91Ó°ÊÓ

Construct stem-and-leaf plots. Divorce Rate The following data represent the divorce rates (per 1000 population) for most states in the United States in the year \(2001 .\) (Note: The list includes the District of Columbia but excludes California, Colorado, Indiana, and Louisiana because of failure to report.) $$\begin{array}{lllllll} 5.3 & 4.1 & 4.2 & 6.6 & 2.9 & 4.0 & 2.3 \\ \hline 5.4 & 3.8 & 3.8 & 5.6 & 3.2 & 3.2 & 3.2 \\ \hline 5.5 & 3.9 & 3.0 & 2.4 & 3.9 & 3.3 & 5.4 \\ \hline 4.3 & 2.6 & 3.7 & 6.8 & 5.0 & 3.5 & 5.1 \\ \hline 3.0 & 4.5 & 2.7 & 4.0 & 3.4 & 4.9 & 3.2 \\ \hline 3.3 & 3.5 & 3.4 & 5.2 & 4.1 & 4.4 & 4.0 \\ \hline 4.3 & 4.5 & 5.2 & 3.2 & 6.1 & & \end{array}$$

Step by step solution

01

Understand Stem-and-Leaf Plots

Stem-and-leaf plots split each data point into a 'stem' (all but the final digit) and a 'leaf' (the final digit).

02

Identify the Data Range

Review the given data to determine the range of numbers. Here, the divorce rates range from 2.3 to 6.8.

03

Create the Stem

Divide the numbers into stems. In this case, the stems will be the integer part of the rates: 2, 3, 4, 5, and 6.

04

List the Leaves

For each stem, list the leaves, which are the decimal part of the rates. The stems (2, 3, 4, 5, and 6) will each have their respective leaves.

05

Construct the Plot

Arrange the stems in a column and align the corresponding leaves to the right of their stems.

06

Review and Verify

Ensure all data points are correctly represented in the plot.

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Key Concepts

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

data visualization

Data visualization is the graphical representation of information and data. Using visual elements like charts, graphs, and plots, data visualization tools provide an accessible way to see and understand trends, outliers, and patterns in data. In this exercise, we focus on stem-and-leaf plots, which are a simple yet powerful way to visualize numerical data.

• Helps in quickly identifying the distribution of the data.
• Allows easy comparison of data sets.
• Useful for small to medium-sized data sets.

By organizing data into 'stems' and 'leaves', a stem-and-leaf plot helps to display the shape and distribution of data while preserving the original data values. This makes it easy to see where data clusters and to spot any outliers.

descriptive statistics

Descriptive statistics involves summarizing and organizing data so it can be easily understood. It provides simple summaries about the sample and the measures. For instance, a stem-and-leaf plot is a form of descriptive statistics as it condenses the data into a visual format without losing the actual data points.

• Mean: The average of the data set.
• Median: The middle value when data is ordered.
• Mode: The most frequently occurring value.
• Range: The difference between the highest and lowest values.

These measures help to describe the center, spread, and shape of the data distribution. Understanding these aspects can provide insights into the overall structure and tendencies within the data, such as identifying typical or extreme values.

divorce rates

Divorce rates are a critical socio-economic indicator. They can provide insights into the stability and dynamics of family structures within a region. In this exercise, we examine the divorce rates across various states in the U.S. for the year 2001.

• Rates are expressed per 1000 individuals.
• Help in analyzing trends over time and comparing different regions.
• Impacted by socio-economic factors like education, income, and cultural norms.

By visualizing these rates using stem-and-leaf plots, one can better understand the distribution and range, assisting policymakers, sociologists, and demographers in their analyses. This can lead to informed decisions and targeted interventions aimed at addressing underlying issues.