Q.2.30 - Elementary Statistics

Question

U.S. Regions. The U.S. Census Bureau divides the states in the United States into four regions: Northeast (NE), Midwest (MW), South (SO), and West (WE). The following table gives the region of each of the $50$ states.

Step-by-Step Solution

Answer

a). The frequency distribution,

b). The relative frequency,

$\begin{array}{|ccc|}\hline \text{ Class }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ NE }& 9& \frac{9}{50}=0.18\\ \text{ MW }& 12& \frac{12}{50}=0.24\\ \text{ SO }& 16& \frac{16}{50}=0.32\\ \text{ WE }& 13& \frac{13}{50}=0.26\\ \text{ Total }& 50& 1\\ \hline\end{array}$

c) Pie- chart,

d). Bar chart,

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2: Explanation

The following is the process for determining the qualitative data frequency distribution:

• Begin by listing 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 for each.

In the table below, you can see the frequency distribution.

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

The relative frequency is expressed as follows:  

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

The frequency distribution is presented in the table below. 

$\begin{array}{|ccc|}\hline \text{ Class }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ NE }& 9& \frac{9}{50}=0.18\\ \text{ MW }& 12& \frac{12}{50}=0.24\\ \text{ SO }& 16& \frac{16}{50}=0.32\\ \text{ WE }& 13& \frac{13}{50}=0.26\\ \text{ Total }& 50& 1\\ \hline\end{array}$

Part (c) Step 1: Given Information

Given data:

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 ${360}^o$ 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.
• Select your CLASS LEVELS.
• Go to the Labels tab.
• Navigate to the Slide Labels tab.
• Under Label pie pieces, check Category name and Percent.
• Click OK

The pie chart of the data set:

Part (d) Step 1: Given Information

Given data,

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 to represent the menu. Click OK after selecting Simple.
• Add one column of CLASS LIMITS to Categorical variables.
• Select your chart options
• Click the Show $Y$ as Percent option.
• Click OK

The figure shows the bar chart for the supplied data set.