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.
Correct Answer
A) $445,000
(400000+2×440000+500000)/4=445000. The median receives twice the weight of either quartile.
Why This Is the Correct Answer
Option A is correct because (400,000 + 2 × 440,000 + 500,000) ÷ 4 = (400,000 + 880,000 + 500,000) ÷ 4 = 1,780,000 ÷ 4 = $445,000. The median receives twice the weight of either quartile. Dividing by 4 reflects the total weight of one plus two plus one.
Why the Other Options Are Wrong
Option B: $446,667
Option B, $446,667, comes from giving all three values equal weight: (400,000 + 440,000 + 500,000) ÷ 3 ≈ $446,667. The trimean doubles the median: 1,780,000 ÷ 4 = $445,000.
Option C: $450,000
Option C, $450,000, is the average of the two quartiles, (400,000 + 500,000) ÷ 2, which ignores the median entirely. The trimean is (400,000 + 880,000 + 500,000) ÷ 4 = $445,000.
Option D: $440,000
Option D, $440,000, is the median alone without including the quartiles. The trimean is (400,000 + 2 × 440,000 + 500,000) ÷ 4 = $445,000.
One, two, one over four
Weight Q1 once, the median twice, Q3 once, then divide by the total weight of four.
How to use: Use this whenever a question asks for a trimean from quartiles and the median.
Exam Tip
If you divide by 3, you have forgotten that the median counts twice; the divisor is 4.
Common Mistakes to Avoid
- -Weighting the median only once and dividing by 3
- -Averaging only the two quartiles
- -Reporting the median as the trimean
Concept Deep Dive
Analysis
This question tests applying the trimean formula, (Q1 + 2 × median + Q3) ÷ 4. The median is weighted twice, so the total weight is four. The distractors come from equal weighting, ignoring the median, or reporting the median alone.
Background Knowledge
The trimean is a resistant measure of central tendency that blends the median with the first and third quartiles. Because it uses quartiles rather than extreme values, it is less influenced by outliers than the mean. It reflects some information about skewness that the median alone does not.
Real-World Application
An analyst summarizing a skewed price distribution reports the trimean alongside the median. Because Q3 sits farther above the median than Q1 sits below it, the trimean comes out slightly above the median, reflecting the upward skew.
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.
The positive observations are 10, 15, 22.5. Compute their simple geometric mean (product of all observations)^(1/n). Report as a dimensionless ratio to three decimals.
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
Previous Question
Three ratio/price pairs are 0.85/$80,000,0.95/$200,000 and 1.10/$400,000. Define PRD as mean ratio divided by sale-price-weighted mean ratio. Which rounded PRD and observed sample tendency follow?
Next Question
Under a valid 95% frequentist confidence procedure for a population mean, what does the confidence level describe?