A random variable with a mean equal to 6.0 and a standard deviation of 1.5 has a coefficient of variation equal to ________.
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A. B. C. D. E.Explanation
The coefficient of variation equals the ratio of the standard deviation to the mean.
The coefficient of variation (CV) is a measure of relative variability and is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. It is used to compare the variability of different random variables.
To calculate the coefficient of variation, we divide the standard deviation by the mean and multiply by 100:
CV = (standard deviation / mean) * 100
In this case, the random variable has a mean of 6.0 and a standard deviation of 1.5. Plugging these values into the formula, we get:
CV = (1.5 / 6.0) * 100
Simplifying the expression, we have:
CV = 0.25 * 100
CV = 25
Therefore, the coefficient of variation is 25%. However, none of the available answer choices match this result.