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.
Correct Answer
B) 0.978
Sum=4.89; n=5; mean=4.89/5=0.978. Common errors: using the median instead of the mean gives 0.980; dividing by 4 instead of 5 gives 1.222; using the midrange instead of the mean gives 0.975.
Why This Is the Correct Answer
Option B is correct because the five ratios sum to 0.94 + 0.96 + 0.98 + 1.00 + 1.01 = 4.89, and 4.89 ÷ 5 = 0.978. The arithmetic mean uses all observations and divides by the number of observations.
Why the Other Options Are Wrong
Option A: 0.975
Option A, 0.975, is the midrange, the average of only the lowest and highest ratios: (0.94 + 1.01) ÷ 2 = 0.975. The arithmetic mean uses all five values: 4.89 ÷ 5 = 0.978.
Option C: 0.980
Option C, 0.980, is the median, the middle value of the five ordered ratios, not the mean. The mean is 4.89 ÷ 5 = 0.978.
Option D: 1.222
Option D, 1.222, comes from dividing the sum by 4 instead of 5: 4.89 ÷ 4 = 1.2225, shown as about 1.222. There are five ratios, so the mean is 4.89 ÷ 5 = 0.978.
Add all, divide by all
The mean adds every value and divides by how many values were added. The median just picks the middle, and the midrange averages only the two ends.
How to use: Use this to separate mean, median and midrange when the answer choices are close together.
Exam Tip
Count the observations before dividing; a divisor that is off by one is a common distractor. When choices are very close, check which measure each one represents.
Common Mistakes to Avoid
- -Reporting the median when the mean is asked for
- -Dividing by one fewer than the number of observations
- -Averaging only the highest and lowest values
Concept Deep Dive
Analysis
This question tests the arithmetic mean of a set of assessment-to-sale ratios and distinguishes it from other measures of central tendency. Add all five ratios and divide by the count of five; the median and midrange are different measures that can produce nearby but different results.
Background Knowledge
The arithmetic mean is the sum of the observations divided by their number. In ratio studies it is one of several measures of the level of appraisal, alongside the median, which is the middle value of an ordered odd-numbered set. These measures describe the data and do not by themselves set a value conclusion or a statutory assessment level.
Real-World Application
An assessor's office reviews five recent sales in a neighborhood and computes the mean assessment-to-sale ratio to describe the overall level of assessment. Reporting the median instead would give a slightly different figure, so the office states which measure it used.
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.
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.
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
A ratio study produces ratios of 0.92, 1 and 1.08. Using the sample standard deviation, what is the z-score of the 1.08 ratio, to two decimals?
Next Question
Sale prices are $255,000, $280,000, $300,000, $320,000, $355,000. Using the median of each half including the overall median (Tukey hinges), Q1=$280,000 and Q3=$320,000. Compute the interquartile range Q3−Q1, to the nearest dollar.