Q.2.35 - Elementary Statistics

Question

Medical School Faculty. The Association of American Medical Colleges (AAMC) compiles data on medical school faculty and publishes the results in AAMC Faculty Roster. The following table presents a frequency distribution of rank for medical school faculty during one year.

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,

$\begin{array}{|ccc|}\hline \text{ RANK }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Professor }& 32,511& \frac{32,511}{137,925}=0.2357\\ \text{ Associate Professor }& 28,572& \frac{28,572}{137,925}=0.2072\\ \text{ Assistant Professor }& 59,277& \frac{59,277}{137,925}=0.4298\\ \text{ Instructor }& 14,289& \frac{14,289}{137,925}=0.1036\\ \text{ Other }& 3,276& \frac{3,276}{137,925}=0.0238\\ \text{ Total }& 137,925& 1\\ \hline\end{array}$

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,

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

The table below shows the frequency distribution.

$\begin{array}{|ccc|}\hline \text{ RANK }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Professor }& 32,511& \frac{32,511}{137,925}=0.2357\\ \text{ Associate Professor }& 28,572& \frac{28,572}{137,925}=0.2072\\ \text{ Assistant Professor }& 59,277& \frac{59,277}{137,925}=0.4298\\ \text{ Instructor }& 14,289& \frac{14,289}{137,925}=0.1036\\ \text{ Other }& 3,276& \frac{3,276}{137,925}=0.0238\\ \text{ Total }& 137,925& 1\\ \hline\end{array}$

Part (b) 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 RANK from the Categorical variable 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

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.

- Select OK.

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

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