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 majority of employees have incomes that deviate by $20,000 from the mean income. the highest income in the corporation is $80,000. the middle 50% of employees have incomes that vary by $30,000. the standard deviation indicates that all employees have incomes within $20,000 of the mean.

Explanation:

Step1: Recall measure - spread definitions

The inter - quartile range (IQR) represents the middle 50% of the data. The standard deviation measures how much the data deviates from the mean.

Step2: Analyze each statement

• The standard deviation of $20,000 means the incomes that deviate by $20,000 from the mean. This is correct as per the definition of standard deviation.
• The IQR of $30,000 means the middle 50% of employees have incomes that vary by $30,000. This is correct as IQR is the range between the first and third quartiles which contains the middle 50% of data.

Answer:

1. The incomes that deviate by $20,000 from the mean income.
2. The middle 50% of employees have incomes that vary by $30,000.