Question 63

A large difference between mean and median shows there are outliers to assess.

Using both the mean and median in salary evaluations helps identify the presence of outliers. If the mean is significantly higher or lower than the median, it indicates that extreme values are affecting the average salary, warranting further investigation.

A) A large difference between mean and median shows that some employees need raises.

This option is incorrect because a disparity between the mean and median does not directly indicate that employees require raises. Instead, it suggests that there are outliers influencing the average, which may or may not correlate with the need for salary adjustments.

B) A large difference between mean and median shows there are outliers to assess.

This option is correct as it highlights the importance of assessing outliers when the mean and median diverge significantly. Outliers can skew the mean, leading to a misrepresentation of the typical salary within the department, thus necessitating further evaluation.

C) A large difference between mean and median shows an abnormal standard deviation.

While a large difference can indicate variability in the data, it does not specifically point to an abnormal standard deviation. This choice misinterprets the relationship between these statistical measures, as the difference between mean and median primarily reflects the impact of outliers rather than the standard deviation itself.

D) A large difference between mean and median shows a miscalculation in the analysis.

This option is incorrect because a difference between the mean and median does not necessarily imply an error in calculation. It can be a natural occurrence in datasets with outliers, and thus, it should prompt further analysis rather than suggest miscalculation.

Conclusion

The choice of option B is justified, as it accurately identifies that the presence of outliers is the primary reason for a significant difference between the mean and median in salary evaluations. The other options either misinterpret the implications of the statistical measures or fail to address the core issue of outlier assessment, making them less relevant in this context.