Chapter 2.1, Problem 28E

Education levels: The following frequency distribution categorizes US. adults aged 18 and over by educational attainment in a recent year.

1. Construct a frequency bar graph.
2. Construct a relative frequency distribution.
3. Construct a relative frequency bar graph.
4. Construct a frequency distribution with the following 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).
5. Construct a pie chart for the frequency distribution in part (d).
6. What proportion of people did not graduate from high school?

To determine

To construct: A frequency bar graph.

Explanation of Solution

Given information: The following frequency distribution categorises U.S. adults aged 18 and over by educational attainment in a recent year.

Educational attainment	Frequency(in thousands)
None	834
1-4 years	1764
5-6 years	3618
7-8 years	4575
9 years	4068
10 years	4814
11 years	11429
High school graduate	70441
Some college but no degree	45685
Associates degree (Occupational)	9380
Associates degree (Academic)	12100
Bachelor’s degree	43277
Master’s degree	16625
Professional degree	3099
Doctoral degree	3191

Solution:

From the given table, the frequency bar graph is given by

  

To determine

To construct: The relative frequency distribution.

Explanation of Solution

Given information:The following frequency distribution categorises U.S. adults aged 18 and over by educational attainment in a recent year.

Educational attainment	Frequency(in thousands)
None	834
1-4 years	1764
5-6 years	3618
7-8 years	4575
9 years	4068
10 years	4814
11 years	11429
High school graduate	70441
Some college but no degree	45685
Associates degree (Occupational)	9380
Associates degree (Academic)	12100
Bachelor’s degree	43277
Master’s degree	16625
Professional degree	3099
Doctoral degree	3191

Formula used: $Relativefrequency=\frac{Frequency}{}$

  $Relativefrequency=\frac{Frequency}{ Sum\text{ of all }Frequency}$

Calculation:

From the given table,

The sum of all frequency is $234911$

The table of relative frequency is given by

Educational attainment	Frequency(in thousands)	Relative frequency
None	834	$\frac{834}{234911}=0.0036$
1-4 years	1764	$\frac{1764}{234911}=0.0075$
5-6 years	3618	$\frac{3618}{234911}=0.0154$
7-8 years	4575	$\frac{4575}{234911}=0.0195$
9 years	4068	$\frac{4068}{234911}=0.0173$
10 years	4814	$\frac{4814}{234911}=0.0205$
11 years	11429	$\frac{11429}{234911}=0.0487$
High school graduate	70441	$\frac{70441}{234911}=0.2999$
Some college but no degree	45685	$\frac{45685}{234911}=0.1945$
Associates degree (Occupational)	9380	$\frac{9380}{234911}=0.0399$
Associates degree (Academic)	12100	$\frac{12100}{234911}=0.0515$
Bachelor’s degree	43277	$\frac{43277}{234911}=0.184$
Master’s degree	16625	$\frac{16625}{234911}=0.0708$
Professional degree	3099	$\frac{3099}{234911}=0.0132$
Doctoral degree	3191	$\frac{3191}{234911}=0.0136$

To determine

To construct: A relative frequency bar graph.

Explanation of Solution

Given information:The following frequency distribution categorises U.S. adults aged 18 and over by educational attainment in a recent year.

Educational attainment	Frequency(in thousands)
None	834
1-4 years	1764
5-6 years	3618
7-8 years	4575
9 years	4068
10 years	4814
11 years	11429
High school graduate	70441
Some college but no degree	45685
Associates degree (Occupational)	9380
Associates degree (Academic)	12100
Bachelor’s degree	43277
Master’s degree	16625
Professional degree	3099
Doctoral degree	3191

Definition used:

Histogram based on relative frequency is called relative frequency histogram.

Solution:

The following table gives the relative frequency.

Educational attainment	Relative frequency
None	0.0036
1-4 years	0.0075
5-6 years	0.0154
7-8 years	0.0195
9 years	0.0173
10 years	0.0205
11 years	0.0487
High school graduate	0.2999
Some college but no degree	0.1945
Associates degree (Occupational)	0.0399
Associates degree (Academic)	0.0515
Bachelor’s degree	0.184
Master’s degree	0.0708
Professional degree	0.0132
Doctoral degree	0.0136

From the above table, the relative frequency bar graph is given by

  

To determine

To construct: A frequency distribution with the following 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

Educational attainment	Frequency(in thousands)
8 years or less	10791
9-11 years	20311
High school graduate	70441
Some college but no degree	45685
College degree (Associate’s or Bachelor’s)	64757
Graduate degree (Master’s, professional, or Doctoral)	22915

Explanation of Solution

Given information:The following frequency distribution categorises U.S. adults aged 18 and over by educational attainment in a recent year.

Educational attainment	Frequency(in thousands)
None	834
1-4 years	1764
5-6 years	3618
7-8 years	4575
9 years	4068
10 years	4814
11 years	11429
High school graduate	70441
Some college but no degree	45685
Associates degree (Occupational)	9380
Associates degree (Academic)	12100
Bachelor’s degree	43277
Master’s degree	16625
Professional degree	3099
Doctoral degree	3191

Solution:

The required frequency distribution with the given categories is given by

Educational attainment	Frequency(in thousands)
8 years or less	$834+1764+3618+4575=10791$
9-11 years	$4068+4814+1429=20311$
High school graduate	70441
Some college but no degree	45685
College degree (Associate’s or Bachelor’s)	$9380+12100+43277=64757$
Graduate degree (Master’s, professional, or Doctoral)	$16625+3099+3191=22915$

To determine

To construct: A pie chart

Explanation of Solution

Given information: The following frequency distribution categorises U.S. adults aged 18 and over by educational attainment in a recent year.

Educational attainment	Frequency(in thousands)
8 years or less	10791
9-11 years	20311
High school graduate	70441
Some college but no degree	45685
College degree (Associate’s or Bachelor’s)	64757
Graduate degree (Master’s, professional, or Doctoral)	22915

Solution:

From the given table, the percentage of each gender and age group is given by

Educational attainment	Frequency(in thousands)	Relative frequency	Percentage
8 years or less	10791	0.0459	4.59 %
9-11 years	10311	0.086	8.6%
High school graduate	70441	0.299	29.9%
Some college but no degree	45685	0.1945	19.45%
College degree (Associate’s or Bachelor’s)	64757	0.2757	27.57%
Graduate degree (Master’s, professional, or Doctoral)	22915	0.0975	9.75%

From the above table, the pie chart is given by

  

To determine

To 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

Given information:The following frequency distribution categorises U.S. adults aged 18 and over by educational attainment in a recent year.

Educational attainment	Frequency(in thousands)
8 years or less	10791
9-11 years	20311
High school graduate	70441
Some college but no degree	45685
College degree (Associate’s or Bachelor’s)	64757
Graduate degree (Master’s, professional, or Doctoral)	22915

Solution:

From the given table, the percentage of each gender and age group is given by

Educational attainment	Frequency(in thousands)	Relative frequency
8 years or less	10791	0.0459
9-11 years	20311	0.086
High school graduate	70441	0.299
Some college but no degree	45685	0.1945
College degree (Associate’s or Bachelor’s)	64757	0.2757
Graduate degree (Master’s, professional, or Doctoral)	22915	0.0975

The people did not graduate from high school are people whose educations are 8 years or less and 9-11 years.

The proportion of people did not graduate from high school is $0.0459+0.086=0.132$ .

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