91Ó°ÊÓ

Why do we need to group data in the form of a frequency table? Explain briefly.

The following data give the results of a sample survey. The letters \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) represent the three categories. \(\begin{array}{llllllllll}\text { A } & \text { B } & \text { B } & \text { A } & \text { C } & \text { B } & \text { C } & \text { C } & \text { C } & \text { A } \\ \text { C } & \text { B } & \text { C } & \text { A } & \text { C } & \text { C } & \text { B } & \text { C } & \text { C } & \text { A } \\\ \text { A } & \text { B } & \text { C } & \text { C } & \text { B } & \text { C } & \text { B } & \text { A } & \text { C } & \text { A }\end{array}\) a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of the elements in this sample belong to category \(\mathrm{B}\) ? d. What percentage of the elements in this sample belong to category A or C? e. Draw a bar graph for the frequency distribution.

The following data give the results of a sample survey. The letters \(\mathrm{Y}, \mathrm{N}\), and \(\mathrm{D}\) represent the three categories. \(\begin{array}{llllllllll}\mathrm{D} & \mathrm{N} & \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{Y} & \mathrm{D} & \mathrm{Y} \\\ \mathrm{Y} & \mathrm{Y} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{N} & \mathrm{Y} \\ \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{D} & \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{Y} & \mathrm{Y} \\ \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{N} & \mathrm{Y} & \mathrm{Y} & \mathrm{N} & \mathrm{N} & \mathrm{D} & \mathrm{Y}\end{array}\) C. a. Prepare a frequency distribution table. c. What percentage of the elements in this sample belong to category Y? d. What percentage of the elements in this sample belong to category \(\mathrm{N}\) or \(\mathrm{D}\) ? e. Draw a pie chart for the percentage distribution. b. Calculate the relative frequencies and percentages for all categories.

The following data give the number of turnovers (fumbles and interceptions) made by both teams in each of the football games played by North Carolina State University during the 2009 and 2010 seasons. $$ \begin{array}{llllllllllll} 2 & 3 & 1 & 1 & 6 & 5 & 3 & 5 & 5 & 1 & 5 & 2 \\ 5 & 3 & 4 & 4 & 5 & 8 & 4 & 5 & 2 & 2 & 2 & 6 \end{array} $$ a. Construct a frequency distribution table for these data using single-valued classes. b. Calculate the relative frequency and percentage for each class. c. What is the relative frequency of games in which there were 4 or 5 turnovers? d. Draw a bar graph for the frequency distribution of part a.

Briefly explain how to prepare a stem-and-leaf display for a data set. You may use an example to illustrate.

What advantage does preparing a stem-and-leaf display have over grouping a data set using a frequency distribution? Give one example.

Consider the following stem-and-leaf display. $$ \begin{array}{l|lllllll} 4 & 3 & 6 & & & & & & \\ 5 & 0 & 1 & 4 & 5 & & & & \\ 6 & 3 & 4 & 6 & 7 & 7 & 7 & 8 & 9 \\ 7 & 2 & 2 & 3 & 5 & 6 & 6 & 9 & \\ 8 & 0 & 7 & 8 & 9 & & & & \end{array} $$ Write the data set that is represented by this display.

The following data give the time (in minutes) that each of 20 students waited in line at their bookstore to pay for their textbooks in the beginning of Spring 2012 semester. (Note: To prepare a stem-andleaf display, each number in this data set can be written as a two-digit number. For example, 8 can be written as 08 , for which the stem is 0 and the leaf is \(8 .\) ) \(\begin{array}{rrrrrrrrrr}15 & 8 & 23 & 21 & 5 & 17 & 31 & 22 & 34 & 6 \\ 5 & 10 & 14 & 17 & 16 & 25 & 30 & 3 & 31 & 19\end{array}\) Construct a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order.

Following are the total yards gained rushing during the 2012 season by 14 running backs of 14 college football teams. \(\begin{array}{rrrrrrr}745 & 921 & 1133 & 1024 & 848 & 775 & 800 \\ 1009 & 1275 & 857 & 933 & 1145 & 967 & 995\end{array}\) Prepare a stem-and-leaf display. Arrange the leaves for each stem in increasing order.

The following data give the times served (in months) by 35 prison inmates who were released recently. \(\begin{array}{lllrrlllll}37 & 6 & 20 & 5 & 25 & 30 & 24 & 10 & 12 & 20 \\ 24 & 8 & 26 & 15 & 13 & 22 & 72 & 80 & 96 & 33 \\ 84 & 86 & 70 & 40 & 92 & 36 & 28 & 90 & 36 & 32 \\ 72 & 45 & 38 & 18 & 9 & & & & & \end{array}\) a. Prepare a stem-and-leaf display for these data. b. Condense the stem-and-leaf display by grouping the stems as \(0-2,3-5\), and \(6-9\).