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Chapter 2: Problem 46

Consider this 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 the display.

Short Answer

Expert verified
The data set represented by the stem-and-leaf display is [43, 46, 50, 51, 54, 55, 63, 64, 66, 67, 67, 67, 68, 69, 72, 72, 73, 75, 76, 76, 79, 80, 87, 88, 89].

Step by step solution

01

Understanding the stem and leaf display

Reading each row from the given stem-and-leaf display from left to right, the 'stem' is the left-side digit and the 'leaf' is the right-side digits. Each leaf digit represents a single data point when combined with the stem digit.
02

Creating the data set for the stems 4 and 5

Based on step 1, for the stem 4, the data points are 43 and 46. Similarly, for the stem 5, the data points are 50, 51, 54, and 55.
03

Creating the data set for the stems 6 and 7

Continuing from step 2, for the stem 6, the numbers are 63, 64, 66, 67, 67, 67, 68 and 69. For the stem 7 there are numbers 72, 72, 73, 75, 76, 76 and 79.
04

Creating the data set for the stem 8

Following the same process, for stem 8 the numbers are 80, 87, 88, and 89.
05

Combining the data sets

Combine all data points created in steps 2, 3, and 4 together into a single data set.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Data Representation with Stem-and-Leaf Plots
A stem-and-leaf plot is a simple way to represent data visually. It helps us see data distribution quickly by showing individual values along with their frequencies. In this type of plot, each data point is split into a "stem" and a "leaf."
  • The "stem" represents the leading digit or digits of the number.
  • The "leaf" indicates the trailing digit.
Consider how this works with the numbers: for 43, "4" is the stem, and "3" is the leaf.
This method allows us to gather all values easily while maintaining the original data details. In our example, stems range from 4 to 8, and each stem can have multiple leaves, pointing to numbers like 46 or 73, giving a clear snapshot of the data.
The Role of Statistics Education in Mastering Data Interpretation
Statistics education plays a vital role in helping individuals understand and interpret data. It provides tools and concepts like stem-and-leaf plots to visualize data effectively. Learning to manage and understand these tools can help students in various fields, from science to business.
Statistics education not only involves understanding various data representation methods but also teaches:
  • Critical thinking to analyze results.
  • Basic calculation skills for interpreting data.
  • Application of different techniques to solve real-world problems.
When students grasp these concepts, they can make informed decisions based on data trends and analysis.
Enhancing Visual Data Interpretation Skills
Visual data interpretation involves analyzing graphical data displays, such as stem-and-leaf plots, and extracting meaningful insights from them. By visually breaking down data, students and professionals can spot trends, significant points, and patterns efficiently.
Consider the following tips:
  • Identify stems and leaves first to understand the range and specific data points.
  • Look for clustering and gaps to see where data is concentrated or sparse.
  • Use the plot to quickly assess measures like the median or mode by looking at the distribution.
By mastering these skills, individuals can interact with data more intuitively, leading to better decision-making and hypothesis testing.

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Most popular questions from this chapter

Create a dotplot for the following data set. $$ \begin{array}{llllllllll} 1 & 2 & 0 & 5 & 1 & 1 & 3 & 2 & 0 & 5 \\ 2 & 1 & 2 & 1 & 2 & 0 & 1 & 3 & 1 & 2 \end{array} $$

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

Twenty-four students from a university in Oregon were asked to name the five current members of the U.S. House of Representatives from their state. The following data give the numbers of correct names given by these students. $$ \begin{array}{llllllllllll} 5 & 5 & 1 & 2 & 4 & 5 & 3 & 1 & 5 & 5 & 0 & 1 \\ 2 & 3 & 5 & 4 & 3 & 1 & 5 & 2 & 5 & 4 & 5 & 3 \end{array} $$ Create a dotplot for these data.

The following table, reproduced from Exercise 2.14, gives the frequency distribution of the number of credit cards possessed by 80 adults. $$ \begin{array}{lc} \hline \text { Number of Credit Cards } & \text { Number of Adults } \\ \hline 0 \text { to } 3 & 18 \\ 4 \text { to } 7 & 26 \\ 8 \text { to } 11 & 22 \\ 12 \text { to } 15 & 11 \\ 16 \text { to } 19 & 3 \\ \hline \end{array} $$ a. Prepare a cumulative frequency distribution. b. Calculate the cumulative relative frequencies and cumulative percentages for all classes. c. Find the percentage of these adults who possess 7 or fewer credit cards. d. Draw an ogive for the cumulative percentage distribution. e. Using the ogive, find the percentage of adults who possess 10 or fewer credit cards.

Explain for what kind of frequency distribution an ogive is drawn. Can you think of any use for an ogive? Explain.
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