Question

1. fuel economy the boxplot shows the fuel economy ratings for 67 subcompact cars. some summary statistics are also provided. the extreme outlier is the mitsubishi i - miev, an electric car whose electricity usage is equivalent to 112 miles per gallon.

combined fuel economy

mean stdev min q1 med q3 max n
23.76 11.87 14 20 22 25 112 67

if that electric car is removed from the data set, how will the standard deviation be affected? the iqr?

1. test scores correction after entering the test scores from her statistics class of 25 students, the instructor calculated

Explanation:

Step1: Understand the impact on standard - deviation

The standard deviation measures the spread of data from the mean. An outlier like the electric car with a value of 112 (far from the other values) increases the spread. Removing it will decrease the spread of the data values from the mean. So, the standard deviation will decrease.

Step2: Understand the impact on IQR

The inter - quartile range (IQR) is \(Q3 - Q1\). The outlier is an extreme value and does not affect the calculation of the quartiles \(Q1\) and \(Q3\) (since quartiles are based on the position of data values in an ordered list and not on the actual extreme values far from the middle 50% of the data). So, the IQR will remain the same.

Answer:

The standard deviation will decrease. The IQR will remain the same.