Q. 2.27 - Elementary Statistics

Question

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. draw a pie chart.

d. construct a bar chart.

From NCAA.com-the official Web site for NCAA sports-we obtained the National Collegiate Athletic Association wrestling champions for the years $1989-2013$ in the document "Championship History." They are displayed in the following table.

Step-by-Step Solution

Answer

(a) The Frequency Distribution is given below: 

    $\begin{array}{|ccc|}\hline \text{ Class }& \text{ Tally Marks }& \text{ Frequency }\\ \text{ Oklahoma St. }& \text{ IIII III}& 7\\ \text{ Iowa }& \text{ IIII IIII IIII }& 12\\ \text{ Minnesota }& \text{III}& 3\\ \text{ Penn State }& \text{III}& 3\\ \text{ Total }& & 25\\ \hline\end{array}$

(b) The Frequency Distribution is given below: 

    $\begin{array}{|ccc|}\hline \text{ Class }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ Oklahoma St. }& 7& \frac{7}{25}=0.28\\ \text{ Iowa }& 12& \frac{12}{25}=0.48\\ \text{ Minnesota }& 3& \frac{3}{25}=0.12\\ \text{ Penn State }& 3& \frac{3}{25}=0.12\\ \text{ Total }& 25& 1\\ \hline\end{array}$

(c) The pie chart is given below :  

     

(d) The Bar Graph is given below:  

   

Part(a) Step 1: Given Information

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 data set value appears in the second column.

- In the third column, count the number of tally marks and enter the frequency.

Part(b) Step 1: Given Information

Part(b) Step 2: Explanation

The expression for the relative frequency is given by,

$\text{ Relative Frequency }=\frac{\text{ Frequency }}{\text{ Number of Observations }}$

Part(c) Step 1: Given Information

Part(c) Step 2: Explanation

The portion for each class in a pie chart is calculated by multiplying $360°$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.

- Pick your data.

- Go to the Labels tab.

- Navigate to the Slide Labels tab.

- Under Label pie pieces, check Category name and Percent.

- Click OK

Part(d) Step 1: Given Information

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 represent menu.

- Click OK after selecting Simple.

- Enter one column of DATA in Categorical variables.

- Select your chart options

- Click the Show Y as Percent option.

- Click OK