Final answer:
The statement that best describes the relationship between pools of data with different frequencies of claims and numbers of exposures is B) The pool with a greater standard deviation of claims is riskier due to higher variability. Higher standard deviation indicates more spread and thus greater risk, while lower standard deviation suggests less variability and potentially lower risk.
Step-by-step explanation:
The relationship between pools of data with different frequencies of claims and numbers of exposures can be described by their variability, which is measured by the standard deviation. A pool with a higher standard deviation indicates a greater spread around the mean, which typically signifies higher variability and therefore more risk. Conversely, a pool with a lower standard deviation suggests that claims are more consistently near the mean, indicating less variability and potentially less risk. However, risk is also influenced by the frequency of events and the number of exposures, not just variability.
A pool with a greater standard deviation of claims is considered riskier ('B' is the correct choice) due to higher variability—as the claims are more spread out around the mean, the uncertainty for an insurer, for example, increases as predictions about future claims become less certain. On the other hand, if the standard deviation is zero, all data values are the same, and there is no variability. This is a highly predictable (and thus less risky) scenario for most risk-related industries.
Using the standard deviation is crucial because it can provide insights into the risk profiles of different cohorts, especially in studies such as epidemiological research or insurance claims analysis where comparing different groups with different frequencies and exposures is common.