Q. 2.28 - Elementary Statistics

Question

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. draw a pie chart.

d. construct a bar chart.

The following table provides data on college for the students in one section of the course Introduction to Computer Science during one semester at Arizona State University. In the table, we use the abbreviations BUS for Business, ENG for Engineering and Applied Sciences, and LIB for Liberal Arts and Sciences.

Step-by-Step Solution

Answer

(a) The Frequency Distribution is given below:  

    $\begin{array}{|ccs|}\hline \text{ Class }& \text{ Tally Marks }& \text{ Frequency }\\ \text{ ENG }& \text{ IIII IIII I}& 9\\ \text{ BUS }& \text{ IIII IIII IIII}& 12\\ \text{ LIB }& \text{IIII}& 4\\ \text{ Total }& & 25\\ \hline\end{array}$ 

(b) The Frequency Distribution is given below:   

    $\begin{array}{|ccc|}\hline \text{ Class }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ ENG }& 9& \frac{9}{25}=0.36\\ \text{ BUS }& 12& \frac{12}{25}=0.48\\ \text{ LIB }& 4& \frac{4}{25}=0.16\\ \text{ Total }& 25& 1\\ \hline\end{array}$

(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 that represent the 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