A set of sale prices has a mean of $580,000, a median of $500,000 and a mean absolute deviation from the median of $200,000. An appraiser measures skewness as the difference between the mean and the median relative to that deviation. What is this skewness ratio, to two decimals?
Correct Answer
A) 0.40
(580000 − 500000) / 200000 = 0.4. The denominator here is an average absolute deviation, not a standard deviation or the median of absolute deviations.
Why This Is the Correct Answer
Option A is correct because (mean − median) / mean absolute deviation = ($580,000 − $500,000) / $200,000 = $80,000 / $200,000 = 0.40. The positive result reflects a mean above the median, a pattern consistent with right skew in the sample.
Why the Other Options Are Wrong
Option B: 0.14
Option B, 0.14, divides the $80,000 mean-median gap by the $580,000 mean (about 0.138) instead of by the mean absolute deviation. The defined denominator is $200,000, so the ratio is $80,000 / $200,000 = 0.40.
Option C: 0.86
Option C, 0.86, is the median divided by the mean ($500,000 / $580,000 ≈ 0.86), which is not the defined ratio. The formula gives ($580,000 − $500,000) / $200,000 = 0.40.
Option D: 2.90
Option D, 2.90, is the mean divided by the mean absolute deviation ($580,000 / $200,000), leaving out the median. The numerator should be the mean minus the median, giving $80,000 / $200,000 = 0.40.
Gap divided by spread
The ratio is the gap between mean and median divided by the typical spread around the median.
How to use: Use this to set up any mean-minus-median skewness measure.
Exam Tip
When a question defines its own formula, apply it exactly. Distractors often drop one term or divide the wrong pair of numbers.
Common Mistakes to Avoid
- -Dividing the mean by the deviation without subtracting the median
- -Dividing the mean-median gap by the mean instead of the stated spread measure
- -Dividing the median by the mean
Concept Deep Dive
Analysis
This question tests applying a defined formula exactly as stated. The skewness ratio here is the difference between the mean and median divided by the mean absolute deviation from the median. Plug in the three given figures and divide.
Background Knowledge
When a distribution has a long right tail, the mean is typically pulled above the median. Scaling the mean-median gap by a measure of spread makes the result unit-free and comparable across data sets. The denominator in this question is the average absolute deviation from the median, not a standard deviation or a median of absolute deviations.
Real-World Application
An appraiser notices that a few high-end sales lift the neighborhood mean above the median. A positive skewness ratio quantifies that pull, supporting the choice to emphasize the median as the typical price.
More Statistics Questions
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An appraiser estimates a market-wide price trend using only sales data from one brokerage that specializes in luxury homes, without checking how other segments are represented. What is the principal concern?
Compared with analyzing one matched sale pair for one feature, what can a suitably specified multiple regression do?
The base-period median sale price is $400,000 and the current-period median is $460,000. Compute the price relative defined as current ÷ base, as a decimal to three places.
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Assessment-to-sale ratios are 0.94, 0.96, 0.98, 1, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Market data show a first quartile sale price of $405,000 and a third quartile sale price of $495,000. What is the interquartile range, to the nearest dollar?
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Previous Question
Assessment-to-sale ratios are 1.2, 1.1, 1, 0.9; corresponding sale prices are $100,000, $200,000, $300,000, $400,000 in the same order. Compute PRD as the arithmetic mean ratio divided by the sale-price-weighted mean ratio. Round to two decimals.
Next Question
Four parcels have assessed value/sale price pairs of $120,000/$100,000, $210,000/$200,000, $255,000/$300,000 and $300,000/$400,000. Compute each assessment-to-sale ratio. Define PRD as their arithmetic mean divided by total assessed value/total sale price. Which rounded PRD and observed sample tendency follow?