/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 According to an article in The S... [FREE SOLUTION] | 91Ó°ÊÓ

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According to an article in The Seattle Times (Meckler, 2003 ), living organ donors are most often related to the organ recipient. Table 9.5 gives the percentages of each type of relationship for all 6613 cases in which an organ was transplanted from a living donor in 2002 in the United States. Create a pie chart displaying the relationship of the donor to the recipient, and write a few sentences describing the data.$$\begin{array}{lc}\hline \text { Relationship } & \text { Percent of Donors } \\\\\hline \text { Sibling } & 30 \% \\\\\text { Child } & 19 \% \\\\\text { Parent } & 13 \% \\\\\text { Spouse } & 11 \% \\\\\text { Other relative } & 8 \%\\\\\text { Not related } & 19 \% \\\\\hline\end{array}$$

Short Answer

Expert verified
Create a pie chart using the given percentages; Sibling is the largest category with 30%.

Step by step solution

01

Understanding the Data

The data provided indicates the percentages of the relationships between living organ donors and recipients in the United States in 2002. There are six categories of relationships: Sibling, Child, Parent, Spouse, Other relative, and Not related. Each category is assigned a specific percentage that represents its share of the total 6613 cases of organ donations.
02

Verifying Total Percentage

Add up all the percentages to ensure that they total 100%. This is crucial to check if the data is consistent and accurate for creating a pie chart.\[ 30\% + 19\% + 13\% + 11\% + 8\% + 19\% = 100\% \]
03

Constructing the Pie Chart

Convert each percentage into a proportional angle for the pie chart. The total circle is 360 degrees. Use the formula: \[ \text{Angle for each category} = \frac{\text{Percentage}}{100} \times 360 \]Calculate the angle for each category:- Sibling: \(0.30 \times 360 = 108\) degrees- Child: \(0.19 \times 360 = 68.4\) degrees- Parent: \(0.13 \times 360 = 46.8\) degrees- Spouse: \(0.11 \times 360 = 39.6\) degrees- Other relative: \(0.08 \times 360 = 28.8\) degrees- Not related: \(0.19 \times 360 = 68.4\) degrees
04

Drawing the Pie Chart

Use the calculated angles to draw the pie chart. Each segment of the pie chart represents the different relationships. Label each segment with its relationship category and include the percentage.
05

Interpreting the Pie Chart

The pie chart visually demonstrates that the most common relationship between donor and recipient is Sibling, at 30% of the cases. Child and Not related are both significant categories, each making up 19% of the donors. Parent, Spouse, and Other relative relationships are less common.

