Question 58

The Z-score will transform different data sets to the same scale for comparison.

The Z-score is a statistical measure that indicates how many standard deviations an element is from the mean. This allows the manager to standardize different data sets, making it possible to compare the projections effectively.

A) Median

The median represents the middle value in a data set when arranged in order. While it is useful for understanding the central tendency of a data set, it does not standardize or transform different data sets to a common scale, which is essential for the manager's comparison of projections.

B) Mode

The mode is the value that appears most frequently in a data set. Similar to the median, it provides insight into the data set's distribution but fails to normalize or scale different data sets for comparison, making it inadequate for the manager's needs.

C) Variance

Variance measures the spread of a data set by calculating the average of the squared differences from the mean. While it is useful for understanding data spread, it does not transform data sets to the same scale, which is necessary for comparing different projections.

D) Z-score

The Z-score standardizes values from different data sets by indicating how far each value is from the mean in terms of standard deviations. This transformation enables the manager to compare the likelihood of losses across various projections effectively.

Conclusion

The Z-score is the appropriate choice as it allows for the comparison of projections by transforming different data sets into a common scale. The other options, while valuable in their own contexts, do not serve the purpose of standardization for effective comparison as required by the manager's evaluation of risk.