Use the images to answer the question.

Question

A histogram is titled 'Employee Salaries at Speedy Shipping Co.' The x-axis ranges from 0 to 300,000 in increments of 60,000 and is labeled 'Salaries in Dollars.' The y-axis ranges from 0 to 5 in increments of 1 and is unlabeled.

A histogram is titled 'Employee Salaries at Northern Parcel Express.' The x-axis contains the following unit increments: 15,000, 49,000, 83,000, 117,000, 151,000, and 185,000. The y-axis ranges from 0 to 8 by 2-unit increments and is unlabeled.

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?

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

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.
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.

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

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

Answer 1

To determine which statement best compares the median salaries at Speedy Shipping Co. and Northern Parcel Express based on the provided histograms, we need to consider the shapes of the data distributions and the respective salary ranges.

1. Speedy Shipping Co. Histogram: The x-axis indicates ranges up to $300,000, and the increments suggest that the distribution may cover a wide range of salaries, potentially showing a higher concentration in the higher salary brackets. The lack of labels on the y-axis makes it difficult to identify exact frequency counts within the categories, but if the distribution skews toward lower salaries, the median will likely be lower.

2. Northern Parcel Express Histogram: The x-axis shows ranges up to $185,000, which implies overall lower salaries compared to Speedy Shipping Co., given the broader range of the latter. The y-axis shows increments of 2, suggesting there could be more frequency count in lower salary brackets, possibly indicating a left-skewed distribution if more employees are clustered at lower salary ranges.

Based on these observations, we can evaluate the statements:

• If the histogram data for Northern Parcel Express shows that a significant number of salaries are lower (resulting in left-skew), it could indicate a higher median because more data could be accumulated in the higher salary brackets relative to their right side.
• Conversely, if the salaries at Speedy Shipping Co. are higher but not as many employees are earning those wages (possibly skewed right), the median might be inflated due to the presence of outliers (very high salaries) affecting the average.

Given this, the most accurate comparison appears in this context:

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.

This indicates that while both datasets have differing distributions, Speedy Shipping Co.'s overall higher salaries, despite potential skew, would lead to a higher median than Northern Parcel Express.