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Chapter 2: Problem 24

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

Short Answer

Expert verified
Stem-and-leaf displays maintain the original data points for visual representation while frequency distributions lose this data. Therefore, stem-and-leaf displays have an advantage if there is a need to view or show the original data set as compared to using a frequency distribution.

Step by step solution

01

Define frequency distribution

A frequency distribution is a tabular arrangement of data by classes or groups along with their corresponding frequency or count. Being in table format, it provides an overview of all possible values, and their counts.
02

Define stem-and-leaf display

A stem-and-leaf display is another data representation technique that might be considered as a form of histogram. It's used to portray quantitative data in a graphical format similar to a histogram, making it more user-friendly. With a stem-and-leaf display, one can easily see the distribution of data and the central tendency.
03

Compare frequency distribution and stem-and-leaf display

While frequency distributions offer the advantage of easy data arrangement, they unfortunately lose the actual data points. With frequency distributions, the original data cannot be retrieved while stem-and-leaf displays retain the original data and provide a graphical representation of it.
04

Give an example

For instance, if we use a dataset like [1, 2, 2, 3, 4, 4, 4, 5], frequency distribution would summarize as: Value of 1 occurs 1 time, Value of 2 occurs 2 times, Value of 3 occurs 1 time, Value of 4 occurs 3 times, Value of 5 occurs 1 time. When using a stem-and-leaf display, we would have: \[1|1\] (for '1' occurs 1 time); \[2|22\] (for '2' occurs 2 times); \[3|3\] (for '3' occurs 1 time); \[4|444\] (for '4' occurs 3 times); \[5|5\] (for '5' occurs 1 time). The second representation is more visual and shows the exact data values.

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Most popular questions from this chapter

The following data give the number of text messages sent on 40 randomly selected days during 2015 by a high school student. \(\begin{array}{llllllllll}32 & 33 & 33 & 34 & 35 & 36 & 37 & 37 & 37 & 37 \\\ 38 & 39 & 40 & 41 & 41 & 42 & 42 & 42 & 43 & 44 \\ 44 & 45 & 45 & 45 & 47 & 47 & 47 & 47 & 47 & 48 \\ 48 & 49 & 50 & 50 & 51 & 52 & 53 & 54 & 59 & 61\end{array}\) Create a dotplot for these data.

The National Highway Traffic Safety Administration collects data on fatal accidents that occur on roads in the United States. The following data represent the number of vehicle fatalities for 39 counties in South Carolina for 2012 (www-fars.nhtsa.dot.gov/States). $$ \begin{array}{rrrrrrrr} 4 & 48 & 9 & 9 & 31 & 22 & 26 & 17 \\ 20 & 12 & 6 & 5 & 14 & 9 & 16 & 27 \\ 3 & 33 & 9 & 20 & 68 & 13 & 51 & 13 \\ 48 & 23 & 12 & 13 & 10 & 15 & 8 & 1 \\ 2 & 4 & 17 & 16 & 6 & 52 & 50 & \end{array} $$ Prepare a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order.

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.

What are the benefits of preparing a dotplot? Explain.

The following data give the taxes paid (rounded to thousand dollars) in 2014 by a random sample of 30 families. $$ \begin{array}{rrrrrrrrrr} 11 & 17 & 35 & 3 & 15 & 9 & 21 & 13 & 5 & 19 \\ 5 & 12 & 8 & 16 & 10 & 8 & 12 & 6 & 14 & 18 \\ 8 & 12 & 5 & 3 & 14 & 28 & 38 & 18 & 22 & 15 \end{array} $$ a. Prepare a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order. b. Prepare a split stem-and-leaf display for these data. Split each stem into two parts. The first part should contain the leaves 0 through 4 , and the second part should contain the leaves 5 through 9
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