Option D: $260,000
Option D ($260,000) is the fourth value in the ordered dataset, not the middle value. This represents a common error where someone might count incorrectly from either end of the ordered sequence or misunderstand which position represents the median.
Middle Child Method
Think of the median as the 'middle child' - always arrange the 'siblings' (data points) in order from smallest to largest, then pick the one exactly in the middle. For odd numbers, it's the center child; for even numbers, it's the average of the two middle children.
How to use: When you see a median question, immediately write out the numbers in ascending order, count the total number of values, and identify the middle position. For 5 values, the median is always the 3rd value when ordered.
Exam Tip
Always arrange data in ascending order first, then count carefully to find the exact middle position. Double-check your ordering and counting, as these are the most common sources of error on median questions.
Common Mistakes to Avoid
- -Calculating the mean instead of the median
- -Forgetting to arrange data in ascending order before finding the middle
- -Miscounting the position of the middle value in the ordered sequence
Concept Deep Dive
Analysis
This question tests understanding of central tendency measures, specifically the median, which is crucial 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 not skewed by outliers or extreme values. In this case, the $310,000 sale is significantly higher than the others, making the median more representative of typical market value than the mean would be. Understanding when to use median versus mean is essential for appraisers when analyzing market data and selecting appropriate comparables.
Background Knowledge
The median is the middle value in an ordered dataset and is one of three primary measures of central tendency along with mean and mode. In real estate appraisal, the median is often preferred over the mean because property values can have significant outliers that skew the average, making the median more representative of typical market conditions.
Real-World Application
Appraisers use median sale prices when analyzing neighborhood comparables because a few luxury sales or distressed properties can skew the mean. For example, if most homes sell for $250,000-$260,000 but one luxury home sells for $500,000, the median better represents typical market value than the inflated mean.
More Statistics Questions
A building cost $2,500,000 to construct 8 years ago. Using straight-line depreciation over a 40-year life, what is the current depreciated value?
The following sale prices were recorded: $245,000, $250,000, $250,000, $255,000, $280,000. What is the mode?
A property has a replacement cost of $1,800,000. Physical deterioration is estimated at $200,000, functional obsolescence at $150,000, and external obsolescence at $100,000. What is the depreciated value using the breakdown method?
What is the present value of $150,000 to be received in 5 years, assuming a discount rate of 8%?
A triangular lot has a base of 100 feet and a height of 80 feet. What is the area in square feet?
An irregular lot can be divided into a rectangle (100' × 80') and a triangle (base 60', height 40'). What is the total area in acres?
A property has a net operating income of $85,000 and annual debt service of $68,000. What is the debt coverage ratio?
A warehouse has interior dimensions of 120 feet × 80 feet × 20 feet high. What is the volume in cubic feet?
A property is purchased for $500,000 with a loan of $400,000. What is the loan-to-value ratio?
A property sold for $400,000 with annual gross rent of $40,000. What is the gross rent multiplier?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Related Tools
Previous Question
The following sale prices were recorded: $245,000, $250,000, $250,000, $255,000, $280,000. What is the mode?
Next Question
A comparable property sold for $350,000 but has a swimming pool worth $15,000 that the subject property lacks. What is the adjusted sale price for comparison purposes?