Q.2.41 - Elementary Statistics

Question

Ballot Preferences. In Issue $338$ of the Amstat News, then president of the American Statistical Association, F. Scheuren, reported the results of a survey on how members would prefer to receive ballots in annual elections. On the WeissStats site, you will find data for preference and highest degree obtained for the $566$ respondents.

Step-by-Step Solution

Answer

a). Frequency distributions,

$\begin{array}{|cc|}\hline \text{ Preference }& \text{ Frequency }\\ \text{ Email }& 239\\ \text{ Mail }& 86\\ \text{ Both }& 112\\ \text{ Not applicable }& 129\\ \hline\end{array}$

$\begin{array}{|cc|}\hline \text{ Highest degree }& \text{ Frequency }\\ \text{ PhD }& 388\\ \text{ MA }& 167\\ \text{ Other }& 11\\ \hline\end{array}$

b). Relative frequency,

$\begin{array}{|ccc|}\hline \text{ Drinking }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ PhD }& 388& \frac{388}{566}=0.686\\ \text{ MA }& 167& \frac{167}{566}=0.295\\ \text{ Other }& 11& \frac{11}{566}=0.019\\ \text{ Total }& 566& 1\\ \hline\end{array}$

c). Pie chart,

d). Bar chart,

Part (a) Step 1: Given Information

Given data:

On the WeissStats site, you will find data for preference and the highest degree obtained for the $566$ respondents.

Part (b) Step 2: Explanation

MINITAB is used to calculate the frequency.

The following is the technique for obtaining the frequency.

• Select Stat > Tables > Tally Individual Variables from the menu bar.
• Select Preference from the Variables menu.
• Select Counts from the Display menu.
• Click OK

The output of MINITAB is displayed below.

$\begin{array}{|cc|}\hline \text{ Preference }& \text{ Frequency }\\ \text{ Email }& 239\\ \text{ Mail }& 86\\ \text{ Both }& 112\\ \text{ Not applicable }& 129\\ \hline\end{array}$

Part (a) Step 3: Explanation

The following is the technique for obtaining the frequency.

• Select Stat > Tables > Tally Individual Variables from the menu bar.
• Select Degree from the Variables menu.
• Select Counts from the Display menu.
• Click OK

The output of MINITAB is displayed below.

$\begin{array}{|cc|}\hline \text{ Highest degree }& \text{ Frequency }\\ \text{ PhD }& 388\\ \text{ MA }& 167\\ \text{ Other }& 11\\ \hline\end{array}$

Part (b) Step 1: Given Information

Given data:

On the WeissStats site, you will find data for preference and the highest degree obtained for the $566$ respondents.

Part (b) Step 2: Explanation

The relative frequency is calculated as follows:
$\text{ Relative Frequency }=\frac{\text{ Frequency }}{\text{ Number of Observations }}$

$\begin{array}{|ccc|}\hline \text{ Status }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Email }& 239& \frac{239}{566}=0.422\\ \text{ Mail }& 86& \frac{86}{566}=0.152\\ \text{ Both }& 112& \frac{112}{566}=0.198\\ \text{ Not applicable }& 129& \frac{129}{566}=0.228\\ \text{ Total }& 566& 1\\ \hline\end{array}$

The following table depicts the relative frequency distribution of different types of drinking among US adults.

$\begin{array}{|ccc|}\hline \text{ Drinking }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ PhD }& 388& \frac{388}{566}=0.686\\ \text{ MA }& 167& \frac{167}{566}=0.295\\ \text{ Other }& 11& \frac{11}{566}=0.019\\ \text{ Total }& 566& 1\\ \hline\end{array}$

Part (c) Step 1: Given Information

Given data:

On the WeissStats site, you will find data for preference and the highest degree obtained for the $566$ respondents.

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

Figure 1 shows the pie chart for the supplied data set.

Below is a pie chart for the highest level of degree.

Part (d) Step 1: Given Information

Given data:

On the WeissStats site, you will find data for preference and the highest degree obtained for the $566$ respondents.

Part (d) Step 2: Explanation

MINITAB has been used to create the bar chart.

The steps to making a bar chart are as follows:

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

Figure 1 shows the bar chart for the supplied data set.

The following is a bar chart for the highest degree.