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
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Chapter 2.2, Problem 44E

Ogive: Using the data in Exercise 28:

  1. Compute the cumulative frequencies for the classes in the American League frequency distribution.
  2. Construct a frequency ogive for the American League frequency distribution.
  3. Compute the cumulative relative frequencies for the classes in the American League frequency distribution.
  4. Construct a relative frequency ogive for the American League, using the same classes.
  5. Compute the cumulative frequencies for the classes in the National League frequency distribution.
  6. Construct a frequency ogive for the National League frequency distribution.
  7. Compute the cumulative relative frequencies for the classes in the National League frequency distribution.
  8. Construct a relative frequency ogive for the National League, using the same classes.

a.

Expert Solution
Check Mark
To determine

To compute:The cumulative frequencies for the classes in the American League frequency distribution.

Answer to Problem 44E

    Batting averageAmerican League Cumulative Frequency
    0.180-0.1992
    0.200-0.2199
    0.220-0.23930
    0.240-0.25960
    0.260-0.27986
    0.280-0.299107
    0.300-0.319119
    0.320-0.339124
    0.340-0.359124

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: The cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.

Calculation:

The cumulative classes are given by in the following table.

    Batting averageAmerican LeagueFrequencyAmerican League Cumulative Frequency
    0.180-0.19922
    0.200-0.21972+7=9
    0.220-0.2392121+9=30
    0.240-0.2593030+30=60
    0.260-0.2792626+60=86
    0.280-0.2992121+86=107
    0.300-0.3191212+107=119
    0.320-0.33955+119=124
    0.340-0.3590124+0=124

Hence, the cumulative frequency for American league is given by

    Batting averageAmerican League Cumulative Frequency
    0.180-0.1992
    0.200-0.2199
    0.220-0.23930
    0.240-0.25960
    0.260-0.27986
    0.280-0.299107
    0.300-0.319119
    0.320-0.339124
    0.340-0.359124

b.

Expert Solution
Check Mark
To determine

To find:The frequency ogive for the frequency distribution.

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:An ogive plots the cumulative frequencies.

Solution:

The table of cumulative American League frequency is given by

    Batting averageAmerican League Cumulative Frequency
    0.180-0.1992
    0.200-0.2199
    0.220-0.23930
    0.240-0.25960
    0.260-0.27986
    0.280-0.299107
    0.300-0.319119
    0.320-0.339124
    0.340-0.359124

The frequency ogivefor American League frequency distribution is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 44E , additional homework tip  1

c.

Expert Solution
Check Mark
To determine

To compute: The cumulative relative frequencies for the classes in the American league frequency distribution.

Answer to Problem 44E

    Batting averageCumulative relative Frequency
    0.180-0.1990.016
    0.200-0.2190.073
    0.220-0.2390.242
    0.240-0.2590.484
    0.260-0.2790.694
    0.280-0.2990.863
    0.300-0.3190.960
    0.320-0.3391.000
    0.340-0.3591.000

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: The cumulative relative frequency of a class is given by

  cumulative relative frequency=cumulative frequencySum of all frequency

Calculation:

The cumulative classes are given by in the following table.

    Batting averageAmerican League Cumulative FrequencyAmerican League relative Cumulative Frequency
    0.180-0.19922124=0.016
    0.200-0.21999124=0.073
    0.220-0.2393030124=0.242
    0.240-0.2596060124=0.484
    0.260-0.2798686124=0.694
    0.280-0.299107107124=0.863
    0.300-0.319119119124=0.960
    0.320-0.339124124124=1.000
    0.340-0.359124124124=1.000

Hence, the cumulative relative frequency is given by

    Batting averageCumulative relative Frequency
    0.180-0.1990.016
    0.200-0.2190.073
    0.220-0.2390.242
    0.240-0.2590.484
    0.260-0.2790.694
    0.280-0.2990.863
    0.300-0.3190.960
    0.320-0.3391.000
    0.340-0.3591.000

d.

Expert Solution
Check Mark
To determine

To find: The relative frequency ogive for the American league frequency distribution.

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:A relative frequency ogive plots the cumulative relative frequencies..

