In a set of sale prices, the first quartile is $380,000 and the third quartile is $460,000. What is the quartile deviation, to the nearest dollar?
Correct Answer
B) $40,000
Q3−Q1=460000−380000=80000; divide by 2 to obtain 40000. The quartile deviation is half the interquartile range; the median and full range are different quantities.
Why This Is the Correct Answer
Option B is correct because the interquartile range is Q3 - Q1 = $460,000 - $380,000 = $80,000. Dividing by 2 gives a quartile deviation of $40,000.
Why the Other Options Are Wrong
Option A: $80,000
Option A, $80,000, is the interquartile range Q3 - Q1 = $460,000 - $380,000 without the final division by 2. The quartile deviation is $80,000 / 2 = $40,000.
Option C: $420,000
Option C, $420,000, comes from adding the quartiles instead of subtracting them, ($380,000 + $460,000) / 2 = $420,000, which is a midpoint, not a measure of spread. The quartile deviation is ($460,000 - $380,000) / 2 = $40,000.
Option D: $460,000
Option D, $460,000, simply reports Q3 rather than computing anything from the two quartiles. The quartile deviation is ($460,000 - $380,000) / 2 = $40,000.
Subtract, Then Halve
Quartile deviation is the gap between the quartiles cut in half: Q3 minus Q1, divided by 2.
How to use: Use this two-step phrase to avoid stopping at the interquartile range or adding the quartiles.
Exam Tip
A spread measure is a difference between values, so an answer that sits between the quartiles, like $420,000, is a location measure, not a spread.
Common Mistakes to Avoid
- -Forgetting to divide the interquartile range by 2
- -Averaging the quartiles instead of subtracting them
- -Confusing quartile deviation with the full range
Concept Deep Dive
Analysis
This question tests the quartile deviation, also called the semi-interquartile range. It is half the distance between the third and first quartiles. The distractors come from forgetting to halve, averaging the quartiles, or reporting a quartile itself.
Background Knowledge
The interquartile range covers the middle 50% of the data, and the quartile deviation is half of it. Because quartiles are not influenced by extreme values, these are resistant measures of spread, unlike the full range, which is the largest value minus the smallest.
Real-World Application
An appraiser summarizes a neighborhood's sale prices with Q1 of $380,000 and Q3 of $460,000. Reporting a quartile deviation of $40,000 describes the typical spread of the middle half of prices without being distorted by a few extreme sales.
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