Q.2.34 - Elementary Statistics

Question

Freshmen Politics. The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In $2000,27.7\%$of incoming freshmen characterized their political views as liberal, $51.9\%$ as moderate, and $20.4\%$ as conservative. For this year, a random sample of $500$ incoming college freshmen yielded the following frequency distribution for political views.

a. obtain a relative-frequency distribution.

b. draw a pie chart.

c. construct a bar chart.

Step-by-Step Solution

Answer

a). The frequency distribution is,

$\begin{array}{|ccl|}\hline \text{ View }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Liberal }& 147& \frac{147}{500}=0.294\\ \text{ Moderate }& 237& \frac{237}{500}=0.474\\ \text{ Conservative }& 116& \frac{116}{500}=0.232\\ \text{ Total }& 500& 1\\ \hline\end{array}$

b). The pie-chart,

c). The bar-chart,

Part (a) Step 1: Given Information

The data is given as,

Part (a) Step 2: Explanation

The relative frequency can be calculated using the formula,

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

In the table below, the frequency distribution is presented.

$\begin{array}{|ccl|}\hline \text{ View }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Liberal }& 147& \frac{147}{500}=0.294\\ \text{ Moderate }& 237& \frac{237}{500}=0.474\\ \text{ Conservative }& 116& \frac{116}{500}=0.232\\ \text{ Total }& 500& 1\\ \hline\end{array}$

Part (a) Step 1: Given Information

The data is given as,

Part (b) 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 ${360}^{\circ }$ by the appropriate relative frequencies.

The steps of drawing a pie chart are as follows:

- Select Graph > Pie Chart from the menu bar.

- Choose values for the chart from the table.

- Select Viewunder Categorical Variable from the drop-down menu.

- Under Summary variables, choose Frequency.

- Go to the Labels tab and then to the Slide Labels tab.

- Under Label pie pieces with, double-check Category name and Percentage.

- Select OK.

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

Part (c) Step 1: Given Information

The data is given as,

Part (c) Step 2: Explanation

The construction of the bar chart is depicted in the diagram below. 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 drop-down menu.

- Select Values from a table from the Bars represent section.

- Click OK after selecting Simple.

- Add one column of FREQUENCY to Categorical variables.

- Select options for the chart

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

- Select OK.

The supplied data set's bar chart is depicted in the picture below.