Coefficient of Variance: Relative Risk Measure

The question asks for a measure of relative risk, calculated as the standard deviation divided by the expected value.

Identifying the Correct Measure

• Standard Deviation ($\sigma$): Measures the dispersion of data points around the mean.
• Expected Value ($\mu$): The mean or average of a probability distribution.
• Relative Risk: Risk expressed as a proportion or percentage of the baseline risk, allowing comparison across different scales.

Coefficient of Variance (CV) Explained

The Coefficient of Variance (CV), also known as relative standard deviation, fits this description precisely.

• It is calculated as the ratio of the standard deviation to the mean (expected value).
• The formula is:

  $ CV = \frac{\sigma}{\mu} $

  or

  $ CV = \frac{\text{Standard Deviation}}{\text{Expected Value}} $

• CV expresses variability relative to the mean, making it useful for comparing the risk or variability of datasets with different units or vastly different mean values. It's a unitless measure, often expressed as a percentage.

Analyzing Other Options

• Variance: This is the square of the standard deviation ($\sigma^2$). It measures absolute variability, not relative risk, and has units that are the square of the original data.
• Co-Variance: This measures how two variables change together. It is not a measure of relative risk for a single variable and is dependent on the units of both variables.
• Geometric Mean: This is a type of average, calculated by multiplying the terms and taking the nth root. It's typically used for averaging rates or ratios, not for measuring relative risk in this manner.

Therefore, the Coefficient of Variance is the correct measure.