Q. 27 - Elementary Statistics

Question

U.S. Divisions. The U.S. Census Bureau divides the states in the United States into nine divisions: East North Central (ENC), East South Central (ESC), Middle Atlantic (MAC), Mountain (MTN),
New England (NED), Pacific (PAC), South Atlantic (SAC), West North Central (WNC), and West South Central (WSC). The following table gives the divisions of each of the 50 states. 

a. Identify the population and variable under consideration.
b. Obtain both a frequency distribution and a relative-frequency distribution of the divisions.cc

c. Draw a pie chart of the divisions.
d. Construct a bar chart of the divisions.
e. Interpret your results. Interpret your results. 

Step-by-Step Solution

Answer

a. The Population is all the states in the variable under study is division of the state

b.  Frequency distribution 

Relative-frequency distribution 

c. Pie chat 

d.Bar chart

e.  From the above results the bar graph gives clear representation for the divisions of the 50 states. It is observed that MTN (Mountain) division repeated for more states than other states. 

Part (a) Step 1. Given information

U.S. Divisions. The U.S. Census Bureau divides the states in the United States into nine divisions: East North Central (ENC), East South Central (ESC), Middle Atlantic (MAC), Mountain (MTN),
New England (NED), Pacific (PAC), South Atlantic (SAC), West North Central (WNC), and West South Central (WSC). The following table gives the divisions of each of the 50 states.

ESC PAC MTN WSC PAC MTN NED SAC SAC SAC PAC MTN ENC ENC WNC WNC ESC WSC NED SAC NED ENC WNC ESC WNC MTN WNC MTN NED MAC MTN MAC SAC WNC ENC WSC PAC MAC NED SAC WNC ESC WSC MTN NED SAC PAC SAC ENC MTN 

Part (a) Step 2.Identify the population and variable under consideration.

The Population is all the states in the variable under study is division of the state

Part (b) Step 1. Given information

U.S. Divisions. The U.S. Census Bureau divides the states in the United States into nine divisions: East North Central (ENC), East South Central (ESC), Middle Atlantic (MAC), Mountain (MTN),
New England (NED), Pacific (PAC), South Atlantic (SAC), West North Central (WNC), and West South Central (WSC). The following table gives the divisions of each of the 50 states.

ESC PAC MTN WSC PAC MTN NED SAC SAC SAC PAC MTN ENC ENC WNC WNC ESC WSC NED SAC NED ENC WNC ESC WNC MTN WNC MTN NED MAC MTN MAC SAC WNC ENC WSC PAC MAC NED SAC WNC ESC WSC MTN NED SAC PAC SAC ENC MTN 

Part (b). Obtain both a frequency distribution and a relative-frequency distribution of the divisions.

We have to construct the frequency distribution for the divisions of the 50 states.The frquency distribution for the given data is obtained below 

The realative frequency of the data can be calculated as follows

Relative frequency=$\frac{frequency of the class}{total frequency}$

we can calculated the relative frequency for each class and tabulated as follows:

Part( c). Given information

U.S. Divisions. The U.S. Census Bureau divides the states in the United States into nine divisions: East North Central (ENC), East South Central (ESC), Middle Atlantic (MAC), Mountain (MTN),
New England (NED), Pacific (PAC), South Atlantic (SAC), West North Central (WNC), and West South Central (WSC). The following table gives the divisions of each of the 50 states.

ESC PAC MTN WSC PAC MTN NED SAC SAC SAC PAC MTN ENC ENC WNC WNC ESC WSC NED SAC NED ENC WNC ESC WNC MTN WNC MTN NED MAC MTN MAC SAC WNC ENC WSC PAC MAC NED SAC WNC ESC WSC MTN NED SAC PAC SAC ENC MTN 

Part (c). Draw a pie chart of the divisions.

we have to draw a pie chart for the divisions of the 50 states.

Using mintab software,the pie chart for the given data is show below

From the pie chart, we can observe that, of the 50 states, 10% of states are ENC, 8% of states are ENC,6% states are MAC,16% of states are MTN,12% of states are NED,10% of states are PAC,16% of states are SAC,14% of states are WNC, and 8% of states are WSC. 

Part (d). Given infornation

U.S. Divisions. The U.S. Census Bureau divides the states in the United States into nine divisions: East North Central (ENC), East South Central (ESC), Middle Atlantic (MAC), Mountain (MTN),
New England (NED), Pacific (PAC), South Atlantic (SAC), West North Central (WNC), and West South Central (WSC). The following table gives the divisions of each of the 50 states.

ESC PAC MTN WSC PAC MTN NED SAC SAC SAC PAC MTN ENC ENC WNC WNC ESC WSC NED SAC NED ENC WNC ESC WNC MTN WNC MTN NED MAC MTN MAC SAC WNC ENC WSC PAC MAC NED SAC WNC ESC WSC MTN NED SAC PAC SAC ENC MTN 

Part (d). Construct a bar chart of the divisions.

We have to construct bar chart for the divisions of the 50 states. 

Using Minitab software, the bar chart for the given data is shown below. 

From the bar chart, we can observe that MTN (Mountain) division repeated for more states than other states 

Part (e). Given information

U.S. Divisions. The U.S. Census Bureau divides the states in the United States into nine divisions: East North Central (ENC), East South Central (ESC), Middle Atlantic (MAC), Mountain (MTN),
New England (NED), Pacific (PAC), South Atlantic (SAC), West North Central (WNC), and West South Central (WSC). The following table gives the divisions of each of the 50 states.

ESC PAC MTN WSC PAC MTN NED SAC SAC SAC PAC MTN ENC ENC WNC WNC ESC WSC NED SAC NED ENC WNC ESC WNC MTN WNC MTN NED MAC MTN MAC SAC WNC ENC WSC PAC MAC NED SAC WNC ESC WSC MTN NED SAC PAC SAC ENC MTN 

Step (e). Interpret your results.

 From the above results the bar graph gives clear representation for the divisions of the 50 states. It is observed that MTN (Mountain) division repeated for more states than other states.