Five closed sales have sale-to-final-list-price ratios of 0.94, 0.97, 1.00, 1.02 and 1.05. What is the arithmetic mean of those individual ratios, to three decimal places?
Correct Answer
C) 0.996
The five ratios sum to 4.98, and 4.98 ÷ 5 = 0.996. The median is 1.000 and the midrange (0.94 + 1.05) ÷ 2 is 0.995; both are different statistics. Dividing by 4 instead of 5 gives 1.245. Use the same population, period and price/listing definition throughout; this statistic alone does not establish causation or a future selling period.
Why This Is the Correct Answer
Option C is correct because the five ratios sum to 0.94 + 0.97 + 1.00 + 1.02 + 1.05 = 4.98, and 4.98 / 5 = 0.996. The arithmetic mean uses all the observations and divides by the count of observations.
Why the Other Options Are Wrong
Option A: 0.995
Option A is wrong because 0.995 is the midrange, not the mean: (0.94 + 1.05) / 2 = 0.995. The midrange uses only the lowest and highest values, while the mean is 4.98 / 5 = 0.996.
Option B: 1.000
Option B is wrong because 1.000 is the median, the middle value of the ordered ratios. The question asks for the arithmetic mean, which is 4.98 / 5 = 0.996.
Option D: 1.245
Option D is wrong because 1.245 comes from dividing the sum by 4 instead of 5: 4.98 / 4 = 1.245. There are five sales, so the mean is 4.98 / 5 = 0.996.
Mean uses all, median middle
Mean uses all the values divided by how many there are; median is the middle one; midrange is just the two ends averaged.
How to use: Use this to match each answer choice to the statistic that produced it.
Exam Tip
Before calculating, count the observations; dividing by the wrong count is a common trap built into distractors.
Common Mistakes to Avoid
- -Reporting the median or midrange when the mean is requested
- -Dividing the sum by the wrong number of observations
- -Treating one ratio statistic as proof of a future selling period
Concept Deep Dive
Analysis
This question tests whether you can compute an arithmetic mean and distinguish it from other measures of central tendency such as the median and midrange. Add all five ratios, divide by the number of observations (5), and round to three decimals.
Background Knowledge
The mean, median and midrange are different measures of location: the mean averages all values, the median is the middle ordered value, and the midrange averages the extremes. Sale-to-list price ratios help indicate negotiating conditions, but the statistic should be computed on a consistent population and period and does not by itself establish causation or a future selling period.
Real-World Application
An appraiser summarizes five recent competing sales and their sale-to-final-list-price ratios. Reporting the mean of 0.996 alongside the median of 1.000 lets the reader see that sales generally closed near final list price.
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