How does the weighting of the weighted mean ratio differ from that of the median and the mean ratio?
Correct Answer
D) It gives equal weight to each dollar of value, not each parcel
The weighted mean gives equal weight to each dollar of value in the sample, whereas the median and mean give equal weight to each parcel.
Why This Is the Correct Answer
Option D is correct because the weighted mean gives equal weight to each dollar of value in the sample, whereas the median and mean give equal weight to each parcel. In practice, high-priced properties carry more influence in the weighted mean than low-priced properties. That is the key difference from the other two measures.
Why the Other Options Are Wrong
Option A: It gives each sale equal weight, in the same way as the median
Option A says the weighted mean gives each sale equal weight like the median, but equal weight per sale describes the median and mean ratio, not the weighted mean. The weighted mean weights by dollars of value, so higher-value sales count more.
Option B: It gives more weight to sales with ratios that are near 1.00
Option B says the weighted mean gives more weight to ratios near 1.00, but its weighting depends on dollar value, not on how close a ratio is to 1.00. A high-value sale with a ratio far from 1.00 still carries heavy weight.
Option C: It gives more weight to the most recent sales in the sample
Option C says the weighted mean favors the most recent sales, but sale date plays no role in its weighting. The weighting comes from each sale's dollar value in the totals.
Weighted mean counts dollars
Median and mean: one parcel, one vote. Weighted mean: one dollar, one vote.
How to use: Use this when a question asks which measure lets expensive properties dominate the result.
Exam Tip
When you see weighted mean in a ratio-study question, think total assessed value over total sale price, which weights each dollar of value equally.
Common Mistakes to Avoid
- -Assuming the weighted mean weights each parcel equally like the median
- -Thinking the weighting is based on sale recency
- -Believing ratios close to 1.00 receive extra weight
Concept Deep Dive
Analysis
This question tests how the three common ratio-study measures of central tendency weight the observations. The median and the mean ratio treat each parcel as one equal observation, while the weighted mean is built from total assessed value divided by total sale price. Because larger-value sales contribute more dollars to those totals, the weighted mean gives equal weight to each dollar of value rather than to each parcel.
Background Knowledge
In a ratio study, the mean ratio averages the individual assessment-to-sale ratios, the median is the middle ratio, and the weighted mean divides total assessed value by total sale price. Because the weighted mean works from dollar totals, it reflects the overall level of value in dollar terms. Comparing it with the mean and median can reveal whether high-value and low-value properties are assessed at different levels.
Real-World Application
An assessor's ratio study includes several luxury homes with low ratios and many modest homes near 1.00. The weighted mean comes out noticeably below the median because the luxury sales contribute so many dollars. The analyst notes the gap as a possible sign that higher-value properties are under-assessed relative to lower-value ones.
More Statistics Questions
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