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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Chapter 2.2, Problem 28E

Batting average: The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

Chapter 2.2, Problem 28E, Batting average: The following frequency distribution presents the batting averages of Major League

  1. Construct a frequency histogram for the American League.
  2. Construct a frequency histogram for the National League.
  3. Construct a relative frequency distribution for the American League.
  4. Construct a relative frequency distribution for the National League.
  5. Construct a relative frequency histogram for the American League.
  6. Construct a relative frequency histogram for the National League.
  7. What percentage of American League players had batting averages of 0.300 or more?
  8. What percentage of National League players had batting averages of 0.300 or more?
  9. Compare the relative frequency histograms. What is the main difference between the distributions of batting averages in the two leagues?

a.

Expert Solution
Check Mark
To determine

To construct: A frequency histogram for American League.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19922
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Definition used: Histograms based on frequency distributions are called frequency histogram.

Solution:

The following frequency distribution presents the batting averages of Major League Baseball players in the American Leaguewho had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequency
    0.180-0.1992
    0.200-0.2197
    0.220-0.23921
    0.240-0.25930
    0.260-0.27926
    0.280-0.29921
    0.300-0.31912
    0.320-0.3395
    0.340-0.3590

The frequency histogram for American League is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 28E , additional homework tip 1

b.

Expert Solution
Check Mark
To determine

To construct: A frequency histogram for National League.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19922
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Definition used: Histograms based on frequency distributions are called frequency histogram.

Solution:

The following frequency distribution presents the batting averages of Major League Baseball players in the American Leaguewho had 300 or more plate appearances during a recent season.

    Batting averageNational LeagueFrequency
    0.180-0.1992
    0.200-0.2197
    0.220-0.23920
    0.240-0.25929
    0.260-0.27932
    0.280-0.29930
    0.300-0.31917
    0.320-0.3395
    0.340-0.3591

The frequency histogram for American League is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 28E , additional homework tip 2

c.

Expert Solution
Check Mark
To determine

To construct: A relative frequency distribution for American League.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19922
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Formula used:  Relative frequency=Frequency Sum of all Frequency

Solution:

From the given table,

The sum of all frequency for American League is 2+7+21+30+26+21+12+5+0=124

The table of relative frequency is given by

    Batting averageAmerican LeagueFrequencyAmerican LeagueRelative frequency
    0.180-0.19922124=0.016
    0.200-0.21977124=0.056
    0.220-0.2392121124=0.169
    0.240-0.2593030124=0.242
    0.260-0.2792626124=0.210
    0.280-0.2992121124=0.169
    0.300-0.3191212124=0.097
    0.320-0.33955124=0.040
    0.340-0.35900124=0.000

The relative frequency for the American League is given by

    Batting averageAmerican LeagueRelative frequency
    0.180-0.1990.016
    0.200-0.2190.056
    0.220-0.2390.169
    0.240-0.2590.242
    0.260-0.2790.210
    0.280-0.2990.169
    0.300-0.3190.097
    0.320-0.3390.040
    0.340-0.3590.000

d.

Expert Solution
Check Mark
To determine

To construct: A relative frequency distribution for National League.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19922
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Formula used:  Relative frequency=Frequency Sum of all Frequency

Solution:

From the given table,

The sum of all frequency for National League is 2+7+20+29+32+30+17+5+1=143

The table of relative frequency is given by

    Batting averageNational LeagueFrequencyNational LeagueRelative frequency
    0.180-0.19922143=0.014
    0.200-0.21977143=0.049
    0.220-0.2392020143=0.140
    0.240-0.2592929143=0.203
    0.260-0.2793232143=0.224
    0.280-0.2993030143=0.210
    0.300-0.3191717143=0.119
    0.320-0.33955143=0.035
    0.340-0.35911143=0.007

The relative frequency for the NationalLeague is given by

    Batting averageNational LeagueRelative frequency
    0.180-0.1990.014
    0.200-0.2190.049
    0.220-0.2390.140
    0.240-0.2590.203
    0.260-0.2790.224
    0.280-0.2990.210
    0.300-0.3190.119
    0.320-0.3390.035
    0.340-0.3590.007

e.

Expert Solution
Check Mark
To determine

To construct: A relative frequency histogram for American League.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19922
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Definition used: Histograms based on relative frequency distributions are called relative frequency histogram.

