Chapter 2.1, Problem 9E

Degrees Awarded Annually. Nearly 1.9 million bachelor’s degrees and over 758,000 master’s degrees are awarded annually by U.S. postsecondary institutions as of 2018 (National Center for Education Statistics website). The Department of Education tracks the field of study for these graduates in the following categories: Business (B), Computer Sciences and Engineering (CSE), Education (E), Humanities (H), Natural Sciences and Mathematics (NSM), Social and Behavioral Sciences (SBS), and Other (O). Consider the following samples of 100 graduates:

Bachelor’s Degree Field of Study

Master’s Degree Field of Study

1. a. Provide a percent frequency distribution of field of study for each degree.
2. b. Construct a bar chart for field of study for each degree.
3. c. What is the lowest percentage field of study for each degree?
4. d. What is the highest percentage field of study for each degree?
5. e. Which field of study has the largest increase in percentage from bachelor’s to masters’?

To determine

Construct the percent frequency distribution of the field of study for each degree.

Answer to Problem 9E

The percent frequency distribution for bachelor’s degree is given below:

Bachelor’s degree	Percent frequency
B	21%
CSE	9%
E	6%
H	16%
NSM	8%
O	24%
SBS	16%
Total	100

The percent frequency distribution for master’s degree is given below:

Master’s degree	Percent frequency
B	27%
CSE	9%
E	24%
H	8%
NSM	2%
O	24%
SBS	6%
Total	100

Explanation of Solution

Calculation:

The data represent the U.S postsecondary institutions that provide the annual awards for the 1.9 million bachelor’s degrees and the 758,000 master’s degrees. The graduate categories are Business (B), Computer science and Engineering (CSE), Education (E), Humanities (H), Natural sciences and Mathematics (NSM), Social and Behavioral sciences (SBS), and other (O).

For Bachelor’s degree:

Frequency:

The frequencies are calculated using the tally marks. Here, the number of times each class repeats is the frequency of that particular class.

Here, “B (business)” is the department type data, which is repeated 21 times in the data set, and thus, 21 is the frequency for the category “business (B)”.

Similarly, the frequency of the remaining types of network is given below:

Bachelor’s degree	Tally	Frequency
B	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}|$	21
CSE	$\cancel{\left|\right|\left|\right|}\left|\right|\left|\right|$	9
E	$\cancel{\left|\right|\left|\right|}|$	6
H	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}|$	16
NSM	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\left|\right||$	8
O	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\left|\right|\left|\right|$	24
SBS	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}|$	16
Total		100

Relative frequency:

The general formula for the relative frequency is given below:

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

Therefore,

$\begin{array}{c}\text{Relative}\text{Frequency}\text{for B (Business)}=\frac{21}{100}\\ =0.21\end{array}$

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

Bachelor’s degree	Frequency	Relative frequency
B	21	0.21
CSE	9	$\frac{9}{100}=0.09$
E	6	$\frac{6}{100}=0.06$
H	16	$\frac{16}{100}=0.16$
NSM	8	$\frac{8}{100}=0.08$
O	24	$\frac{24}{100}=0.24$
SBS	16	$\frac{16}{100}=0.16$
Total	100	1.00

Percentage frequency distribution:

The general formula for the percent frequency is given below:

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

Therefore,

$\begin{array}{c}\text{Percent Frequency}\text{for B "(Business)"}=0.21\times 100\\ =21\%\end{array}$

The percent frequencies for the remaining categories of education fields for bachelor degree are obtained below:

Bachelor’s degree	Relative frequency	Percent frequency
B	0.21	21%
CSE	0.09	$0.09\times 100=9\%$
E	0.06	$0.06\times 100=6\%$
H	0.16	$0.16\times 100=16\%$
NSM	0.08	$0.08\times 100=8\%$
O	0.24	$0.24\times 100=24\%$
SBS	0.16	$0.16\times 100=16\%$
Total	1.00	100

For master’s degree:

Here, “B (business)” is the department type data, which is repeated 27 times in the data set, and thus, 27 is the frequency for the category “business (B)”.

