91Ó°ÊÓ

Briefly explain how to prepare a dotplot for a data set. You may use an example to illustrate.

The following data give the political party of each of the first 30 U.S. presidents. In the data, D stands for Democrat, DR for Democratic Republican, \(\mathrm{F}\) for Federalist, \(\mathrm{R}\) for Republican, and \(\mathrm{W}\) for Whig. $$ \begin{array}{llllllllll} \text { F } & \text { F } & \text { DR } & \text { DR } & \text { DR } & \text { DR } & \text { D } & \text { D } & \text { W } & \text { W } \\ \text { D } & \text { W } & \text { W } & \text { D } & \text { D } & \text { R } & \text { D } & \text { R } & \text { R } & \text { R } \\ \text { R } & \text { D } & \text { R } & \text { D } & \text { R } & \text { R } & \text { R } & \text { D } & \text { R } & \text { R } \end{array} $$ a. Prepare a frequency distribution table for these data. b. Calculate the relative frequency and percentage distributions. c. Draw a bar graph for the relative frequency distribution and a pie chart for the percentage distribution. d. Make a Pareto chart for the frequency distribution. e. What percentage of these presidents were Whigs?

The following data give the number of text messages sent on 40 randomly selected days during 2015 by a high school student: $$ \begin{array}{llllllllll} 32 & 33 & 33 & 34 & 35 & 36 & 37 & 37 & 37 & 37 \\ 38 & 39 & 40 & 41 & 41 & 42 & 42 & 42 & 43 & 44 \\ 44 & 45 & 45 & 45 & 47 & 47 & 47 & 47 & 47 & 48 \\ 48 & 49 & 50 & 50 & 51 & 52 & 53 & 54 & 59 & 61 \end{array} $$ a. Construct a frequency distribution table. Take 32 as the lower limit of the first class and 6 as the class width. b. Calculate the relative frequency and percentage for each class. c. Construct a histogram for the frequency distribution of part a. d. On what percentage of these 40 days did this student send 44 or more text messages? e. Prepare the cumulative frequency, cumulative relative frequency, and cumulative percentage distributions.

The following data give the amounts (in dollars) spent on refreshments by 30 spectators randomly selected from those who patronized the concession stands at a recent Major League Baseball game. $$ \begin{array}{rrrrrrrr} 4.95 & 27.99 & 8.00 & 5.80 & 4.50 & 2.99 & 4.85 & 6.00 \\ 9.00 & 15.75 & 9.50 & 3.05 & 5.65 & 21.00 & 16.60 & 18.00 \\ 21.77 & 12.35 & 7.75 & 10.45 & 3.85 & 28.45 & 8.35 & 17.70 \\ 19.50 & 11.65 & 11.45 & 3.00 & 6.55 & 16.50 & & \end{array} $$ a. Construct a frequency distribution table using the less-than method to write classes. Take \(\$ 0\) as the lower boundary of the first class and \(\$ 6\) as the width of each class. b. Calculate the relative frequencies, and percentages for all classes. c. Draw a histogram for the frequency distribution. d. Prepare the cumulative frequency, cumulative relative frequency, and cumulative percentage distributions.

Suppose a data set contains the ages of 135 autoworkers ranging from 20 to 53 years. a. Using Sturge's formula given in footnote 1 in section \(2.2 .2\), find an appropriate number of classes for a frequency distribution for this data set. b. Find an appropriate class width based on the number of classes in part a.

Stem-and-leaf displays can be used to compare distributions for two groups using a back-to-back stem-and-leaf display. In such a display, one group is shown on the left side of the stems, and the other group is shown on the right side. When the leaves are ordered, the leaves increase as one moves away from the stems. The following stem-and-leaf display shows the money earned per tournament entered for the top 30 money winners in the \(2008-09\) Professional Bowlers Association men's tour and for the top 21 money winners in the 2008 09 Professional Bowlers Association women's tour. $$ \begin{array}{r|c|l} \text { Women's } & & \text { Men's } \\ \hline 8 & 0 & \\ 8871 & 1 & \\ 65544330 & 2 & 334456899 \\ 840 & 3 & 03344678 \\ 52 & 4 & 011237888 \\ 21 & 5 & 9 \\ & 6 & 9 \\ 5 & 7 & \\ & 8 & 7 \\ & 9 & 5 \end{array} $$ The leaf unit for this display is 100 . In other words, the data used represent the earnings in hundreds of dollars. For example, for the women's tour, the first number is 08 , which is actually 800 . The second number is 11 , which actually is 1100 . a. Do the top money winners, as a group, on one tour (men's or women's) tend to make more money per tournament played than on the other tour? Explain how you can come to this conclusion using the stem-and-leaf display. b. What would be a typical earnings level amount per tournament played for each of the two tours? c. Do the data appear to have similar spreads for the two tours? Explain how you can come to this conclusion using the stemand-leaf display. d. Does either of the tours appears to have any outliers? If so, what are the earnings levels for these players?