Q. 2.26 - 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 the TV by the Numbers website, we obtained the networks for the top $20$ primetime broadcast TV shows by total viewership for the week ending August $18, 2013$.

Step-by-Step Solution

Answer

(a) The frequency distribution is given below.

    $\begin{array}{|ccc|}\hline \text{ Class }& \text{ Tally Marks }& \text{ Frequency }\\ \text{ ABC }& \text{II}& 2\\ \text{ CBS }& \text{ IIII IIII III }& 11\\ \text{ FOX }& \text{II}& 2\\ \text{ NBC }& \text{IIII I}& 5\\ \text{ Total }& & 20\\ \hline\end{array}$

(b) The frequency distribution is given below. 

    $\begin{array}{|ccc|}\hline \text{ Class }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ ABC }& 2& \frac{2}{20}=0.1\\ \text{ CBS }& 11& \frac{11}{20}=0.55\\ \text{ FOX }& 2& \frac{2}{20}=0.10\\ \text{ NBC }& 5& \frac{5}{20}=0.25\\ \text{ Total }& 20& 1\\ \hline\end{array}$

(c) The pie chart is given below :  

   

(d) The Bar Graph is given below:   

   

Part(a) Step 1: Given Information

The given data sets is CBS, NBC, NBC, ABC, CBS, CBS, CBS, CBS, CBS, FOX, CBS.CBS, CBS, CBS, NBC, NBC, FOX, CBS, NBC, ABC.

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

The given data sets is CBS, NBC, NBC, ABC, CBS, CBS, CBS, CBS, CBS, FOX, CBS.CBS, CBS, CBS, NBC, NBC, FOX, CBS, NBC, ABC.

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 3: Given Information

The given data sets is CBS, NBC, NBC, ABC, CBS, CBS, CBS, CBS, CBS, FOX, CBS.CBS, CBS, CBS, NBC, NBC, FOX, CBS, NBC, ABC.

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

The given data sets is CBS, NBC, NBC, ABC, CBS, CBS, CBS, CBS, CBS, FOX, CBS.CBS, CBS, CBS, NBC, NBC, FOX, CBS, NBC, ABC.

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