Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
3rd Edition
ISBN: 9781259969454
Author: William Navidi Prof.; Barry Monk Professor
Publisher: McGraw-Hill Education
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Textbook Question
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.

Chapter 2.1, Problem 28E, Education levels: The following frequency distribution categorizes US. adults aged 18 and over by

  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?

a.

Expert Solution
Check Mark
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)
    None834
    1-4 years1764
    5-6 years3618
    7-8 years4575
    9 years4068
    10 years4814
    11 years11429
    High school graduate70441
    Some college but no degree45685
    Associates degree (Occupational)9380
    Associates degree (Academic)12100
    Bachelor’s degree43277
    Master’s degree16625
    Professional degree3099
    Doctoral degree3191

Solution:

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

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.1, Problem 28E , additional homework tip  1

b.

Expert Solution
Check Mark
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)
    None834
    1-4 years1764
    5-6 years3618
    7-8 years4575
    9 years4068
    10 years4814
    11 years11429
    High school graduate70441
    Some college but no degree45685
    Associates degree (Occupational)9380
    Associates degree (Academic)12100
    Bachelor’s degree43277
    Master’s degree16625
    Professional degree3099
    Doctoral degree3191

Formula used:  Relative frequency=Frequency

   Relative frequency=Frequency Sum 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
    None834834234911=0.0036
    1-4 years17641764234911=0.0075
    5-6 years36183618234911=0.0154
    7-8 years45754575234911=0.0195
    9 years40684068234911=0.0173
    10 years48144814234911=0.0205
    11 years1142911429234911=0.0487
    High school graduate7044170441234911=0.2999
    Some college but no degree4568545685234911=0.1945
    Associates degree (Occupational)93809380234911=0.0399
    Associates degree (Academic)1210012100234911=0.0515
    Bachelor’s degree4327743277234911=0.184
    Master’s degree1662516625234911=0.0708
    Professional degree30993099234911=0.0132
    Doctoral degree31913191234911=0.0136

c.

Expert Solution
Check Mark
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)
    None834
    1-4 years1764
    5-6 years3618
    7-8 years4575
    9 years4068
    10 years4814
    11 years11429
    High school graduate70441
    Some college but no degree45685
    Associates degree (Occupational)9380
    Associates degree (Academic)12100
    Bachelor’s degree43277
    Master’s degree16625
    Professional degree3099
    Doctoral degree3191

Definition used:

Histogram based on relative frequency is called relative frequency histogram.

Solution:

The following table gives the relative frequency.

    Educational attainment Relative frequency
    None0.0036
    1-4 years0.0075
    5-6 years0.0154
    7-8 years0.0195
    9 years0.0173
    10 years0.0205
    11 years0.0487
    High school graduate0.2999
    Some college but no degree0.1945
    Associates degree (Occupational)0.0399
    Associates degree (Academic)0.0515
    Bachelor’s degree0.184
    Master’s degree0.0708
    Professional degree0.0132
    Doctoral degree0.0136

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

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.1, Problem 28E , additional homework tip  2

d.

Expert Solution
Check Mark
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 attainmentFrequency(in thousands)
    8 years or less10791
    9-11 years20311
    High school graduate70441
    Some college but no degree45685
    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)
    None834
    1-4 years1764
    5-6 years3618
    7-8 years4575
    9 years4068
    10 years4814
    11 years11429
    High school graduate70441
    Some college but no degree45685
    Associates degree (Occupational)9380
    Associates degree (Academic)12100
    Bachelor’s degree43277
    Master’s degree16625
    Professional degree3099
    Doctoral degree3191

Solution:

The required frequency distribution with the given categories is given by

    Educational attainment Frequency(in thousands)
    8 years or less834+1764+3618+4575=10791
    9-11 years4068+4814+1429=20311
    High school graduate70441
    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

e.

Expert Solution
Check Mark
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 attainmentFrequency(in thousands)
    8 years or less10791
    9-11 years20311
    High school graduate70441
    Some college but no degree45685
    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 attainmentFrequency(in thousands)Relative frequencyPercentage
    8 years or less107910.04594.59 %
    9-11 years103110.0868.6%
    High school graduate704410.29929.9%
    Some college but no degree456850.194519.45%
    College degree (Associate’s or Bachelor’s)647570.275727.57%
    Graduate degree (Master’s, professional, or Doctoral)229150.09759.75%

From the above table, the pie chart is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.1, Problem 28E , additional homework tip  3

f.

Expert Solution
Check Mark
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 attainmentFrequency(in thousands)
    8 years or less10791
    9-11 years20311
    High school graduate70441
    Some college but no degree45685
    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 attainmentFrequency(in thousands)Relative frequency
    8 years or less107910.0459
    9-11 years203110.086
    High school graduate704410.299
    Some college but no degree456850.1945
    College degree (Associate’s or Bachelor’s)647570.2757
    Graduate degree (Master’s, professional, or Doctoral)229150.0975

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.

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Chapter 2 Solutions

Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561

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