Q. 2.21 - Elementary Statistics

Question

we have presented some simple qualitative data sets for practicing the concepts. For each data set.

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. draw a pie chart.

d. construct a bar chart.

Step-by-Step Solution

Answer

(a) The Frequency Distribution is given below: 

    $\begin{array}{|ccc|}\hline \text{ Class }& \text{ Tally Marks }& \text{ Frequency }\\ \mathrm{A}& \text{III}& 3\\ \mathrm{B}& \text{I}& 1\\ \mathrm{C}& \text{I}& 1\\ \text{ Total }& & 5\\ \hline\end{array}$

(b) The Frequency Distribution is given below: 

    $\begin{array}{|ccc|}\hline \text{ Class }& \text{ Frequency }& \text{ Relative Frequency }\\ \mathrm{A}& 3& \frac{3}{5}=0.6\\ \mathrm{B}& 1& \frac{1}{5}=0.2\\ \mathrm{C}& 1& \frac{1}{5}=0.2\\ \text{ Total }& 5& 1\\ \hline\end{array}$

(c) The pie chart is given below :

   

(d) The Bar Graph is given below: 

   

Part(a) Step 1:Given Information

The given data set is C,A,A,B,A.

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.

Part(b) Step 1: Given Information

The given data set is C,A,A,B,A.

Part(b) Step 2: Explanation

The relative frequency is calculated as follows:

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

Part(c) Step 1: Given Information

The given data set is C,A,A,B,A.

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 $360°$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

The given data set is C,A,A,B,A.

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