Similarly, the frequency of the remaining types of department fields is given below:

Master’s degree	Tally	Frequency
B	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\left|\right|$	27
CSE	$\cancel{\left|\right|\left|\right|}\left|\right|\left|\right|$	9
E	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\left|\right|\left|\right|$	24
H	$\cancel{\left|\right|\left|\right|}\left|\right||$	8
NSM	$\left|\right|$	2
O	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\left|\right|\left|\right|$	24
SBS	$\cancel{\left|\right|\left|\right|}|$	6
Total		100

Relative frequency:

$\begin{array}{c}\text{Relative}\text{Frequency}\text{for B (Business)}=\frac{27}{100}\\ =0.27\end{array}$

Similarly, the relative frequencies for the remaining types of department fields are obtained below:

Master’s degree	Frequency	Relative frequency
B	27	0.27
CSE	9	$\begin{array}{l}\frac{9}{100}=0.09\\ \frac{9}{100}=0.09\end{array}$0.09
E	24	$\frac{24}{100}=0.24$
H	8	$\frac{8}{100}=0.08$
NSM	2	$\frac{2}{100}=0.02$
O	24	$\frac{24}{100}=0.24$
SBS	6	$\frac{6}{100}=0.06$
Total	100	1.00

Percentage frequency distribution:

$\begin{array}{c}\text{Percent Frequency}\text{for B "(Business)"}=0.27\times 100\\ =27\%\end{array}$

The percent frequencies for the remaining types of categories of education fields for master’s degree are obtained below:

Master’s degree	Relative frequency	Percent frequency
B	0.27	27%
CSE	0.09	$0.09\times 100=9\%$9%
E	0.24	$0.24\times 100=24\%$
H	0.08	$0.08\times 100=8\%$
NSM	0.02	$0.02\times 100=2\%$
O	0.24	$0.24\times 100=24\%$
SBS	0.06	$0.06\times 100=6\%$
Total	1.00	100

To determine

Construct the bar chart for each degree.

Answer to Problem 9E

Output obtained from Excel for bachelor’s degree is given below:

Output obtained from Excel for Master’s degree is given below:

Explanation of Solution

Calculation:

For Bachelor’s degree:

Software procedure:

Step-by-step procedure to draw the bar chart for bachelor’s degree using Excel:

• In Excel sheet, enter Bachelor’s degree in one column and Frequency in another column.
• Select the data and then choose Insert > Insert Column Bar Charts.
• Select Clustered Column Under More Column Charts.
• For master’s degree:

Software procedure:

Step-by-step procedure to draw the bar chart for master’s degree using Excel:

• In Excel sheet, enter Master’s degree in one column and Frequency in another column.
• Select the data and then choose Insert > Insert Column Bar Charts.
• Select Clustered Column Under More Column Charts.

To determine

Find the lowest percentage field of study for each degree.

Answer to Problem 9E

The lowest percentage for a bachelor’ degree is Education.

The lowest percentage for a master’s degree is Natural sciences and Mathematics.

Explanation of Solution

For bachelor’ degree, the percentage for education is 6%, which is low when compared to the other categories.

For master’s degree, the percentage for Natural science and Mathematics is 2%, which is low when compared to other categories.

To determine

Find the highest percentage field of study for each degree.

Answer to Problem 9E

The highest percentage field of study for a bachelor’ degree is Others.

The highest percentage field of study for a master’s degree is Business.

Explanation of Solution

For bachelor’ degree, the percentage for others is 24%, which is high when compared to the other categories.

For master’s degree, the percentage for business is 27%, which is high when compared to the other categories.

To determine

Identify the field of study that has the largest increase in percentage from bachelor’s to masters’ degree.

Answer to Problem 9E

The field of study “Education” has the largest increase in percentage from bachelor’s to masters’ degree.

Explanation of Solution

Calculation:

In order to obtain the study field that has the largest increase in percentage from the bachelor’s to master’s degree, the difference between the two respective percentages should be found.

$\text{Difference}=\text{Master's percent frequency}-\text{Bachelor}\text{'}\text{s percent frequency}$

Therefore,

$\begin{array}{c}\text{Difference for Business(B)}=\text{Master's percent frequency(B)}-\text{Bachelor's percent frequency(B)}\\ \text{=}27\%-21\%\\ =6\%\end{array}$

The differences between the two fields are tabulated below:

Field	Bachelor’s	Master’s	Difference
B	21%	27%	6%
CSE	9%	9%	0%
E	6%	24%	18%
H	16%	8%	8%
NSM	8%	2%	6%
O	24%	24%	0%
SBS	16%	6%	10%

From the table, it is observed that the field of study “Education” has the largest increase in percentage from bachelor’s to master’s degree.