To infer details about the data from a box plot, we can make the following observations based on typical characteristics of box plots:
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The mean is equal to the median: This is generally not true unless the data is symmetrically distributed. Without seeing the actual box plot, we cannot confirm this.
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The mean is probably more than 30 mph: This could be inferred if the right whisker (upper range) of the box plot extends significantly above 30 mph, indicating that there are higher speeds that could pull the mean upwards.
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If an officer captures an additional speed of 70 mph, the median must change: The median is the middle value, and adding a speed of 70 mph (which is likely above the current median value) could shift the median, especially if the new value would affect the middle of the sorted data set.
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The mean is probably less than 30 mph: This could be inferred if the left whisker (lower range) of the box plot and the box itself suggest a concentration of data on the lower end, making it possible that the average is pulled down.
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If an officer captures an additional speed of 70 mph, the mean must change: This is true as the mean is influenced by changes in the dataset, especially if 70 mph is an outlier or significantly different from the others.
Based on the usual characteristics of box plots, the most reasonable selections would likely be:
- The mean is probably more than 30 mph. (if the data shows skewness to the right)
- If an officer captures an additional speed of 70 mph, the median must change. (if 70 mph is above the current median)
- If an officer captures an additional speed of 70 mph, the mean must change.
So the correct responses to select, without seeing the box plot but based on typical characteristics, would likely be the last two statements regarding changes in mean and median when adding a high speed. The inference about the mean being more or less than 30 mph cannot be definitively made without the box plot context.
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