Question

question 4 of 5
iqr
standard deviation
answer bank
this is the range of the middle half of differences in mpg (highway - city) for 21 model year 2020 midsize cars.
this tells us the amount by which the difference in mpg (highway - city) for 21 model year 2020 midsize cars typically varies from the mean difference.
this is the difference between the largest and smallest difference in mpg (highway - city) for 21 model year 2020 midsize cars.
which is the more appropriate measure of variability for this distribution: the interquartile range or the standard deviation?

Explanation:

The inter - quartile range (IQR) is the range of the middle half of the data. It is calculated as the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). The standard deviation measures the amount by which individual data points typically vary from the mean. If the data has outliers, the IQR is a more robust measure of variability as it is not affected by extreme values, while the standard deviation is sensitive to outliers. Without knowing the distribution of the MPG differences (if it has outliers or not), we note the definitions. For the IQR, it is the range of the middle half of differences in MPG. For the standard deviation, it tells us the amount by which the difference in MPG typically varies from the mean difference.

Answer:

IQR: This is the range of the middle half of differences in MPG (highway - city) for 21 model year 2020 midsize cars.
Standard deviation: This tells us the amount by which the difference in MPG (highway - city) for 21 model year 2020 midsize cars typically varies from the mean difference.