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Comparing measures of center and variation The salaries of the employees at four companies are summarized below. Answer the questions about them. Company A: The mean salary is \( \$ 24,000 \) and the range of salaries is \( \$ 53,000 \). Company B: The mean salary is \( \$ 23,000 \) and the range of salaries is \( \$ 57,000 \). Company C: The mean salary is \( \$ 16,000 \) and the range of salaries is \( \$ 51,000 \). Company D: The mean salary is \( \$ 22,000 \) and the range of salaries is \( \$ 58,000 \). (a) Based on the information above, which company's salaries have the most variability? O Company A Company B (b) Based on the information above, which company has the highest salaries on average? O Company A Company B Company C

Ask by Parsons Donnelly. in the United States
Mar 08,2025

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Answer

**(a)** Company D has the most variability. **(b)** Company A has the highest salaries on average.

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**(a)** To determine variability, we compare the range (the difference between the highest and lowest salaries) for each company: - Company A: Range = \( \$53,\!000 \) - Company B: Range = \( \$57,\!000 \) - Company C: Range = \( \$51,\!000 \) - Company D: Range = \( \$58,\!000 \) Since \( \$58,\!000 \) is the largest range, Company D has the most variability. **(b)** To determine which company has the highest salaries on average, we compare the mean salaries: - Company A: Mean = \( \$24,\!000 \) - Company B: Mean = \( \$23,\!000 \) - Company C: Mean = \( \$16,\!000 \) - Company D: Mean = \( \$22,\!000 \) Since \( \$24,\!000 \) is the highest mean, Company A has the highest salaries on average.

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The company with the most variability in salaries is determined by the range of salaries. Company D has the widest range of \( \$ 58,000 \), indicating the highest variability among the salaries it offers. So, for question (a), the answer is: Company D. For the highest average salaries, we look at the mean values. Company A leads the pack with a mean salary of \( \$ 24,000 \), which is the highest compared to all other companies. Therefore, for question (b), the answer is: Company A.

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