Connect Hosted by ALEKS Access Card or Elementary Statistics
Connect Hosted by ALEKS Access Card or Elementary Statistics
3rd Edition
ISBN: 9781260373752
Author: William Navidi Prof., Barry Monk Professor
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
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

  Connect Hosted by ALEKS Access Card or Elementary Statistics, 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

  Connect Hosted by ALEKS Access Card or Elementary Statistics, 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

  Connect Hosted by ALEKS Access Card or Elementary Statistics, 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

  Connect Hosted by ALEKS Access Card or Elementary Statistics, 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

  Connect Hosted by ALEKS Access Card or Elementary Statistics, Chapter 2.2, Problem 28E , additional homework tip  5

The relative frequency histogram for the National League is given by

  Connect Hosted by ALEKS Access Card or Elementary Statistics, 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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
There are four white, fourteen blue and five green marbles in a bag.  A marble is selected from the bag without looking.  Find the odds of the following:    The odds against selecting a green marble. The odds in favour of not selecting a green marble The odds in favor of the marble selected being either a white or a blue marble. What is true about the above odds?  Explain
Please show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy.    1. The probability of a soccer game in a particular league going into overtime is 0.125.  Find the following:   a. The odds in favour of a game going into overtime. b. The odds in favour of a game not going into overtime. c. If the teams in the league play 100 games in a season, about how many games would you expect to go into overtime?
explain the importance of the Hypothesis test in a business setting, and give an example of a situation where it is helpful in business decision making.

