Witte & Witte, 9e Page 1 of 3 Pages
Chapter 3 Exercises
Chapter 3 Describing Data with Averages
Exercise 1
The 500 Home Run Club includes the baseball players who have hit at least 500 home runs in their professional careers. The table below shows the names of the 500 Home Run Club members, their career home runs, and their age when they hit home run number 500.
Name / Career Home Runs / #500 AgeHank Aaron / 755 / 34
Ernie Banks / 512 / 39
Barry Bonds / 762 / 36
Jimmie Foxx / 534 / 32
Ken Griffey, Jr. / 611 / 34
Reggie Jackson / 563 / 38
Harmon Killebrew / 573 / 35
Mickey Mantle / 536 / 35
Eddie Mathews / 512 / 35
Willie Mays / 660 / 34
Willie McCovey / 521 / 40
Mark McGwire / 583 / 35
Eddie Murray / 504 / 40
Mel Ott / 511 / 36
Rafael Palmeiro / 569 / 38
Manny Ramirez / 527 / 36
Frank Robinson / 586 / 36
Alex Rodriguez / 553 / 32
Babe Ruth / 714 / 34
Mike Schmidt / 548 / 37
Sammy Sosa / 609 / 34
Frank Thomas / 521 / 39
Jim Thome / 541 / 37
Ted Williams / 521 / 41
Gary Sheffield / 500 / 40
Source: www.baseball-almanac.com/hitting/hi500c.shtml
1. Determine the mean, median, and mode for career home runs.
Answers: Mean = 573.04, Median = 548, Mode = 521 with a frequency of 3.
2. Determine the mean, median, and mode for age.
Answers: Mean = 36.28, Median = 36, Mode = 34
Exercise 2
Indicate whether the following skewed distributions are positively skewed because the mean exceeds the median or negatively skewed because the median exceeds the mean.
1. A distribution of ages of attendees at an André Rieu concert with most attendees in their sixties and seventies.
Answer: Negatively skewed
2. An income distribution in Great Britain for the years 2003-2004 where the mean was £408 while the median was £336. Source: http://www.ifs.org.uk/comms/comm99.pdf
Answer: Positively skewed
3. A distribution of actors’ wages in 2008 where the median hourly wage was $16.59 and the mean hourly wage was $29.05. Source: http://www.bls.gov/oes/current/oes_nat.htm
Answer: Positively skewed
4. A distribution academic physicians’ weekly computer use, ranging from 0 to 40 hours, with a median of 8 hours and a mean of 9.7 hours. Source: http://smi-web.stanford.edu/pubs/SMI_Reports/SMI-94-0528.pdf
Answer: Positively skewed
5. A distribution of daily time spent doing homework by fourth graders in 2000 with 43% reporting 30 minutes or less and 16% reporting more than 60 minutes. Source: http://nces.ed.gov/programs/digest/d04/tables/dt04_140.asp
Answer: Positively skewed
6. A distribution of grade point averages of graduate students with most falling between 3.8 and 4.0 and very few less than 3.4.
Answer: Negatively skewed
Exercise 3
Researchers surveyed college-educated women to find out what they find most appealing in men: physically attractive, sense of humor, earning power, or confidence. The results were as follows:
earning power / physically attractiveearning power / sense of humor
confidence / earning power
sense of humor / earning power
sense of humor / sense of humor
confidence / earning power
earning power / confidence
Find the mode, and if possible, the median.
Answer: The mode is earning power with a frequency of 6. This is nominally scaled data, and a median cannot be determined.