Elementary Statistics: A Step-by-Step Approach with Formula Card
Elementary Statistics: A Step-by-Step Approach with Formula Card
9th Edition
ISBN: 9780078136337
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Textbook Question
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Chapter 3.2, Problem 48EC

Pearson Coefficient of Skewness A measure to determine the skewness of a distribution is called the Pearson coefficient (PC) of skewness. The formula is

The values of the coefficient usually range from −3 to +3. When the distribution is symmetric, the coefficient is zero; when the distribution is positively skewed, it is positive; and when the distribution is negatively skewed, it is negative.

Using the formula, find the coefficient of skewness for each distribution, and describe the shape of the distribution.

a. Mean = 10, median = 8, standard deviation = 3.

b. Mean = 42, median = 45, standard deviation = 4.

c. Mean = 18.6, median = 18.6, standard deviation = 1.5.

d. Mean = 98, median = 97.6, standard deviation = 4.

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Chapter 3 Solutions

Elementary Statistics: A Step-by-Step Approach with Formula Card

Ch. 3.1 - Teacher Salaries The following data from several...Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Observers in the Frogwatch Program The number of...Ch. 3.1 - Prob. 5ECh. 3.1 - Earnings of Nonliving Celebrities Forbes magazine...Ch. 3.1 - Prob. 7ECh. 3.1 - Top-Paid CEOs The data shown are the total...Ch. 3.1 - Prob. 9E
Ch. 3.1 - Foreign Workers The number of foreign workers...Ch. 3.1 - Distances of Stars Of the 25 brightest stars, the...Ch. 3.1 - Contest Spelling Words The last words given and...Ch. 3.1 - Prob. 13ECh. 3.1 - Hourly Compensation for Production Workers The...Ch. 3.1 - Prob. 15ECh. 3.1 - Percentage of Foreign-Born People The percentage...Ch. 3.1 - Percentage of College-Educated Population over 25...Ch. 3.1 - Net Worth of Corporations These data represent the...Ch. 3.1 - Specialty Coffee Shops A random sample of 30...Ch. 3.1 - Commissions Earned This frequency distribution...Ch. 3.1 - Prob. 21ECh. 3.1 - Enrollments for Selected Independent Religiously...Ch. 3.1 - Automobile Selling Prices Find the weighted mean...Ch. 3.1 - Fat Grams Using the weighted mean, find the...Ch. 3.1 - Diet Cola Preference A recent survey of a new diet...Ch. 3.1 - Costs of Helicopters The costs of three models of...Ch. 3.1 - Final Grade An instructor grades exams, 20%; term...Ch. 3.1 - Final Grade Another instructor gives four 1-hour...Ch. 3.1 - For these situations, state which measure of...Ch. 3.1 - Describe which measure of central tendencymean,...Ch. 3.1 - What types of symbols are used to represent sample...Ch. 3.1 - A local fast-food company claims that the average...Ch. 3.1 - If the mean of five values is 64, find the sum of...Ch. 3.1 - If the mean of five values is 8.2 and four of the...Ch. 3.1 - Find the mean of 10, 20, 30, 40, and 50. a. Add 10...Ch. 3.1 - Harmonic Mean The harmonic mean (HM) is defined as...Ch. 3.1 - Geometric Mean The geometric mean (GM) is defined...Ch. 3.1 - Quadratic Mean A useful mean in the physical...Ch. 3.1 - Median for Grouped Data An approximate median can...Ch. 3.2 - Blood Pressure The table lists means and standard...Ch. 3.2 - What is the relationship between the variance and...Ch. 3.2 - Why might the range not be the best estimate of...Ch. 3.2 - What are the symbols used to represent the...Ch. 3.2 - What are the symbols used to represent the sample...Ch. 3.2 - Why is the unbiased estimator of variance used?Ch. 3.2 - The three data sets have the same mean and range,...Ch. 3.2 - Prob. 7ECh. 3.2 - Cigarette Taxes The increases (in cents) in...Ch. 3.2 - Prob. 9ECh. 3.2 - Size of U.S. States The total surface area (in...Ch. 3.2 - Multiple Births The numbers of various multiple...Ch. 3.2 - Starting Teachers Salaries Starting teachers...Ch. 3.2 - Ages of U.S. Astronaut Candidates The average age...Ch. 3.2 - Times Spent in Rush-Hour Traffic A sample of 12...Ch. 3.2 - Prob. 15ECh. 3.2 - Passenger Vehicle Deaths The number of people...Ch. 3.2 - Annual Precipitation Days The number of annual...Ch. 3.2 - Use the data from Exercises 7, 15, and 17...Ch. 3.2 - Prob. 19ECh. 3.2 - Automotive Fuel Efficiency Thirty automobiles were...Ch. 3.2 - Murders in Cities The data show the number of...Ch. 3.2 - Reaction Times In a study of reaction times to a...Ch. 3.2 - FM Radio Stations A random sample of 30 states...Ch. 3.2 - Murder Rates The data represent the murder rate...Ch. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Missing Work The average number of days that...Ch. 3.2 - Suspension Bridges The lengths (in feet) of the...Ch. 3.2 - Hospital Emergency Waiting Times The mean of the...Ch. 3.2 - Ages of Accountants The average age of the...Ch. 3.2 - Using Chebyshevs theorem, solve these problems for...Ch. 3.2 - The mean of a distribution is 20 and the standard...Ch. 3.2 - In a distribution of 160 values with a mean of 72,...Ch. 3.2 - Calories in Bagels The average number of calories...Ch. 3.2 - Time Spent Online Americans spend an average of 3...Ch. 3.2 - Solid Waste Production The average college student...Ch. 3.2 - Sale Price of Homes The average sale price of...Ch. 3.2 - Trials to Learn a Maze The average of the number...Ch. 3.2 - Farm Sizes The average farm in the United States...Ch. 3.2 - Citrus Fruit Consumption The average U.S. yearly...Ch. 3.2 - SAT Scores The national average for mathematics...Ch. 3.2 - Work Hours for College Faculty The average...Ch. 3.2 - Serum Cholesterol Levels For this data set, find...Ch. 3.2 - Ages of Consumers For this data set, find the mean...Ch. 3.2 - Prob. 45ECCh. 3.2 - Use this data set: 10, 20, 30, 40, 50 a. Find the...Ch. 3.2 - Mean Deviation The mean deviation is found by...Ch. 3.2 - All values of a data set must be within sn1 of the...Ch. 3.2 - Pearson Coefficient of Skewness A measure to...Ch. 3.3 - Determining Dosages In an attempt to determine...Ch. 3.3 - What is a z score?Ch. 3.3 - Define percentile rank.Ch. 3.3 - What is the difference between a percentage and a...Ch. 3.3 - Define quartile.Ch. 3.3 - What is the relationship between quartiles and...Ch. 3.3 - What is a decile?Ch. 3.3 - How are deciles related to percentiles?Ch. 3.3 - To which percentile, quartile, and decile does the...Ch. 3.3 - Vacation Days If the average number of vacation...Ch. 3.3 - Age of Senators The average age of Senators in the...Ch. 3.3 - Prob. 11ECh. 3.3 - Teachers Salary The average teachers salary in a...Ch. 3.3 - Prob. 13ECh. 3.3 - College and University Debt A student graduated...Ch. 3.3 - Annual Miles Driven The average miles driven...Ch. 3.3 - Which score indicates the highest relative...Ch. 3.3 - College Room and Board Costs Room and board costs...Ch. 3.3 - Prob. 19ECh. 3.3 - Airplane Speeds The airborne speeds in miles per...Ch. 3.3 - Average Weekly Earnings The average weekly...Ch. 3.3 - Test Scores Find the percentile rank for each test...Ch. 3.3 - Hurricane Damage Find the percentile rank for each...Ch. 3.3 - Test Scores Find the percentile rank for each test...Ch. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Police Calls in Schools The number of incidents in...Ch. 3.3 - Prob. 29ECh. 3.3 - Check each data set for outliers. a. 88, 72, 97,...Ch. 3.3 - Another measure of the average is called the...Ch. 3.3 - An employment evaluation exam has a variance of...Ch. 3.3 - A particular standardized test has scores that...Ch. 3.4 - Applying the Concepts 34 The Noisy Workplace...