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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?

(1 point)
Responses

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

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.

1 answer

To accurately compare the distributions represented by the box plots, we can analyze their typical characteristics such as median, spread, and the presence of outliers.

  1. If the box plot for 'Without Insurance' shows a higher median and a wider range compared to 'With Insurance', we could conclude that cars without insurance were typically more expensive to repair.

  2. If the 'With Insurance' plot shows most of its data points below $300, this suggests that insurance helps keep repair costs lower.

Based on the statements given, here are the key comparisons:

  • The first two statements revolve around the average or likelihood of higher costs for repairs without insurance.
  • The third statement claims insurance always leads to lower costs, which may not be true if there are instances where the cost is close or overlaps.
  • The fourth statement suggests that most repairs with insurance are below $300, which aligns with expectations of insurance helping cover costs.

Without seeing the actual box plots, we can't definitively state one of these options as correct. However, if the data shown in the box plots confirms these interpretations, the most accurate statement is likely to be:

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

This indicates that without insurance, costs tend to be greater, aligning with common knowledge about repairs and the influence of insurance.