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?
Answer:
If the extreme outlier, which is the electric car with an electricity usage equivalent to 112 miles per gallon, is removed from the dataset, the standard deviation and the interquartile range (IQR) will be affected as follows:
1. Standard Deviation:
The standard deviation measures the spread or variability of the data points from the mean. When the extreme outlier is removed, the overall spread of the data will likely decrease, resulting in a lower standard deviation. This is because the extreme value was pulling the standard deviation upwards due to its large difference from the other data points.
2. Interquartile Range (IQR):
The IQR is a measure of statistical dispersion, specifically the range between the first quartile (Q1) and the third quartile (Q3) of the data. The removal of the extreme outlier will not have a significant impact on the IQR, as the IQR focuses on the middle 50% of the data, which is less influenced by extreme values.
However, it is important to note that the specific impact on the standard deviation and IQR would depend on the values of the remaining data points. Removing an outlier does not guarantee a predictable change in these measures, as they are influenced by the entire dataset.
In summary, removing the extreme outlier, the electric car with an electricity usage equivalent to 112 miles per gallon, would likely result in a decrease in the standard deviation, while the impact on the IQR would be minimal.