Question

Class Levels. Earlier in this section, we considered the political party affiliations of the students in Professor Weiss's introductory statistics course. The class levels of those students are as follows, where Fr, So, Jr, and Sr denote freshman, sophomore, junior, and senior, respectively.

Short answer

a). The frequency distribution is,

b). The relative frequency is

$\begin{array}{|ccc|}\hline \text{Class}& \text{Frequency}& \text{Relative Frequency}\\ \mathrm{Fr}& 6& \frac{6}{40}=0.15\\ \text{So}& 15& \frac{15}{40}=0.375\\ \text{Jr}& 12& \frac{12}{40}=0.3\\ \text{Sr}& 7& \frac{7}{40}=0.175\\ \text{Total}& 40& 1\\ \hline\end{array}$

c). The pie chart,

d). The bar chart,

Step-by-step solution

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2: Explanation

The following is the process for determining the frequency distribution of qualitative data:

• List the various values in the first column.
• Use tally marks to represent the number of times each value in the data set appears in the second column.
• In the third column, count the number of tally marks and enter the frequency.

The table below shows the frequency distribution:

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

The relative frequency is expressed as follows:

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

The frequency distribution is presented in the table below.

$\begin{array}{|ccc|}\hline \text{Class}& \text{Frequency}& \text{Relative Frequency}\\ \mathrm{Fr}& 6& \frac{6}{40}=0.15\\ \text{So}& 15& \frac{15}{40}=0.375\\ \text{Jr}& 12& \frac{12}{40}=0.3\\ \text{Sr}& 7& \frac{7}{40}=0.175\\ \text{Total}& 40& 1\\ \hline\end{array}$

Part (c) Step 1: Given Information

Given data:

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 your CLASS LEVELS.
• Go to the Labels tab.
• Navigate to the Slide Labels tab.
• Under Label pie pieces, check Category name and Percent.
• Click OK

The pie chart of the data set:

Part (d) Step 1: Given Information

Given data:

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.