Question

maki observed that the range in his monthly commuting expenses was $60. the standard deviation was $20, and the iqr was $25. based on these measures of spread, which statement is true? maki spends an average of $60 on his commute every month. the middle 50% of the months, makis transportation costs varied by a small margin of $25. makis commuting expenses change by exactly $20 each month. every month, maki spends the same amount on commuting.

Explanation:

Step1: Recall measure - spread concepts

Range is the difference between the maximum and minimum values. Standard deviation measures the average amount by which data points deviate from the mean. IQR (Inter - Quartile Range) is the range of the middle 50% of the data.

Step2: Analyze each statement

• The average of $60$ is just the mean. The range being $60$ doesn't mean the average is $60$ in a way that implies consistency.
• The middle 50% of the months having transportation costs varied by a small margin is consistent with an IQR of $25$. IQR represents the spread of the middle 50% of the data.
• A standard deviation of $20$ doesn't mean the expenses change by exactly $20$ each month. Standard deviation is an average measure of deviation from the mean.
• If the range is $60$, it is not true that he spends the same amount every month.

Answer:

The middle 50% of the months, Makhi's transportation costs varied by a small margin of $25$.