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Chapter 2: Problem 44

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

Short Answer

Expert verified
A stem-and-leaf display is created by grouping similar data points and sorting them into 'stems' and 'leaves', in which the stem is the first digit or digits of the data point and the leaf is the last digit. This is done by sorting the data, identifying the stems and leaves, and arranging them in a display. For example, for the data set (10, 12, 24, 28, 30, 33, 35, 39, 42, 45), the stem-and-leaf display would be: \[\begin{array}{rl} 1 & 0, 2 \\ 2 & 4, 8 \\ 3 & 0, 3, 5, 9 \\ 4 & 2, 5 \end{array}\]

Step by step solution

01

Understanding Stem-and-Leaf Display

A stem-and-leaf display is a data visualization tool that groups data points with similar values and processes them categorically into 'stems' and 'leaves'. The stem is the first digit (or digits) and the leaf is the last digit (for one or two-digit numbers). For larger numbers, the leaf might be more than just the last digit.
02

Gather and Sort Data

Choose a simple data set, for example: 12, 10, 33, 24, 35, 45, 39, 28, 30, 42. Begin with sorting the data in ascending order, this makes it easier to create the stem and leaf display: 10, 12, 24, 28, 30, 33, 35, 39, 42, 45.
03

Identifying and Organizing Stems and Leaves

The stem is the decade digit of each data point, and the leaf the unit digit. In our example, our stems and leaves are from 1-4 (stems) and 0-9 (leaves). Start writing stems in a column. Next to them place the leaves belonging to each stem. For example: \[\begin{array}{rl} 1 & 0, 2 \\ 2 & 4, 8 \\ 3 & 0, 3, 5, 9 \\ 4 & 2, 5 \end{array}\]
04

Interpreting the Display

Each row corresponds to a data group (in this case, numbers in the 10s, 20s, 30s, and 40s). Each leaf entry represents a single data point in that group. This gives a quick overview of the dataset's distribution, with an unsophisticated and quickly readable format.

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Most popular questions from this chapter

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.

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 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 \(6-9\).

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.

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