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Two box plots, titled ‘Cost of Repairs’, are placed one above the other on a number line, from 0 to 7 in increments of ten, labeled ‘hundreds of dollars’. The top box plot is labeled ‘With Insurance’ and the bottom is labeled ‘Without Insurance’.

These box plots summarize the cost of repairs at a car shop. Which statement best compares the distributions?

Responses

Cars without insurance were more likely to have a higher repair cost.
Cars without insurance were more likely to have a higher repair cost.

Cars with insurance always had a lower repair cost.
Cars with insurance always had a lower repair cost.

Most repairs for cars with insurance were less than $300.
Most repairs for cars with insurance were less than $300.

The mean repair cost for a car without insurance was greater than $500.

1 answer

To determine which statement best compares the distributions shown in the box plots for the cost of repairs with and without insurance, let's analyze the likely characteristics of the two distributions based on usual patterns observed in similar datasets.

  1. Cars without insurance were more likely to have a higher repair cost.

    • Typically, cars without insurance may indicate higher risk and, consequently, higher repair costs. This statement could be true if the upper quartile of the box plot for "Without Insurance" is significantly higher than for "With Insurance."

  2. Cars with insurance always had a lower repair cost.

    • This is a definitive statement and typically would not be supported by box plots unless the medians and all quartiles of the "With Insurance" box plot are lower than the corresponding ones for "Without Insurance." "Always" implies an absolute and is less likely to be accurate in statistical comparisons.

  3. Most repairs for cars with insurance were less than $300.

    • This statement could be true if the median and upper quartile of the "With Insurance" box plot are close to or below $300.

  4. The mean repair cost for a car without insurance was greater than $500.

    • This would require specific data about the mean, which cannot be accurately inferred from box plots without additional summary statistics.

Based on common outcomes in insurance contexts, the first statement is generally likely to hold true. Therefore, the best choice among the responses provided is:

Cars without insurance were more likely to have a higher repair cost.