Question

a financial analyst is examining the income distribution of employees in a large corporation. the analyst finds that the range of incomes is $80,000, the interquartile range (iqr) is $30,000, and the standard deviation is $20,000. based on these measures of spread, select two correct answers. the highest income in the corporation is $80,000. the majority of employees have incomes that deviate by $20,000 from the mean income. the standard deviation indicates that all employees have incomes within $20,000 of the mean. the middle 50% of employees have incomes that vary by $30,000.

Explanation:

Step1: Understand range

The range is the difference between the highest and lowest values. Just knowing the range is $80,000$ doesn't mean the highest income is $80,000$. So the statement "The highest income in the corporation is $80,000$" is wrong.

Step2: Understand standard - deviation

The standard deviation of $20,000$ doesn't mean that all employees have incomes within $20,000$ of the mean or that the majority deviate by exactly $20,000$ from the mean. Standard - deviation is a measure of the spread around the mean, but not all data points are within one standard - deviation.

Step3: Understand inter - quartile range

The inter - quartile range (IQR) represents the middle 50% of the data. If the IQR is $30,000$, it means the middle 50% of employees have incomes that vary by $30,000$.

Answer:

The middle 50% of employees have incomes that vary by $30,000$.