Q. 29 - Elementary Statistics

Question

U.S. Divisions and Regions. The U.S. Census Bureau classifies the states in the United States by region and division. The data giving the region and division of each state are presented on the WeissStats site. Use the technology of your choice to determine the mode(s) of the

a. regions.

b. divisions.

Step-by-Step Solution

Answer

Ans: 

Part (a). The mode of the regions is "south".

Part (b). The division's distribution of states is bimodal, as it has two modes "Mountain", and "8" 

Step 1. Given information:

• The data giving the region and division of each state are presented on the WeissStats site 

Step 2. Solving Part (a):

We need to identify the modes of regions of all states.

The MINITAB output for the frequency distribution of all the four regions is as follows.

                                         Tally for Discrete Variables: REGION

REGION	Count
Midwest	12
Northeast	9
South	16
West	13
N =	50

Step 3. Continue:

From the above output, we have the largest frequency is identified for the region "south".

According to the definition of the mode; the largest frequency value is the modal value of the data.

Therefore, the mode of the regions is "south".

Step 4. Solving Part (b):

We need to identify the modes of the division of all states.

According to the definition of the mode; the largest frequency value is the modal value of the data.

Step 5. Continue:

The MINITAB output for the frequency distribution of all the four regions is as follows.

                            

                           Tally for Discrete Variables: DIVISION

DIVISION	Count
East North Central	5
East South Central	4
Middle Atlantic	3
Mountain	8
New England	6
Pacific	5
South Atlantic	8
West North Central	7
West South Central	4
N =	50

From the above, output, we can say that the largest frequency is 8, and is identified for the two divisions "Mountain", "8".

Therefore, the division's distribution of states is bimodal, as it has two modes "Mountain", and "8".