91Ó°ÊÓ

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.

The following table lists the average price per gallon for unleaded regular gasoline in the United States from 1999 to 2008 . $$ \begin{array}{lc} \hline \text { Year } & \begin{array}{c} \text { Average Price per Gallon } \\ \text { (dollars) } \end{array} \\ \hline 1999 & 1.136 \\ 2000 & 1.484 \\ 2001 & 1.420 \\ 2002 & 1.345 \\ 2003 & 1.561 \\ 2004 & 1.852 \\ 2005 & 2.270 \\ 2006 & 2.572 \\ 2007 & 2.796 \\ 2008 & 3.246 \\ \hline \end{array} $$ Draw two bar graphs for these data-the first without truncating the axis on which price is marked, and the second by truncating this axis. In the second graph, mark the prices on the vertical axis starting with $$\$ 1.00 .$$ Briefly comment on the two bar graphs.

The following frequency distribution table gives the age distribution of drivers who were at fault in auto accidents that occurred during a 1 -week period in a city. $$ \begin{array}{lr} \hline \text { Age (years) } & \boldsymbol{f} \\ \hline \text { 18 to less than } 20 & 7 \\ 20 \text { to less than } 25 & 12 \\ 25 \text { to less than } 30 & 18 \\ 30 \text { to less than } 40 & 14 \\ 40 \text { to less than } 50 & 15 \\ 50 \text { to less than } 60 & 16 \\ 60 \text { and over } & 35 \\ \hline \end{array} $$ a. Draw a relative frequency histogram for this table. b. In what way(s) is this histogram misleading? c. How can you change the frequency distribution so that the resulting histogram gives a clearer picture?