Chapter 2 Solutions

Connect Hosted by ALEKS Access Card or Elementary Statistics

Ch. 2.1 - Following is a pie chart that presents the...Ch. 2.1 - Government spending: The following pie chart...Ch. 2.1 - U.S. population: The following side-by-side bar...Ch. 2.1 - Super Bowl: The following side-by-side bar graph...Ch. 2.1 - Smartphone sales: The following frequency...Ch. 2.1 - Popular video games: The following frequency...Ch. 2.1 - More smartphones: Using the data in Exercise 19:...Ch. 2.1 - More video games: Using the data in Exercise 20:...Ch. 2.1 - Hospital admissions: The following frequency...Ch. 2.1 - World population: Following are the populations of...Ch. 2.1 - Ages of video garners: The Nielsen Company...Ch. 2.1 - How secure is your job? In a survey, employed...Ch. 2.1 - Back up your data: In a survey commissioned by the...Ch. 2.1 - Education levels: The following frequency...Ch. 2.1 - Twitter followers: The following frequency...Ch. 2.1 - Music sales: The following frequency distribution...Ch. 2.1 - Keeping up with the Kardashians: The following...Ch. 2.1 - Bought a new car lately? The following table...Ch. 2.1 - Bought a new- truck lately? The following table...Ch. 2.1 - Happy Halloween: The following table presents...Ch. 2.1 - Native languages: The following frequency...Ch. 2.1 - Proportion of females: Following are the...Ch. 2.2 - Prob. 5ECh. 2.2 - In Exercises 5—8, fill in each blank with the...Ch. 2.2 - In Exercises 5—8, fill in each blank with the...Ch. 2.2 - In Exercises 5—8, fill in each blank with the...Ch. 2.2 - In Exercises 9—12, determine whether the...Ch. 2.2 - In Exercises 9—12, determine whether the...Ch. 2.2 - In Exercises 9—12, determine whether the...Ch. 2.2 - In Exercises 9—12, determine whether the...Ch. 2.2 - In Exercises 13—16, classify the histogram as...Ch. 2.2 - In Exercises 13—16, classify the histogram as...Ch. 2.2 - In Exercises 13—16, classify the histogram as...Ch. 2.2 - In Exercises 13—16, classify the histogram as...Ch. 2.2 - In Exercises 17 and 18, classify the histogram as...Ch. 2.2 - In Exercises 17 and 18, classify the histogram as...Ch. 2.2 - Student heights: The following frequency histogram...Ch. 2.2 - Trained rats: Forty rats were trained to run a...Ch. 2.2 - Cholesterol: The following histogram shows the...Ch. 2.2 - Blood pressure: The following histogram shows the...Ch. 2.2 - Olympic athletes: The following frequency...Ch. 2.2 - Hows the weather? The following relative frequency...Ch. 2.2 - Skewed which way? For which of the following data...Ch. 2.2 - Skewed which way? For which of the following data...Ch. 2.2 - Batting average: The following frequency...Ch. 2.2 - Batting average: The following frequency...Ch. 2.2 - Time spent playing video games: A sample of 200...Ch. 2.2 - Murder, she wrote: The following frequency...Ch. 2.2 - BMW prices: The following table presents the...Ch. 2.2 - Geysers: The geyser Old Faithful in Yellowstone...Ch. 2.2 - Hail to the chief: There have been 58 presidential...Ch. 2.2 - Internet radio: The following table presents the...Ch. 2.2 - Brothers and sisters: Thirty students in a...Ch. 2.2 - Cough, cough: The following table presents the...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Frequency polygon: Using the data in Exercise 29:...Ch. 2.2 - Prob. 42ECh. 2.2 - Ogive: Using the data in Exercise 27: Compute the...Ch. 2.2 - Ogive: Using the data in Exercise 28: Compute the...Ch. 2.2 - Ogive: Using the data in Exercise 29: Compute the...Ch. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Frequencies and relative frequencies: The...Ch. 2.3 - In Exercises 3—6, fill in each blank with the...Ch. 2.3 - In Exercises 3—6, fill in each blank with the...Ch. 2.3 - In Exercises 3—6, fill in each blank with the...Ch. 2.3 - In Exercises 3—6, fill in each blank with the...Ch. 2.3 - Prob. 7ECh. 2.3 - In Exercises 7—10, determine whether the...Ch. 2.3 - In Exercises 7—10, determine whether the...Ch. 2.3 - In Exercises 7—10, determine whether the...Ch. 2.3 - Construct a stem-and-leaf plot for the following...Ch. 2.3 - Construct a stem-and-leaf plot for the following...Ch. 2.3 - List the data in the following stem-and-leaf plot....Ch. 2.3 - List the data in the following stein-and-leaf...Ch. 2.3 - Construct a dotplot for the data in Exercise 11.Ch. 2.3 - Prob. 16ECh. 2.3 - BMW prices: The following table presents the...Ch. 2.3 - Hows the weather? The following table presents the...Ch. 2.3 - Air pollution: The following table presents...Ch. 2.3 - Technology salaries: The following table presents...Ch. 2.3 - Tennis and golf: Following are the ages of the...Ch. 2.3 - Pass the popcorn: Following are the running times...Ch. 2.3 - More weather: Construct a dotplot for the data in...Ch. 2.3 - Prob. 24ECh. 2.3 - Looking for a job: The following table presents...Ch. 2.3 - Prob. 26ECh. 2.3 - Military spending: The following table presents...Ch. 2.3 - Prob. 28ECh. 2.3 - Dining out: The following time-series plot...Ch. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - More gold: The following time series plot presents...Ch. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Vote: The following time-series plot presents the...Ch. 2.3 - Arctic ice sheet: The following table presents the...Ch. 2.3 - Prob. 37ECh. 2.4 - In Exercises 3 and 4, fill in each blank with the...Ch. 2.4 - In Exercises 3 and 4, fill in each blank with the...Ch. 2.4 - CD sales decline: Sales of CDs have been declining...Ch. 2.4 - Music sales: The following time-series plot and...Ch. 2.4 - Stock market prices: The Dow Jones Industrial...Ch. 2.4 - Save your money: In 2007, U.S. residents saved...Ch. 2.4 - Ill take mine with mustard: The following bar...Ch. 2.4 - Stream or download? The following bar graph...Ch. 2.4 - Female senators: Of the 100 members of the United...Ch. 2.4 - Age at marriage: Data compiled by the U.S. Census...Ch. 2.4 - College degrees: Both of the following time-series...Ch. 2.4 - Food expenditures: Both of the following...Ch. 2.4 - Prob. 15ECh. 2 - Following is the list of letter grades for...Ch. 2 - Prob. 2CQCh. 2 - Construct a frequency bar graph for the data in...Ch. 2 - Prob. 4CQCh. 2 - Prob. 5CQCh. 2 - Prob. 6CQCh. 2 - Prob. 7CQCh. 2 - Prob. 8CQCh. 2 - Prob. 9CQCh. 2 - Prob. 10CQCh. 2 - Following are the prices (in dollars) for a sample...Ch. 2 - Prob. 12CQCh. 2 - Prob. 13CQCh. 2 - Prob. 14CQCh. 2 - Prob. 15CQCh. 2 - Trust your doctor: The General Social Survey...Ch. 2 - Internet browsers: The following relative...Ch. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - House freshmen: Newly elected members of the U.S....Ch. 2 - More freshmen: For the data in Exercise 6:...Ch. 2 - Royalty: Following are the ages at death for all...Ch. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Explain why the frequency bar graph and the...Ch. 2 - Prob. 2WAICh. 2 - Prob. 3WAICh. 2 - Prob. 4WAICh. 2 - Prob. 5WAICh. 2 - In the chapter introduction, we presented gas...Ch. 2 - In the chapter introduction, we presented gas...Ch. 2 - In the chapter introduction, we presented gas...Ch. 2 - Prob. 4CSCh. 2 - In the chapter introduction, we presented gas...Ch. 2 - Prob. 6CSCh. 2 - In the chapter introduction, we presented gas...Ch. 2 - Prob. 8CSCh. 2 - In the chapter introduction, we presented gas...
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
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