Solution:

    Batting averageAmerican LeagueRelative frequency
    0.180-0.1990.016
    0.200-0.2190.056
    0.220-0.2390.169
    0.240-0.2590.242
    0.260-0.2790.210
    0.280-0.2990.169
    0.300-0.3190.097
    0.320-0.3390.040
    0.340-0.3590.000

The relative frequency histogram for the given data is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 28E , additional homework tip 3

f.

Expert Solution
Check Mark
To determine

To construct: A relative frequency histogram for National League.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19922
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Definition used: Histograms based on relative frequency distributions are called relative frequency histogram.

Solution:

    Batting averageNationalLeagueRelative frequency
    0.180-0.1990.014
    0.200-0.2190.049
    0.220-0.2390.140
    0.240-0.2590.203
    0.260-0.2790.224
    0.280-0.2990.210
    0.300-0.3190.119
    0.320-0.3390.035
    0.340-0.3590.007

The relative frequency histogram for the given data is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 28E , additional homework tip 4

g.

Expert Solution
Check Mark
To determine

To find: The percentage of American League players who had batting averages of 0.300 or more.

Answer to Problem 28E

The percentage of American League players who had batting averages of 0.300 or more is 13.7%.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19922
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Calculation:

The relative frequency for American League is given by

    Batting averageAmerican LeagueRelative frequency
    0.180-0.1990.016
    0.200-0.2190.056
    0.220-0.2390.169
    0.240-0.2590.242
    0.260-0.2790.210
    0.280-0.2990.169
    0.300-0.3190.097
    0.320-0.3390.040
    0.340-0.3590.000

From the above data, the relative frequencies of batting averages of 0.300 or more are 0.097, 0.040 and 0.000

The sum of all the above relative frequencies is 0.097+0.040+0.000=0.137 .

Then, its percentage is 13.7%

Hence, the percentage of American League players who had batting averages of 0.300 or more is 13.7%.

h.

Expert Solution
Check Mark
To determine

To find: The percentage of National League players who had batting averages of 0.300 or more.

Answer to Problem 28E

The percentage of National League players who had batting averages of 0.300 or more is 16.1%.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19922
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Calculation:

The relative frequency for National League is given by

    Batting averageNationalLeagueRelative frequency
    0.180-0.1990.014
    0.200-0.2190.049
    0.220-0.2390.140
    0.240-0.2590.203
    0.260-0.2790.224
    0.280-0.2990.210
    0.300-0.3190.119
    0.320-0.3390.035
    0.340-0.3590.007

From the above data, the relative frequencies of batting averages of 0.300 or more are 0.119, 0.035 and 0.007.

The sum of all the above relative frequencies is 0.119+0.035+0.007=0.161 .

Then, its percentage is 16.1%

Hence, the percentage of National League players who had batting averages of 0.300 or more is 16.1%.

i.

Expert Solution
Check Mark
To determine

To find: The percentage of players who had batting averages less than 0.220.

Answer to Problem 28E

The batting averages tend to be a bit higher in the National League.

Explanation of Solution

Given information:The following frequency distribution presents the batting averages of Major League Baseball players in both the American League and the National League who had 300 or more plate appearances during a recent season.

    Batting averageAmerican LeagueFrequencyNational LeagueFrequency
    0.180-0.19927
    0.200-0.21977
    0.220-0.2392120
    0.240-0.2593029
    0.260-0.2792632
    0.280-0.2992130
    0.300-0.3191217
    0.320-0.33955
    0.340-0.35901

Solution:

The relative frequency histogram for American League is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 28E , additional homework tip 5

The relative frequency histogram for the National League is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 28E , additional homework tip 6

From the above two histograms, we can see that the relative frequency for National league is bit higher than the National League.

Hence, the batting averages tend to be a bit higher in the National League.

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Chapter 2 Solutions

Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561

Ch. 2.1 - In Exercises 5-8, fill in each blank with the...Ch. 2.1 - In Exercises 5-8, fill in each blank with the...Ch. 2.1 - In Exercises 5-8, fill in each blank with the...Ch. 2.1 - In Exercises 5-8, fill in each blank with the...Ch. 2.1 - In Exercises 9—12, determine whether the...Ch. 2.1 - In Exercises 9—12, determine whether the...Ch. 2.1 - In Exercises 9—12, determine whether the...Ch. 2.1 - In Exercises 9—12, determine whether the...Ch. 2.1 - The following bar graph presents the average...Ch. 2.1 - The most common blood typing system divides human...
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The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License