Chapter 2.1, Problem 9E

The Pew Research Center’s Social & Demographic Trends project found that 46% of U.S. adults would rather live in a different type of community than the one where they are living now (Pew Research Center, January 29, 2009). The national survey of 2260 adults asked: “Where do you live now?” and “What do you consider to be the ideal community?” Response options were City (C), Suburb (S), Small Town (T), or Rural (R). A representative portion of this survey for a sample of 100 respondents is as follows.

Where do you live now?

S

T

R

C

R

R

T

C

S

T

C

S

C

S

T

S

S

C

S

S

T

T

C

C

S

T

C

S

T

C

T

R

S

S

T

C

S

C

T

C

T

C

T

C

R

C

C

R

T

C

S

S

T

S

C

C

C

R

S

C

S

S

C

C

S

C

R

T

T

T

C

R

T

C

R

C

T

R

R

C

T

C

C

R

T

T

R

S

R

T

T

S

S

S

S

S

C

C

R

T

What do you consider to be the ideal community?

S

C

R

R

R

S

T

S

S

T

T

S

C

S

T

C

C

R

T

R

S

T

T

S

S

C

C

T

T

S

S

R

C

S

C

C

S

C

R

C

T

S

R

R

R

C

T

S

T

T

T

R

R

S

C

C

R

R

S

S

S

T

C

T

T

C

R

T

T

T

C

T

T

R

R

C

S

R

T

C

T

C

C

T

T

T

R

C

R

T

T

C

S

S

C

S

T

S

S

R

1. a. Provide a percent frequency distribution for each question.
2. b. Construct a bar chart for each question.
3. c. Where are most adults living now?
4. d. Where do most adults consider the ideal community?
5. e. What changes in living areas would you expect to see if people moved from where they currently live to their ideal community?

To determine

Construct the percent frequency distribution for each question.

Answer to Problem 9E

The percent frequency distribution for live now:

Live now	Percent frequency
City	32%
Suburb	26%
Small Town	26%
Rural Area	16%
Total	100

The percent frequency distribution for Ideal Community:

Ideal Community	Percent frequency
City	24%
Suburb	25%
Small Town	30%
Rural Area	21%
Total	100

Explanation of Solution

The given information is that Pew Research Centers Social & Demographic Trends project show that 46% of U.S adults would rather live in a different type of community than where they are living now. In the national survey of 2,260 adults are asked two types of questions. A sample of 100 respondents is provided. The respective living areas are City, Suburb, Small Town and Rural Area.

Calculation:

For live now:

Frequency:

The frequencies are calculated by using the tally mark.

Here, the number of times each class repeats is the frequency of that particular class.

Here, “City” is repeated for 32 times in the data set and thus 32 is the frequency for the category City.

Similarly, the frequency of remaining types of living area is given below:

Live Now	Tally	Frequency
City	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\left|\right|$	32
Suburb	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}|$	26
Small Town	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}|$	26
Rural Area	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}|$	16
Total		100

Relative frequency:

The general formula for the relative frequency is,

$\text{Relative}\text{Frequency = }\frac{\text{Frequency}}{\text{Total frequency}}$

Therefore,

$\begin{array}{c}\text{Relative}\text{Frequency}\text{for City}=\frac{32}{100}\\ =0.32\end{array}$

Similarly, the relative frequencies for the remaining types of living area are obtained below:

Live Now	Frequency	Relative frequency
City	32	0.32
Suburb	26	0.26
Small Town	26	0.26
Rural Area	16	0.16
Total	100	1.00

Percentage frequency distribution:

The general formula for the percent frequency is,

$\text{Percent Frequency}=\text{Relative}\text{Frequency}\times \text{100}$

Therefore,

$\begin{array}{c}\text{Percent Frequency}\text{for City}=0.32\times 100\\ =32\%\end{array}$

The percent frequencies for the remaining types of categories of living area for live now are obtained below:

Live Now	Relative frequency	Percent frequency
City	0.32	32%
Suburb	0.26	26%
Small Town	0.26	26%
Rural Area	0.16	16%
Total	1.00	100

For ideal community:

Here, city is repeated for 24 times in the data set and thus 24 is the frequency for the living area city.

Similarly, the frequency of remaining types of living area is given below:

Ideal community	Tally	Frequency
City	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\left|\right|\left|\right|$	24
Suburb	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}$	25
Small Town	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}$	30
Rural Area	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}|$	21
Total		100

Relative frequency:

$\begin{array}{c}\text{Relative}\text{Frequency}\text{for city}=\frac{24}{100}\\ =0.24\end{array}$

Similarly, the relative frequencies for the remaining types of living area are obtained below:

Ideal community	Frequency	Relative frequency
City	24	0.24
Suburb	25	0.25
Small Town	30	0.30
Rural Area	21	0.21
Total	100	1.00

Percentage frequency distribution:

$\begin{array}{c}\text{Percent Frequency}\text{for city}=0.24\times 100\\ =24\%\end{array}$

The percent frequencies for the remaining types of categories of living area of ideal community are obtained below:

Ideal community	Relative Frequency	Percent frequency
City	0.24	24%
Suburb	0.25	25%
Small Town	0.30	30%
Rural Area	0.21	21%
Total	1.00	100

To determine

Construct the bar chart for each question.

Explanation of Solution

Output obtained from MINITAB software for live now is:

Output obtained from MINITAB software for Ideal community is:

Calculation:

For live now:

Software procedure:

Step by step procedure to draw the bar chart for bachelor’s degree using MINITAB software.

• Choose Graph > Bar Chart.
• From Bars represent, choose unique values from table.
• Choose Simple. Click OK.
• In Graph variables, enter the column of Live now.
• Click OK
• For ideal community:

Step by step procedure to draw the bar chart for Master’s degree using MINITAB software.

• Choose Graph > Bar Chart.
• From Bars represent, choose unique values from table.
• Choose Simple. Click OK.
• In Graph variables, enter the column of Ideal Community.
• Click OK

To determine

Find the living area where the most adults are living now.

Answer to Problem 9E

The most adults in living now consider a City.

Explanation of Solution

For living now, the percentage for city is 32%, which is high when compared to other categories.

To determine

Find the living area which the most adults are considered as an ideal community.

Answer to Problem 9E

The most adults consider the ideal community is a small town.

Explanation of Solution

For ideal, the percentage for small town is 30%, which is high when compared to other categories.

To determine

Identify the changes in living areas would expect to see if people moved from where they currently live to their ideal community.

Explanation of Solution

The percentage changes can be obtained as follows:

$\text{Difference}=\text{Idealcommunity percent frequency}-\text{living nowpercent frequency}$

Therefore,

$\begin{array}{c}\text{Difference for City}=\left(\begin{array}{l}\text{Ideal Community percent frequency for City}-\\ \text{Living Now percent frequencyfor City}\end{array}\right)\\ \text{=}24\%-32\%\\ =-8\%\end{array}$

The differences between two living areas are tabulated below:

Living Area	Living now	Ideal community	Difference
City	32%	24%	–8%
Suburb	26%	25%	–1%
Small Town	26%	30%	4%
Rural Area	16%	21%	5%

From the table, it is observed that the living areas “small town and rural area” has increased in percentage from “living now” to “ideal community” and the living areas “city and suburb” has decrease in percentage from “living now” to “ideal community”.