Assessment-to-sale ratios are 0.88, 0.94, 0.98, 1.02, 1.08, 1.22. Compute the arithmetic mean. Report as a decimal ratio to three places.
Correct Answer
B) 1.020
Sum=6.12; n=6; mean=6.12/6=1.02. Common errors: using the median instead of the mean gives 1.000; using the midrange instead of the mean gives 1.050; dividing by 5 instead of 6 gives 1.224.
Why This Is the Correct Answer
Option B is correct because the six ratios sum to 0.88 + 0.94 + 0.98 + 1.02 + 1.08 + 1.22 = 6.12. Dividing by n = 6 gives 6.12 / 6 = 1.020. That is the arithmetic mean ratio.
Why the Other Options Are Wrong
Option A: 1.000
Option A, 1.000, is the median, the average of the two middle values (0.98 + 1.02) / 2. The arithmetic mean is 6.12 / 6 = 1.020.
Option C: 1.050
Option C, 1.050, is the midrange, the average of the lowest and highest values (0.88 + 1.22) / 2. The arithmetic mean uses all six values: 6.12 / 6 = 1.020.
Option D: 1.224
Option D, 1.224, divides the sum by 5 instead of 6 (6.12 / 5). There are six ratios, so the mean is 6.12 / 6 = 1.020.
Add all, divide by count
The mean adds every value and divides by how many values there are.
How to use: Use this to check that you used every value and the correct count when computing a mean.
Exam Tip
Count the observations before dividing; a wrong divisor is a common built-in distractor.
Common Mistakes to Avoid
- -Dividing by the wrong number of observations
- -Reporting the median when the mean is asked
- -Averaging only the highest and lowest values
Concept Deep Dive
Analysis
This question tests the arithmetic mean of six ratios. You add all six values and divide by six. The distractors come from computing the median, the midrange, or dividing by the wrong count.
Background Knowledge
The arithmetic mean is the sum of all values divided by the number of values. In ratio studies it is one of several measures of appraisal level, alongside the median and weighted mean, and it is more sensitive to extreme ratios than the median.
Real-World Application
An appraiser reviewing six assessment ratios for a neighborhood computes a mean of 1.020 and a median of 1.000. The gap reminds the appraiser that the high 1.22 ratio pulls the mean upward.
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