An auditor published the salaries of each employee from the CEO to the interns at Speedy Shipping Co. and at Northern Parcel Express. The salaries are summarized in histograms. Which statement best compares the median salaries at the two companies?

(1 point)
Responses

A. The companies have the same median salary because both datasets are skewed right.

B. Speedy Shipping Co. has the greater median salary because the overall salaries are higher, and the data is not as far skewed to the right as Northern Parcel Express.

C. The companies have same median salary because both datasets are symmetric and have the same mean and median.

D. Northern Parcel Express has the greater median salary because the data is skewed left, showing a higher median than Speedy Shipping Co.

1 answer

To compare the median salaries of the two companies based on the provided statements, we need to consider the characteristics of median and the implications of skewness:

A. The companies having the same median salary because both datasets are skewed right is not necessarily true since skewness does not determine equality in medians.

B. Speedy Shipping Co. having a greater median salary because overall salaries are higher and less skewed to the right than Northern Parcel Express implies that the medians could be different, which aligns logically. This statement appears plausible.

C. This option claims that both datasets are symmetric and have the same mean and median. This is not true unless specifically stated, and without visualizations or data validation, we cannot assume the medians are equal.

D. Saying Northern Parcel Express has a greater median salary because the data is skewed left is generally inaccurate because skewness affects the mean more than the median, and a left skew typically implies the median would be lower than a right-skewed dataset with higher salaries.

Based on this analysis, the best option to compare the medians given the skewness and characteristics of the salaries is:

B. Speedy Shipping Co. has the greater median salary because the overall salaries are higher, and the data is not as far skewed to the right as Northern Parcel Express.