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 710, use each boxplot to identify...Ch. 3.4 - For Exercises 710, use each boxplot to identify...Ch. 3.4 - For Exercises 710, use each boxplot to identify...Ch. 3.4 - For Exercises 7-10. use each boxplot to identify-...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Visitors Who Travel to Foreign Countries Construct...Ch. 3.4 - Prob. 15ECh. 3.4 - Size of Dams These data represent the volumes in...Ch. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Unhealthy Smog Days A modified boxplot can be...Ch. 3 - Prob. 3.1.1RECh. 3 - Shark Attacks The number of shark attacks and...Ch. 3 - Prob. 3.1.3RECh. 3 - SAT Scores The mean SAT math scores for selected...Ch. 3 - Households of Four Television Networks A survey...Ch. 3 - Investment Earnings An investor calculated these...Ch. 3 - Prob. 3.2.7RECh. 3 - Tallest Buildings The number of stories in the 13...Ch. 3 - Rise in Tides Shown here is a frequency...Ch. 3 - Fuel Capacity The fuel capacity in gallons for...Ch. 3 - If the range of a data set is 24, find the...Ch. 3 - If the range of a data set is 56, find the...Ch. 3 - Textbooks in Professors Offices If the average...Ch. 3 - Magazines in Bookstores A survey of bookstores...Ch. 3 - Cost of Car Rentals A survey of car rental...Ch. 3 - AID: 1825 | 28/05/2018 16. Average Earnings of...Ch. 3 - Labor Charges The average labor charge for...Ch. 3 - Costs to Train Employees For a certain type of...Ch. 3 - Prob. 3.2.19RECh. 3 - Exam Completion Time The mean time it takes a...Ch. 3 - Prob. 3.2.21RECh. 3 - Exam Grades Which of these exam grades has a...Ch. 3 - Prob. 3.3.23RECh. 3 - Printer Repairs The frequency distribution shows...Ch. 3 - Check each data set for outliers. a. 506, 511,...Ch. 3 - Check each data set for outliers. a. 14, 18, 27,...Ch. 3 - Named Storms The data show the number of named...Ch. 3 - Hours Worked The data shown here represent the...Ch. 3 - From the Data Bank, choose one of the following...Ch. 3 - Prob. 2DACh. 3 - Prob. 3DACh. 3 - Randomly select 10 values from the number of...Ch. 3 - Prob. 5DACh. 3 - AID: 1825 | 28/05/2018 Determine whether each...Ch. 3 - Prob. 2CQCh. 3 - Determine whether each statement is true or false....Ch. 3 - Prob. 4CQCh. 3 - In a data set, the mode will always be unique.Ch. 3 - Prob. 6CQCh. 3 - Determine whether each statement is true or false....Ch. 3 - Prob. 8CQCh. 3 - Determine whether each statement is true or false....Ch. 3 - Prob. 10CQCh. 3 - Prob. 11CQCh. 3 - Prob. 12CQCh. 3 - Which is not part of the five-number summary? a....Ch. 3 - A statistic that tells the number of standard...Ch. 3 - When a distribution is bell-shaped, approximately...Ch. 3 - Prob. 16CQCh. 3 - Generally, Greek letters are used to represent...Ch. 3 - Prob. 18CQCh. 3 - The symbol for the population standard deviation...Ch. 3 - When the sum of the lowest data value and the...Ch. 3 - If the mode is to the left of the median and the...Ch. 3 - An extremely high or extremely low data value is...Ch. 3 - Prob. 23CQCh. 3 - Prob. 24CQCh. 3 - Employee Years of Service In an advertisement, a...Ch. 3 - Newspapers for Sale The average number of...Ch. 3 - Prob. 27CQCh. 3 - Hours Worked The data shown here represent the...Ch. 3 - Prob. 29CQCh. 3 - Prob. 30CQCh. 3 - Exam Scores On a philosophy comprehensive exam,...Ch. 3 - Prob. 32CQCh. 3 - Prob. 1CTCCh. 3 - Ages of U.S. Residents The table shows the median...
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