An analyst wants the range that brackets the middle half of a set of assessment ratios. Which statistic gives it?
Correct Answer
B) The interquartile range
It is the interquartile range, not the COD, that brackets the middle 50 percent of the assessment ratios.
Why This Is the Correct Answer
Option B is correct because the interquartile range spans from the first quartile to the third quartile and so brackets the middle 50 percent of the assessment ratios. It is the interquartile range, not the COD, that brackets the middle half.
Why the Other Options Are Wrong
Option A: The coefficient of dispersion
Option A, the coefficient of dispersion, measures average absolute deviation from the median as a percentage of the median. It summarizes uniformity but does not bracket the middle 50 percent of ratios.
Option C: The median percentage deviation
Option C, the median percentage deviation, is a measure of typical deviation expressed as a percentage. It does not identify the range that holds the middle half of the ratios.
Option D: The price-related differential
Option D, the price-related differential, compares the mean ratio to the weighted mean ratio to detect vertical inequity between low- and high-value properties. It does not bracket a range of ratios.
Inter-quartile, inner half
Inter means between: the interquartile range sits between the first and third quartiles. Between Q1 and Q3 lies the inner half of the data.
How to use: Use this when a question asks for the middle 50 percent of a data set.
Exam Tip
Middle half or middle 50 percent points to the interquartile range. COD and PRD measure uniformity and vertical equity, not a bracketed range.
Common Mistakes to Avoid
- -Confusing the COD with the interquartile range
- -Using the PRD as a dispersion range
- -Treating the full range from minimum to maximum as the middle half
Concept Deep Dive
Analysis
This question tests which ratio-study statistic identifies the range containing the middle half of the data. The interquartile range runs from the first quartile to the third quartile, bracketing the middle 50 percent. Other statistics listed measure average dispersion or vertical inequity rather than bracketing a range.
Background Knowledge
Quartiles divide an ordered data set into four equal parts. The interquartile range is the distance from the first quartile to the third quartile and contains the central half of the observations. In ratio studies, the COD measures uniformity, while the PRD addresses vertical equity.
Real-World Application
An assessment analyst reviewing a ratio study wants to show where the typical ratios fall, excluding the extremes. Reporting the interquartile range shows the band between the first and third quartiles. The analyst reports the COD separately to describe overall uniformity.
More Statistics Questions
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For an independent sale-price sample, the sample standard deviation is $20,000 and n=16. Estimate the standard error of the mean as s/√n. Report to the nearest dollar.
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Ratios are 0.88,0.92,0.96,1.04,1.08 and 1.12. Use the average of the two middle ordered values as median. Define COD=100×mean absolute deviation from that median÷median. What COD results?