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.
Correct Answer
A) 1.150
Price relative = 460000 / 400000 = 1.15. The percentage change would instead subtract one and multiply by 100; this task asks for the relative, not the change.
Why This Is the Correct Answer
Option A is correct because the price relative is the current median divided by the base median. $460,000 / $400,000 = 1.150. A relative above 1 shows that prices rose between the two periods.
Why the Other Options Are Wrong
Option B: 0.150
Option B, 0.150, subtracts 1 from the relative (1.150 - 1), which is the decimal form of the percentage change. The question asks for the relative itself, $460,000 / $400,000 = 1.150.
Option C: 0.870
Option C, 0.870, inverts the fraction: $400,000 / $460,000 = 0.870. The relative is defined as current divided by base, $460,000 / $400,000 = 1.150.
Option D: 1.000
Option D, 1.000, would mean no change between periods, which does not follow from the facts. The median rose from $400,000 to $460,000, so the relative is 1.150.
New over old
A price relative puts the new (current) price over the old (base) price.
How to use: Use this phrase to set up the fraction correctly in time-trend calculations.
Exam Tip
Check whether the question asks for a relative or a percentage change; both are usually offered as choices.
Common Mistakes to Avoid
- -Reporting the percentage change when the relative is asked
- -Dividing base by current instead of current by base
- -Forgetting that a relative above 1 means an increase
Concept Deep Dive
Analysis
This question tests the difference between a price relative and a percentage change. A price relative is current divided by base. The distractors subtract 1, invert the fraction, or ignore the change.
Background Knowledge
A price relative compares a later price level with an earlier one by dividing current by base. Subtracting 1 and multiplying by 100 converts it to a percentage change; appraisers use such relatives when analyzing market conditions over time.
Real-World Application
An appraiser studying market conditions finds the area median sale price rose from $400,000 to $460,000. The price relative of 1.150 helps the appraiser describe the market trend, which, with other evidence, supports a market conditions analysis.
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Previous Question
The assessment-to-sale ratios are 0.9, 0.94, 0.98, 1.02, 1.06, 1.1. 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.
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Observed sale prices are $80,000, $90,000, $100,000, $110,000. Calculate the range (maximum−minimum), to the nearest dollar.