The arithmetic mean is $400,000 and sample standard deviation is $20,000. Compute the coefficient of variation s/mean, expressed as a decimal ratio. Report three decimals.
Correct Answer
C) 0.050
20000/400000=0.05. 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 C is correct because the coefficient of variation is s ÷ mean = $20,000 ÷ $400,000 = 0.050. The stem asks for a decimal ratio to three places, so 0.050 is the required form.
Why the Other Options Are Wrong
Option A: 5.000
Option A, 5.000, is the percentage form (0.050 × 100 = 5), not the decimal ratio the stem requests. The decimal ratio is $20,000 ÷ $400,000 = 0.050.
Option B: 20.000
Option B, 20.000, inverts the ratio: $400,000 ÷ $20,000 = 20. The coefficient of variation is $20,000 ÷ $400,000 = 0.050.
Option D: 0.500
Option D, 0.500, comes from a place-value slip that reads the mean as $40,000: $20,000 ÷ $40,000 = 0.500. With the stated mean of $400,000, the ratio is $20,000 ÷ $400,000 = 0.050.
Decimal or percent, read twice
The same COV can appear as 0.050 or 5.0%. Read the stem to see which form it wants.
How to use: Use this when answer choices differ by a factor of 100.
Exam Tip
When two choices differ by exactly 100 times, the reporting form in the stem decides between them.
Common Mistakes to Avoid
- -Reporting the percentage when a decimal ratio is requested
- -Dividing the mean by the standard deviation
- -Dropping a zero from one of the figures
Concept Deep Dive
Analysis
This question tests the coefficient of variation and the importance of the requested reporting form. Divide the standard deviation by the mean and report the result as a decimal ratio, not a percentage.
Background Knowledge
The coefficient of variation is the ratio of the standard deviation to the mean. It can be reported as a decimal or as a percentage, and the two forms differ by a factor of 100. It is meaningful when the mean is positive.
Real-World Application
A reviewer asks an appraiser to report price dispersion as a decimal for a spreadsheet model. The appraiser enters 0.050 rather than 5, so the model's later calculations are not off by a factor of 100.
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