The boxplot shows the fuel economy ratings for 67 subcompact cars with the same model year. some summary statistics are also provided. the extreme outlier is an electric car whose electricity usage is equivalent to 112 miles

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the boxplot shows the fuel economy ratings for 67 subcompact cars with the same model year. some summary statistics are also provided. the extreme outlier is an electric car whose electricity usage is equivalent to 112 miles per gallon. if that electric car is removed from the data​ set, how will the standard deviation be​ affected? the​ iqr?

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The standard deviation and interquartile range (IQR) are both measures of variability in a dataset.

If the extreme outlier, which is an electric car with an electricity usage equivalent to 112 miles per gallon, is removed from the dataset, the following changes are expected:

  • Standard deviation: The standard deviation is a measure of how spread out the values in a dataset are. Removing an extreme outlier can decrease the overall variability in the dataset, which may result in a decrease in the standard deviation. However, the extent to which the standard deviation will be affected depends on the values of the other data points in the dataset.

  • Interquartile range (IQR): The IQR is a measure of the spread of the middle 50% of the data. Since the extreme outlier is far from the other data points, removing it will not have a significant effect on the IQR. The IQR is only affected by the values within the 25th and 75th percentiles, which are not affected by the extreme outlier.

In summary, removing the extreme outlier may decrease the standard deviation, but it is unlikely to have a notable effect on the IQR.