Solution:

The table of cumulative relative frequency is given by

    Batting averageCumulative relative Frequency
    0.180-0.1990.016
    0.200-0.2190.073
    0.220-0.2390.242
    0.240-0.2590.484
    0.260-0.2790.694
    0.280-0.2990.863
    0.300-0.3190.960
    0.320-0.3391.000
    0.340-0.3591.000

The relative frequency ogive is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 44E , additional homework tip  2

e.

Expert Solution
Check Mark
To determine

To compute: The cumulative frequencies for the classes in the National League frequency distribution.

Answer to Problem 44E

    Batting averageNational League Cumulative Frequency
    0.180-0.1992
    0.200-0.2199
    0.220-0.23929
    0.240-0.25958
    0.260-0.27990
    0.280-0.299120
    0.300-0.319137
    0.320-0.339142
    0.340-0.359143

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: The cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.

Calculation:

The cumulative classes are given by in the following table.

    Batting averageNational LeagueFrequencyNational League Cumulative Frequency
    0.180-0.19922
    0.200-0.21972+7=9
    0.220-0.2392020+9=29
    0.240-0.2592929+29=58
    0.260-0.2793232+58=90
    0.280-0.2993030+90=120
    0.300-0.3191717+120=137
    0.320-0.33955+137=142
    0.340-0.35911+142=143

Hence, the cumulative frequency for National league is given by

    Batting averageNational League Cumulative Frequency
    0.180-0.1992
    0.200-0.2199
    0.220-0.23929
    0.240-0.25958
    0.260-0.27990
    0.280-0.299120
    0.300-0.319137
    0.320-0.339142
    0.340-0.359143

h.

Expert Solution
Check Mark
To determine

To find: The frequency ogive for the National League frequency distribution.

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: An ogive plots the cumulative frequencies.

Solution:

The table of cumulative National League frequency is given by

    Batting averageNational League Cumulative Frequency
    0.180-0.1992
    0.200-0.2199
    0.220-0.23929
    0.240-0.25958
    0.260-0.27990
    0.280-0.299120
    0.300-0.319137
    0.320-0.339142
    0.340-0.359143

The frequency ogive for National League frequency distribution is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 44E , additional homework tip  3

g.

Expert Solution
Check Mark
To determine

To compute: The cumulative relative frequencies for the classes in the National league frequency distribution.

Answer to Problem 44E

    Batting averageCumulative relative Frequency
    0.180-0.1990.014
    0.200-0.2190.063
    0.220-0.2390.203
    0.240-0.2590.406
    0.260-0.2790.629
    0.280-0.2990.839
    0.300-0.3190.958
    0.320-0.3390.993
    0.340-0.3591.000

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: The cumulative relative frequency of a class is given by

  cumulative relative frequency=cumulative frequencySum of all frequency

Calculation:

The cumulative classes are given by in the following table.

    Batting averageNational League Cumulative FrequencyCumulative relative frequency
    0.180-0.19922143=0.014
    0.200-0.21999143=0.063
    0.220-0.2392929143=0.203
    0.240-0.2595858143=0.406
    0.260-0.2799090143=0.629
    0.280-0.299120120143=0.839
    0.300-0.319137137143=0.958
    0.320-0.339142142143=0.993
    0.340-0.359143143143=1.000

Hence, the cumulative relative frequency for National league is given by

    Batting averageCumulative relative Frequency
    0.180-0.1990.014
    0.200-0.2190.063
    0.220-0.2390.203
    0.240-0.2590.406
    0.260-0.2790.629
    0.280-0.2990.839
    0.300-0.3190.958
    0.320-0.3390.993
    0.340-0.3591.000

h.

Expert Solution
Check Mark
To determine

To find: The relative frequency ogive for the National league frequency distribution.

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:A relative frequency ogive plots the cumulative relative frequencies..

Solution:

The table of cumulative relative frequency for the National league frequency distribution is given by

    Batting averageCumulative relative Frequency
    0.180-0.1990.014
    0.200-0.2190.063
    0.220-0.2390.203
    0.240-0.2590.406
    0.260-0.2790.629
    0.280-0.2990.839
    0.300-0.3190.958
    0.320-0.3390.993
    0.340-0.3591.000

The relative frequency ogivefor National League is given by

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 2.2, Problem 44E , additional homework tip  4

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Chapter 2 Solutions

Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561

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