Question

question 8 points 2

in a survey of 50 employees at a company, one executive earns $1,200,000 per year. half of the remaining employees earn $50,000 per year, and the rest earn $55,000 per year. which is the better measure of the \center\ of this data set?

mean

median

Explanation:

Analyze the data distribution

Using the Outlier Effects knowledge point

• Total employees: \(50\)
• One executive earns: \(\$1,200,000\) (extreme outlier)
• Remaining employees: \(49\)
• Half of the remaining (\(24.5\) or approximately \(24\) to \(25\) employees) earn \(\$50,000\)
• The rest earn \(\$55,000\)

Compare measures of center

Using the Measures of Center knowledge point

• The mean is highly sensitive to extreme values and will be pulled upward by the \(\$1,200,000\) salary, making it unrepresentative of a typical employee's earnings.
• The median is resistant to outliers and will lie between \(\$50,000\) and \(\$55,000\), which accurately reflects the center of the vast majority of the data.
• Therefore, the median is the better measure of center.

Answer:

• Mean
• Median (Correct answer)