Problem 1
Find a histogram that shows the distribution of a variable in a newspaper, a magazine, or the Internet. a) Does the article identify the W's? b) Discuss whether the display is appropriate. c) Discuss what the display reveals about the variable and its distribution. d) Does the article accurately describe and interpret the data? Explain.
Problem 4
Find an article in a newspaper, a magazine, or the Internet that discusses a measure of spread. a) Does the article discuss the W's for the data? b) What are the units of the variable? c) Does the article use the range, IQR, or standard deviation? d) Is the choice of measure of spread appropriate for the situation? Explain.
Problem 5
Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain why. a) The number of speeding tickets each student in the senior class of a college has ever had. b) Players' scores (number of strokes) at the U.S. Open golf tournament in a given year. c) Weights of female babies born in a particular hospital over the course of a year. d) The length of the average hair on the heads of students in a large class.
Problem 6
Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain why. a) Ages of people at a Little League game. b) Number of siblings of people in your class. c) Pulse rates of college-age males. d) Number of times each face of a die shows in 100 tosses.
Problem 13
How many points do football teams score in the Super Bowl? Here are the total numbers of points scored by both teams in each of the first 42 Super Bowl games: \(45,47,23,30,29,27,21,31,22,38,46,37,66,50,37,47,44\), \(47,54,56,59,52,36,65,39,61,69,43,75,44,56,55,53,39\), \(41,37,69,61,45,31,46,31\) a) Find the median. b) Find the quartiles. c) Write a description based on the 5 -number summary.
Problem 14
In the Super Bowl, by how many points does the winning team outscore the losers? Here are the winning margins for the first 42 Super Bowl games: \(25,19,9,16,3,21,7,17,10,4,18,17,4,12,17,5,10,29,22\), \(36,19,32,4,45,1,13,35,17,23,10,14,7,15,7,27,3,27,3\), \(3,11,12,3\) a) Find the median. b) Find the quartiles. c) Write a description based on the 5 -number summary.
Problem 15
For each lettered part, a through c, examine the two given sets of numbers. Without doing any calculations, decide which set has the larger standard deviation and explain why. Then check by finding the standard deviations by hand. $$ \begin{array}{ll} {\text { Set 1 }} & {\text { Set 2 }} \\ \hline \text { a) } 4,7,7,7,10 & 4,6,7,8,10 \\ \text { b) } 100,140,150,160,200 & 10,50,60,70,110 \\ \text { c) } 10,16,18,20,22,28 & 48,56,58,60,62,70 \end{array} $$
Problem 16
For each lettered part, a through c, examine the two given sets of numbers. Without doing any calculations, decide which set has the larger standard deviation and explain why. Then check by finding the standard deviations by hand. \(\begin{array}{ll} {\text { Set 1 }} & {\text { Set 2 }} \\ \hline \text { a) } 4,7,7,7,10 & 4,6,7,8,10 \\ \text { b) } 100,140,150,160,200 & 10,50,60,70,110 \\ \text { c) } 10,16,18,20,22,28 & 48,56,58,60,62,70 \end{array}\)
Problem 18
The histogram shows the neck sizes (in inches) of 250 men recruited for a health study in Utah. Which summary statistics would you choose to summarize the center and spread in these data? Why?
Problem 23
Exercise 21 looked at the running times of movies released in \(2005 .\) The standard deviation of these running times is \(19.6\) minutes, and the quartiles are \(Q_{1}=97\) minutes and \(Q_{3}=119\) minutes. a) Write a sentence or two describing the spread in running times based on i) the quartiles. ii) the standard deviation. b) Do you have any concerns about using either of these descriptions of spread? Explain.
