Concept explainers
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 |
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
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
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.
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Chapter 1 Solutions
LaunchPad for Moore's Introduction to the Practice of Statistics (12 month access)
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