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

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 incorrect.

Step2: Understand inter - quartile range (IQR)

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

Step3: Understand standard deviation

The standard deviation of $20,000$ does not mean that all employees have incomes within $20,000$ of the mean or that the majority of employees have incomes that deviate by exactly $20,000$ from the mean. In a normal distribution, about 68% of data is within one standard - deviation of the mean, but we don't know if the income distribution is normal. So the statements "The majority of employees have incomes that deviate by $20,000$ from the mean income" and "The standard deviation indicates that all employees have incomes within $20,000$ of the mean" are incorrect.

Answer:

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