Assessment-to-sale ratios are 0.94, 1.09, 0.98, 1.03, 1.06. Compute the median; order the observations first and average the two middle values if n is even. Report as a decimal ratio to three places.
Correct Answer
D) 1.030
Ordered values: 0.94, 0.98, 1.03, 1.06, 1.09. The middle observation is 1.03. Common errors: taking the middle value of the unordered list gives 0.980; using the mean instead of the median gives 1.020; using the midrange instead of the median gives 1.015.
Why This Is the Correct Answer
Option D is correct because ordering the ratios gives 0.94, 0.98, 1.03, 1.06, 1.09. With five observations, the middle (third) value is 1.03, reported as 1.030. Two ratios fall below it and two above.
Why the Other Options Are Wrong
Option A: 0.980
Option A, 0.980, is the middle (third) value of the list as originally written, 0.94, 1.09, 0.98, 1.03, 1.06. After sorting, the third value is 1.030.
Option B: 1.015
Option B, 1.015, is the midrange, the average of the lowest and highest ratios: (0.94 + 1.09) ÷ 2 = 1.015. The median is the middle ordered value, 1.030.
Option C: 1.020
Option C, 1.020, is the mean: (0.94 + 1.09 + 0.98 + 1.03 + 1.06) ÷ 5 = 5.10 ÷ 5 = 1.020. The median is the middle ordered value, 1.030.
Sort first, then split
Before splitting the data in half to find the median, sort it; the unsorted middle is just a random value.
How to use: Use this reminder whenever ratios or prices are listed out of order.
Exam Tip
When several options are close together, identify which one each measure produces: unsorted middle, mean, midrange and true median.
Common Mistakes to Avoid
- -Taking the middle value of the unsorted list
- -Using the mean instead of the median
- -Using the midrange instead of the median
Concept Deep Dive
Analysis
This question tests finding the median of assessment ratios presented out of order. Sorting is essential, and then the third of five values is the median. Several distractors come from using a different measure of center.
Background Knowledge
In ratio studies, the median assessment-to-sale ratio is a primary measure of the overall assessment level. It is preferred in many analyses because it resists the influence of extreme ratios. Computing it correctly requires ordering the ratios first.
Real-World Application
An assessment analyst reviewing five sales in a district sorts the ratios and finds a median of 1.030. She uses it as the measure of assessment level for that group rather than the mean, which a single high ratio could distort.
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