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?
Correct Answer
D) About 1.09; higher-price sales have lower ratios
Ratios are 120000/100000=1.20,210000/200000=1.05,255000/300000=0.85 and 300000/400000=0.75. Their mean is 0.9625. Weighted mean=885000/1000000=0.885. PRD=0.9625/0.885=1.0876, rounded 1.09. The observed ratios decrease as sale prices rise, a regressive sample pattern; population-level or legal conclusions require more evidence.
Why This Is the Correct Answer
Option D is correct because the ratios are 1.20, 1.05, 0.85 and 0.75, with a mean of 3.85 / 4 = 0.9625. The weighted mean is total assessed value / total sale price = $885,000 / $1,000,000 = 0.885, so PRD = 0.9625 / 0.885 = 1.0876, about 1.09. The ratios fall as sale prices rise, a regressive pattern in this sample.
Why the Other Options Are Wrong
Option A: About 0.92; higher-price sales have higher ratios
Option A says about 0.92 with higher-price sales having higher ratios. 0.92 comes from inverting the division (0.885 / 0.9625 ≈ 0.92), and the ratios actually decline from 1.20 to 0.75 as prices rise; the correct PRD is 0.9625 / 0.885 = 1.09.
Option B: About 1.07; higher-price sales have lower ratios
Option B says about 1.07 with higher-price sales having lower ratios. The tendency is right, but 1.07 comes from using the median ratio, (0.85 + 1.05) / 2 = 0.95, in the numerator: 0.95 / 0.885 = 1.07. The PRD uses the mean ratio, so it is 0.9625 / 0.885 = 1.09.
Option C: About 1.00; ratios show no price-related pattern
Option C says about 1.00 with no price-related pattern. That results from using the simple mean ratio for both parts (0.9625 / 0.9625 = 1.00) instead of the weighted mean of $885,000 / $1,000,000 = 0.885; the PRD is 1.09 and the ratios fall from 1.20 to 0.75 as prices rise.
Totals give the weighted mean
The sale-price-weighted mean ratio equals total assessed value divided by total sale price, so add the columns before dividing.
How to use: Use this shortcut when a PRD question gives assessed values and sale prices.
Exam Tip
For two-part answers, check both the number and the stated tendency. Scan the ratios against the prices to see which way they move.
Common Mistakes to Avoid
- -Inverting the PRD division
- -Averaging ratios when computing the weighted mean instead of using totals
- -Using the median ratio in place of the mean ratio
Concept Deep Dive
Analysis
This question tests a full PRD calculation plus interpretation of the pattern in the ratios. Compute each ratio, average them, compute the aggregate weighted mean, and divide. Then look at how the ratios change as sale prices rise.
Background Knowledge
The PRD is the mean ratio divided by the weighted mean ratio, where the weighted mean equals total assessed value divided by total sale price. A PRD above 1 occurs when higher-priced properties have lower ratios, a regressive pattern. Conclusions about the whole population or legal compliance need more evidence than a four-sale sample.
Real-World Application
An assessment reviewer studies four sales and sees low-priced homes assessed above sale price and high-priced homes well below it. The PRD of about 1.09 flags possible regressivity for study with a larger sample.
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
Previous Question
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?
Next Question
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?