Q.2.39 - Elementary Statistics

Question

Japanese Vehicle Exports. The Japan Automobile Manufacturer's Association provides data on exported vehicles in Motor Vehicle Statistics of Japan. In $2010$, cars, trucks, and buses constituted $88.3\%,9.3\%$, and $2.4\%$ of vehicle exports, respectively. A random sample of last year's exports yielded the vehicle-type data on the WeissStats site.

Step-by-Step Solution

Answer

a). The frequency distribution,

b). Relative frequency,

$\begin{array}{|ccs|}\hline \text{ Type }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Bus }& 21& \frac{21}{750}=0.028\\ \text{ Car }& 667& \frac{667}{750}=0.8893\\ \text{ Truck }& 62& \frac{62}{750}=0.0827\\ \text{ Total }& 750& 1\\ \hline\end{array}$

c). Pie-chart,

d). Bar-chart,

Part (a) Step 1: Given Information

 In $2010$, cars, trucks, and buses constituted $88.3\%,9.3\%$, and $2.4\%$ of vehicle exports, respectively. 

Part (a) Step 2: Explanation

MINITAB is used to get the frequency.

The following is how you get the frequency.

Tally Individual Variables > Stat > Tables

Select TYPE from the Variables menu.

Select Counts in Display.

Click OK

Below is a screenshot of the MINITAB output.

Part (b) Step 1: Given Information

In $2010$, cars, trucks, and buses constituted $88.3\%,9.3\%$, and $2.4\%$ of vehicle exports, respectively. 

Part (b) Step 2: Explanation

The relative frequency is expressed as follows:  

$\text{ RelativeFrequency }=\frac{\text{ Frequency }}{\text{ NumberofObservations }}$

The frequency distribution is presented in the table below.  

$\begin{array}{|ccs|}\hline \text{ Type }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Bus }& 21& \frac{21}{750}=0.028\\ \text{ Car }& 667& \frac{667}{750}=0.8893\\ \text{ Truck }& 62& \frac{62}{750}=0.0827\\ \text{ Total }& 750& 1\\ \hline\end{array}$

Part (c) Step 1: Given Information

In $2010$, cars, trucks, and buses constituted $88.3\%,9.3\%$, and $2.4\%$ of vehicle exports, respectively. 

Part (c) Step 2: Explanation

MINITAB was used to make the pie graph.

The fraction for each class in a pie chart is calculated by multiplying ${360}^o$ by the relative frequencies for that class.

To make a pie chart, follow these steps:

- Select Pie Chart from the Graph menu.

- Choose unique data counts in the chart.

- Select an option.

- Go to the tab Labels.

- Select the Labels for Slides tab.

- Under Label pie slices with, look for Category name and Percent.

- Click OK

The figure following shows the pie chart for the supplied data set.

Part (d) Step 1: Given Information

In $2010$, cars, trucks, and buses constituted $88.3\%,9.3\%$, and $2.4\%$ of vehicle exports, respectively. 

Part (d) Step 2: Explanation

MINITAB has been used to create the bar chart.

The steps to making a bar chart are as follows:

• Navigate to Graph > Bar Chart.
• Select Counts of unique values from the Bars to represent the menu. Click OK after selecting Simple.
• Add one column of CLASS LIMITS to Categorical variables.
• Select your chart options
• Click the Show $Y$ as Percent option.
• Click OK

The figure shows the bar chart for the supplied data set.