Chapter 2.1, Problem 28E

a.

To determine

Construct a frequency bar graph.

Answer to Problem 28E

Output obtained from MINITAB software for the educational attainment is:

Explanation of Solution

Calculation:

The given information is a table representing the frequency distribution categorizes U.S. adults aged 18 and over by educational attainment in a year.

Software procedure:

• Step by step procedure to draw the bar chart for educational attainment 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 Frequency.
• In Categorical variables, enter the column of Educational Attainment.
• Click OK

Observation:

From the bar graph, it can be seen that the most frequent educational attainment is High school graduate.

b.

To determine

Construct a relative frequency distribution for the data.

Answer to Problem 28E

The relative frequency distribution for the data is:

Educational Attainment	Relative Frequency
None	0.004
1-4 years	0.008
5-6 years	0.015
7-8 years	0.019
9 years	0.017
10 years	0.020
11 years	0.049
High school graduate	0.300
Some college but no degree	0.194
Associate’s degree(occupational)	0.040
Associate’s degree(academic)	0.052
Bachelor’s degree	0.184
Master’s degree	0.071
Professional degree	0.013
Doctoral degree	0.014

Explanation of Solution

Calculation:

Relative frequency:

The general formula for the relative frequency is,

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

Therefore,

$\begin{array}{c}\text{Relative}\text{Frequency}\text{for None}=\frac{834}{234,900}\\ =0.003\end{array}$

Similarly, the relative frequencies for the response are obtained below:

Educational Attainment	Frequency	Relative Frequency
None	834	$\frac{834}{234,900}=0.004$
1-4 years	1,764	$\frac{1,764}{234,900}=0.008$
5-6 years	3,618	$\frac{3,618}{234,900}=0.015$
7-8 years	4,575	$\frac{4,575}{234,900}=0.019$
9 years	4,068	$\frac{4,068}{234,900}=0.017$
10 years	4,814	$\frac{4,814}{234,900}=0.020$
11 years	11,429	$\frac{11,429}{234,900}=0.049$
High school graduate	70,441	$\frac{70,441}{234,900}=0.300$
Some college but no degree	42,685	$\frac{45,685}{234,900}=0.194$
Associate’s degree(occupational)	9,380	$\frac{9,380}{234,900}=0.040$
Associate’s degree(academic)	12,100	$\frac{12,100}{234,900}=0.052$
Bachelor’s degree	43,277	$\frac{43,277}{234,900}=0.184$
Master’s degree	16,625	$\frac{16,625}{234,900}=0.071$
Professional degree	3,099	$\frac{3,099}{234,900}=0.013$
Doctoral degree	3,191	$\frac{3,191}{234,900}=0.014$

c.

To determine

Construct a relative frequency bar graph for these data.

Answer to Problem 28E

Output obtained from MINITAB software for the educational attainment is:

Explanation of Solution

Software procedure:

• Step by step procedure to draw the Bar chart for the response 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 Relative Frequency.
• In Categorical variables, enter the column of Educational Attainment.
• Click OK

Observation:

From the graph, it can be seen that most probable educational attainment is High school graduate.

d.

To determine

Construct a frequency distribution for the categories 8 years or less, 9-11 years, High school graduate, Some college but no degree, College degree( Associate’s or Bachelor’s), Graduate degree ( Master’s Professional, or Doctoral).

Answer to Problem 28E

The frequency distribution for the data is:

Educational Attainment	Frequency
8 years or less	10,791
9-11 years	20,311
High school graduate	70,441
Some college but no degree	45,685
College degree	64,757
Graduate degree	22,915

Explanation of Solution

Calculation:

The frequencies for the specified categories are obtained below:

Educational Attainment	Frequency
8 years or less	$834+1,764+3,618+4,575=10,791$
9-11 years	$4,068+4,814+11,429=20,311$
High school graduate	70,441
Some college but no degree	42,685
College degree	$9,380+12,100+43,277=64,757$
Graduate degree	$16,625+3,099+3,191=22,915$

e.

To determine

Construct a pie chart for the frequency distribution in part (d).

Answer to Problem 28E

Output obtained from MINITAB software for frequency distribution in part (d) is:

Explanation of Solution

Calculation:

Software procedure:

• Step by step procedure to draw the bar chart for frequency distribution in part (d) using MINITAB software.
• Choose Graph > Pie Chart.
• Choose Chart values from table.
• Under categorical variable, select Educational Attainment.
• Under Summary variables, select Frequency.
• Click OK.

Observation:

There is about 30.0% of the adults are High school graduate and 4.6% of adults are 8 years or less.

f.

To determine

Find the proportion of people did not graduate from high school.

Answer to Problem 28E

The proportion of people did not graduate from high school is 0.132.

Explanation of Solution

From the pie chart, it can be seen that there is about 4.6% of the adults are 8 years or less, 8.6% of adults are 9-11 years and all others are graduate from high school. Then the total proportion of people did not graduate from high school is $4.6\%+8.6\%=13.2\%$.

Hence, the proportion of people did not graduate from high school is 0.132.