Five adjusted indications (in $000) are 310, 312, 315, 320 and 340. What is the median absolute deviation (MAD) about the median?
Correct Answer
A) 5
The median is 315. Absolute deviations are 5, 3, 0, 5 and 25; sorted 0, 3, 5, 5, 25, their median is 5. The MAD is a robust alternative to the standard deviation.
Why This Is the Correct Answer
Option A is correct because the median of 310, 312, 315, 320 and 340 is 315, and the absolute deviations are 5, 3, 0, 5 and 25. Sorted as 0, 3, 5, 5, 25, their median is 5. The MAD is a robust alternative to the standard deviation.
Why the Other Options Are Wrong
Option B: 3
Option B, 3, is the second-smallest deviation in the sorted list 0, 3, 5, 5, 25, not the middle one. The median of the deviations is 5.
Option C: 7.6
Option C, 7.6, is the mean absolute deviation: (5 + 3 + 0 + 5 + 25) / 5 = 38 / 5 = 7.6. The MAD takes the median of the deviations, which is 5.
Option D: 25
Option D, 25, is the largest deviation (340 − 315), not the median of the deviations. The MAD is 5.
Median of the distances
MAD is a median twice: find the median of the data, then the median of the distances from it.
How to use: Use this to keep MAD separate from the mean absolute deviation.
Exam Tip
Sort the deviations before picking the middle one; leaving them unsorted is an easy way to choose the wrong value.
Common Mistakes to Avoid
- -Averaging the deviations instead of taking their median
- -Forgetting to sort the deviations
- -Reporting the largest deviation
Concept Deep Dive
Analysis
This question tests the median absolute deviation about the median. The steps are to find the median, compute each value's absolute deviation from it, sort those deviations, and take their median. The distractors pick the wrong deviation or average the deviations instead.
Background Knowledge
The median absolute deviation is the median of the absolute distances from the median. Because it relies on medians at both steps, a single extreme value such as 340 has little effect on it. That makes it a robust alternative to the standard deviation as a measure of scale.
Real-World Application
An appraiser reconciling five adjusted indications sees one at $340,000 well above the others. Computing a MAD of $5,000 shows that the remaining indications cluster tightly, and she investigates the outlier before relying on it.
More Statistics Questions
Sale prices are $270,000, $290,000, $300,000, $310,000, $330,000. Treat the listed observations as the complete population and divide by n when computing the standard deviation. Report to the nearest dollar.
A sales sampling frame systematically excludes a relevant part of the target market. What is the principal risk?
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.
The assessment-to-sale ratios are 0.8, 0.85, 0.9, 0.92, 0.95, 0.98, 1.02, 1.05, 1.08, 1.1, 1.15, 1.2. Calculate COD as [average absolute deviation from the median ÷ median]×100. For even n, average the two middle ratios. Report the COD as a percentage to two decimals.
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?
Assessment-to-sale ratios are 0.96, 0.98, 0.99, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Given first quartile $400,000, median $440,000 and third quartile $500,000, compute the trimean (Q1+2×median+Q3)/4. Report to the nearest dollar.
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