Question

1. the following histograms show the distributions of fuel economy (miles per gallon) for 9 different car models and 16 different truck models that run on petroleum gasoline. compare the distributions.

group name|n|mean|sd|min|q1|med|q3|max
car|9|34.678|8.642|23|25.2|34.9|42.8|46.1
truck|16|25.444|6.573|16.7|20.75|24.3|28.55|39.8

Explanation:

Step1: Analyze central - tendency

The mean fuel - economy for cars (34.678 mpg) is higher than that for trucks (25.444 mpg), indicating on average cars have better fuel economy.

Step2: Analyze spread

The standard deviation for cars (8.642) is larger than that for trucks (6.573), meaning the fuel - economy values for cars are more spread out.

Step3: Analyze quartiles and range

The minimum, first quartile ($Q_1$), median (Med), third quartile ($Q_3$), and maximum values for cars are generally higher than those for trucks. The range for cars ($46.1 - 23=23.1$) is larger than for trucks ($39.8 - 16.7 = 23.1$), but considering the quartiles, cars have higher values across the board.

Step4: Analyze histograms

The car histogram has a more spread - out and less concentrated shape compared to the truck histogram. Trucks have a higher frequency in the lower fuel - economy range (around 20 mpg), while cars have a more even distribution across a wider range of fuel - economy values.

Answer:

On average, cars have better fuel economy than trucks. The fuel - economy values for cars are more spread out. Trucks have a higher frequency of lower fuel - economy values, while cars have a more even distribution across a wider range of values.