Q.2.40 - Elementary Statistics

Question

Marital Status and Drinking. Research by W. Clark and L. Midanik (Alcohol Consumption and Related Problems: Alcohol and Health Monograph 1. DHHS Pub. No. (ADM) $82-1190$) examined, among other issues, alcohol consumption patterns of U.S. adults by marital status. Data for marital status and the number of drinks per month, based on the researchers' survey results, are provided on the WeissStats site.

Step-by-Step Solution

Answer

a). The frequency distribution,

$\begin{array}{|cc|}\hline \text{ Status }& \text{ Frequency }\\ \text{ Single }& 354\\ \text{ Married }& 143102.1173.\\ \text{ Divorced }& \\ \text{ Widowed }& \\ \hline\end{array}$

The frequency distribution for adults,

$\begin{array}{|cc|}\hline \text{ Drinking }& \text{ Frequency }\\ \text{ Abstain }& 590\\ 1-60& 957\\ \text{ Over 60 }& 225\\ \hline\end{array}$

b). Relative frequency,

$\begin{array}{|ccc|}\hline \text{ Drinking }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Abstain }& 590& \frac{590}{1772}=0.333\\ 1-60& 957& \frac{957}{1772}=0.540\\ \text{ Over }60& 225& \frac{225}{1772}=0.127\\ \text{ Total }& 1772& 1\\ \hline\end{array}$

c). The Pie-chart,

d) Bar-chart,

Part (a) Step 1: Given Information

Data for marital status and the number of drinks per month, based on the researchers' survey results, are provided on the WeissStats site. 

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.

$\begin{array}{|cc|}\hline \text{ Status }& \text{ Frequency }\\ \text{ Single }& 354\\ \text{ Married }& 143102.1173.\\ \text{ Divorced }& \\ \text{ Widowed }& \\ \hline\end{array}$

Part (a) Step 3: Explanation

The following is the procedure for obtaining the frequency:

• Select Statistics > Tables > Tally. Variables by themselves
• Under Variables, choose Drinking.
• Select Counts in Display - Click OK

Below is the MINITAB output.

$\begin{array}{|cc|}\hline \text{ Drinking }& \text{ Frequency }\\ \text{ Abstain }& 590\\ 1-60& 957\\ \text{ Over 60 }& 225\\ \hline\end{array}$

Part (b) Step 1: Given Information

Data for marital status and the number of drinks per month, based on the researchers' survey results, are provided on the WeissStats site. 

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.  

$\begin{array}{|ccc|}\hline \text{ Status }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Single }& 354& \frac{354}{1772}=0.200\\ \text{ Married }& 1173& \frac{1173}{1772}=0.662\\ \text{ Divorced }& 102& \frac{102}{1772}=0.058\\ \text{ Widowed }& 143& \frac{143}{1772}=0.081\\ \text{ Total }& 1772& \\ \hline\end{array}$

The table below shows the relative frequency distribution of different types of drinking among US adults.

$\begin{array}{|ccc|}\hline \text{ Drinking }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Abstain }& 590& \frac{590}{1772}=0.333\\ 1-60& 957& \frac{957}{1772}=0.540\\ \text{ Over }60& 225& \frac{225}{1772}=0.127\\ \text{ Total }& 1772& 1\\ \hline\end{array}$

Part (c) Step 1: Given Information

Data for marital status and the number of drinks per month, based on the researchers' survey results, are provided on the WeissStats site. 

Part (c) Step 2: Explanation

MINITAB has been used to create the pie chart.

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

The steps of drawing a pie chart are as follows:

• Navigate to Graph > Pie Chart.
• Choose the chart that counts unique data.
• Select a Type.
• Go to the Labels tab.
• Navigate to the Slide Labels tab.
• Under Label pie pieces, check Category name and Percent.
• Click OK

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

The pie chart below depicts the many types of drinking among adults in the United States.

Part (d) Step 1: Given Information

Data for marital status and the number of drinks per month, based on the researchers' survey results, are provided on the WeissStats site. 

Part (d) Step 2: Explanation

MINITAB is used to create the bar graph.

The following is the technique for making a bar chart:

Graph > Bar Chart is the option to select.

Select Counts of Unique Values from the Bars represent menu.

Click OK after choosing Simple.

Enter one column of STATUS in Categorical variables.

Select options for the chart

Choose Show $Y$ as Percentage from the drop-down menu.

Click OK

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

The following graph depicts the various types of drinking among US adults.