Chapter 1, Problem 156E

To determine

To find: The numerical and graphical summary for the provided data of two types of vehicles and a short summary of the major features of this distribution.

Answer to Problem 156E

Solution: The five-number summary for the provided data is shown below:

Car	Minimum	First Quartile	Median	Third Quartile	Maximum
Small Cars	33.00	33.75	34.00	37.00	50.00
Sporty Cars	29.00	29.00	30.00	31.00	33.00

From the boxplot, it can be said that the distribution of the small cars and sporty cars are right skewed with two outliers and symmetric respectively.

Explanation of Solution

Calculation: The numerical summary of the two types of vehicles are provided through the five-number summary. To obtain the five-number summary, follow the below mentioned steps in Minitab software.

Step 1: Enter the observations in the Minitab worksheet.

Step 2: Go to Stat $\to$ Basic Statistics $\to$ Display Descriptive Statistics.

Step 3: Select “MPG” in the variable option. And select “Car_Class” under “By variable” option.

Step 4: Click on the Statistics button.

Step 5: Select minimum, maximum, first quartile, third quartile and median.

Step 6: Click OK.

The below table shows the five number summary of the two types of cars.

Car	Minimum	First Quartile	Median	Third Quartile	Maximum
Small Cars	33.00	33.75	34.00	37.00	50.00
Sporty Cars	29.00	29.00	30.00	31.00	33.00

Graph: To draw the side-by-side boxplots, the below steps are followed in Minitab software.

Step 1: Enter the data in Minitab.

Step 2: Go to “Graph” and select “Boxplot”.

Step 3: Select “With Groups” under “One Y”. Then click on OK.

Step 4: Select the variables “MPG” and “Car_Class” in the “Graph variables” and “Categorical variables for grouping” respectively.

Step 5: Click OK.

The obtained boxplot is shown below.

From the obtained boxplot, it can be said that the data of small cars has two outliers and the distribution is right skewed. But the data on the fuel efficiency of the sporty cars is more or less symmetric according to the boxplot and the data does not have any outliers.

Interpretation: The distribution of fuel efficiency of small cars and sporty cars are right skewed and symmetric respectively.