45. A manager has been asked to evaluate the risk of loss for a new business strategy. The manager plots the results of several simulated projections to determine the likelihood of a result being a loss. Which statistic will transform different data sets to the same scale so that the manager can compare the projections?
Answer: D
The Z-score will transform different data sets to the same scale for comparison.
Using the Z-score allows the manager to standardize the different simulated projections, enabling a direct comparison of their likelihood of resulting in a loss.
A) Mode
The mode represents the value that appears most frequently in a data set. While it provides information about the most common outcome, it does not standardize data across different scales, making it ineffective for comparing the likelihood of losses across varying projections.
B) Variance
Variance measures the spread of data points around the mean but does not transform data sets to a common scale. It shows how much the data varies, but it does not facilitate direct comparisons of loss likelihood between different projections.
C) Median
The median indicates the middle value of a data set when ordered, offering insights into the central tendency. However, like the mode and variance, it does not standardize data sets, which is necessary for comparing the risk of loss across various projections.
D) Z-score
The Z-score standardizes different data sets by indicating how many standard deviations a data point is from the mean. This transformation allows the manager to compare projections on a common scale, making it the most suitable option for evaluating the risk of loss in this context.
Conclusion
The Z-score is the only option that standardizes different data sets, allowing for a meaningful comparison of the likelihood of losses in the manager's projections. All other options fail to provide a scale transformation necessary for effective evaluation, thus making the Z-score the definitive choice for this analysis.