The arithmetic mean is $480,000 and sample standard deviation is $36,000. Compute the coefficient of variation s/mean × 100, expressed as a percentage. Report three decimals.
Correct Answer
A) 7.500%
36000/480000×100=7.5%. The mean is positive and the requested reporting convention is explicit; a ratio and its percentage form differ by a factor of 100.
Why This Is the Correct Answer
Option A is correct because CV = $36,000 / $480,000 x 100 = 0.075 x 100 = 7.500%. A ratio and its percentage form differ by a factor of 100, and the question asks for the percentage.
Why the Other Options Are Wrong
Option B: 0.075%
Option B, 0.075%, is the decimal ratio $36,000 / $480,000 = 0.075 labeled as a percentage without multiplying by 100. The correct result is 0.075 x 100 = 7.500%.
Option C: 13.333%
Option C, 13.333%, inverts the ratio, $480,000 / $36,000 = 13.333, dividing the mean by the standard deviation. The correct calculation is $36,000 / $480,000 x 100 = 7.500%.
Option D: 0.750%
Option D, 0.750%, comes from a place-value slip in the division: $36,000 / $480,000 is taken as 0.0075 instead of 0.075, and 0.0075 x 100 = 0.750%. The correct ratio is 0.075, so the CV is 0.075 x 100 = 7.500%.
Spread Over Mean, Times 100
Put the standard deviation over the mean, then multiply by 100 to get the percentage.
How to use: Use this formula phrase to avoid inverting the ratio or skipping the percentage step.
Exam Tip
Check whether the question wants a decimal ratio or a percentage, and confirm the smaller number is on top.
Common Mistakes to Avoid
- -Forgetting to multiply the ratio by 100
- -Dividing the mean by the standard deviation
- -Misplacing the decimal when dividing the standard deviation by the mean
Concept Deep Dive
Analysis
This question tests calculation of the coefficient of variation as a percentage. The standard deviation is divided by the mean and multiplied by 100, exactly once. The distractors come from skipping the multiplication, misplacing a decimal in the division, or inverting the ratio.
Background Knowledge
The sample coefficient of variation is the ratio of the standard deviation to the mean, often expressed as a percentage. Because it scales spread to the level of the data, it allows variability to be compared across data sets with different means.
Real-World Application
An appraiser computes a CV of 7.5% for adjusted sale prices with a mean of $480,000 and a standard deviation of $36,000. This relatively low figure suggests the adjusted comparables point to a fairly consistent value range.
More Statistics Questions
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