Question

kassandra observed that the range in her monthly grocery bills was $150. the standard deviation was $45, and the iqr was $65. based on these measures of spread, which of the following statements is true?
kassandras average monthly grocery bill was $150.
the middle 50% of the months, kassandras expenses varied by $65.
kassandras monthly grocery expenses vary by exactly $45 each month.
half of the months, kassandra had grocery expenses that differed by $150.

Explanation:

Step1: Recall the definition of IQR

The inter - quartile range (IQR) represents the middle 50% of the data.

Step2: Analyze each statement

• Statement 1: The middle 50% of the months, Kassandra's expenses varied by $65. This is correct because the IQR is a measure of the spread of the middle 50% of the data, and here the IQR is given as $65.
• Statement 2: Kassandra's average monthly grocery bill was $150. The range is not the average. The range is the difference between the maximum and minimum values. So, this statement is incorrect.
• Statement 3: Kassandra's monthly grocery expenses vary by exactly $45 each month. The standard deviation is a measure of the average amount of variation or dispersion from the mean. It does not mean that the expenses vary by exactly that amount each month. So, this statement is incorrect.
• Statement 4: Half of the months, Kassandra had grocery expenses that differed by $150. The range is $150 (difference between max and min), but it doesn't mean that half of the months have expenses that differ by $150. So, this statement is incorrect.

Answer:

The middle 50% of the months, Kassandra's expenses varied by $65.