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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

How are the relative frequencies and percentages of categories obtained from the frequencies of categories? Illustrate with the help of an example.

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. \(\begin{array}{lllllllll}\text { F } & \text { F } & \text { DR } & \text { DR } & \text { DR } & \text { DR } & \text { D } & \text { D } & \text { W } & \text { W } \\ \text { D } & \text { W } & \text { W } & \text { D } & \text { D } & \text { R } & \text { D } & \text { R } & \text { R } & \text { R } \\ \text { R } & \text { D } & \text { R } & \text { D } & \text { R } & \text { R } & \text { R } & \text { D } & \text { R } & \text { R }\end{array}\) 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. What percentage of these presidents were Whigs?

These data give the times (in minutes) taken to commute from home to work for 20 workers. \(\begin{array}{llllllllll}10 & 50 & 65 & 33 & 48 & 5 & 11 & 23 & 39 & 26 \\\ 26 & 32 & 17 & 7 & 15 & 19 & 29 & 43 & 21 & 22\end{array}\) Construct a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order.

Briefly explain the three decisions that have to be made to group a data set in the form of a frequency distribution table.

The following data give the repair costs (in dollars) for 30 cars randomly selected from a list of cars that were involved in collisions. \(\begin{array}{lrrrrr}2300 & 750 & 2500 & 410 & 555 & 1576 \\ 2460 & 1795 & 2108 & 897 & 989 & 1866 \\ 2105 & 335 & 1344 & 1159 & 1236 & 1395 \\ 6108 & 4995 & 5891 & 2309 & 3950 & 3950 \\ 6655 & 4900 & 1320 & 2901 & 1925 & 6896\end{array}\) a. Construct a frequency distribution table. Take \(\$ 1\) as the lower limit of the first class and \(\$ 1400\) as the width of each class. b. Compute the relative frequencies and percentages for all classes. c. Draw a histogram and a polygon for the relative frequency distribution. d. What are the class boundaries and the width of the fourth class?
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