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Key Concepts

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

Pie Chart Interpretation
Pie charts are a way of representing data visually in the form of a circle divided into segments. Each segment, or "slice," corresponds to a proportion of the whole. This makes pie charts especially useful for showing how a complete set of data is broken down into percentages of a whole. In the context of organ donors, a pie chart can help illustrate the relationships between donors and recipients, and how each relationship contributes to the total percentage of cases.
For example, if you were to create a pie chart based on the data provided, you would see that the largest slice belongs to siblings (30%), indicating that the most common relationship between donor and recipient is this one. Smaller slices belong to other relationships such as child (19%) and parent (13%), showing lesser but still significant representations. The pie chart allows you to quickly interpret this data, understanding at a glance which relationships might be more or less common in the case of organ donations.
To make a pie chart, it's important to ensure all your percentage data adds up to 100%, as this represents a full circle. Then, you can convert these percentages into angles to draw each slice accurately. The total circle has 360 degrees, so you calculate the degrees for each slice by multiplying the percentage by 3.6.
Data Analysis
Data analysis involves examining, cleaning, transforming, and modeling data to discover useful information. It helps in making decisions based on the patterns and relationships found within the data. With the organ donor data in this exercise, data analysis allows us to understand the patterns in donor-recipient relationships.
The process begins with understanding the data. Every data set has a story to tell, and identifying the categories present and their respective percentages is crucial before any visualization. Once you have this information, you can check for consistency. In our example, all percentages sum up to 100%, confirming the data's completeness, which is vital for reliable analysis.
Once the data consistency is verified, the next step involves constructing visual representations like pie charts that make the data easy to understand. Analyzing each slice in the pie chart gives insights into which donor relationships are more common. This can be critical for predicting future trends or focusing on specific areas in statistics, research, or policy-making, especially in the healthcare sector.
  • Sibling donors stand out as the most prevalent, sharing 30% of cases.
  • Child donors and those not related appear equally, both at 19%.
  • Other categories such as parent, spouse, and other relatives are even lower.
Statistics Education
Statistics education aims to equip learners with the skills to collect, analyze, interpret, and present data. Understanding statistics is key in many fields, as it provides the tools necessary to make informed decisions using quantitative evidence. One of the most basic tools in statistics is the pie chart, often one of the first types of data visualizations taught in learning these concepts.
In the context of the exercise, statistics education would focus on how to interpret the donor-recipient pie chart effectively. Students learn how to take raw data and turn it into a visual format that is easy to understand. They also practice calculating angles for pie charts, which involves simple arithmetic using percentage and multiplication. By engaging with the data interactively, students develop a deeper understanding of how statistics can simplify complex data sets.
Furthermore, students are taught how to critically evaluate the results of their analyses. This includes questioning if the data presented truly represents the population under study or if there might be biases in how data was collected. By doing so, learners develop a critical mindset towards data and its interpretations, which is an essential skill in statistics and everyday decision-making. In essence, statistics education empowers individuals to understand and apply data in ways that are insightful and invaluable.

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Most popular questions from this chapter

Suppose a real estate company in your area sold 100 houses last month, whereas their two major competitors sold 50 houses and 25 houses, respectively. The top company wants to display its better record with a pictogram using a simple two-dimensional picture of a house. Draw two pictograms displaying this information, one of which is misleading and one of which is not. (The horizontal axis should list the three companies and the vertical axis should list the number of houses sold.)

Give the name of a type of statistical picture that could be used for each of the following kinds of data: a. One categorical variable b. One measurement variable c. Two categorical variables d. Two measurement variables

For each of the following time series, do you think the long-term trend would be positive, negative, or nonexistent? a. The cost of a loaf of bread measured monthly from 1960 to the present month. b. The temperature in Boston measured at noon on the first day of each month from 1960 to the present month. c. The price of a basic computer, adjusted for inflation, measured monthly from 1970 to 2012 . d. The number of personal computers sold in the United States measured monthly from 1970 to 2012 .

Table 9.3 indicates the population (in millions) and the number of violent crimes (in millions) in the United States from 1982 to 1991 , as reported in the World Almanac and Book of Facts \((1993, \mathrm{p}\).948). (Thankfully, both numbers and rates of violent crime started dropping in 1992 and have continued to do so. Thus, the data for this exercise end in 1991 to illustrate the increasing trend up to that time.)$$\begin{array}{lcccccccc}\hline \text { Year } & \mathbf{1 9 8 2} & \mathbf{1 9 8 3} & \mathbf{1 9 8 5} & \mathbf{1 9 8 6} & \mathbf{1 9 8 7} & \mathbf{1 9 8 8} & \mathbf{1 9 8 9} & \mathbf{1 9 9 0} & \mathbf{1 9 9 1} \\\\\hline \begin{array}{l}\text { U.S. } \\\\\text { population }\end{array} & 231 & 234 & 239 & 241 & 243 & 246 & 248 & 249 & 252 \\ \begin{array}{l}\text { Violent } \\\\\text { crime }\end{array} & 1.32 & 1.26 & 1.33 & 1.49 & 1.48 & 1.57 & 1.65 & 1.82 & 1.91 \\\\\hline\end{array}$$,a. Draw two line graphs representing the trend in violent crime over time. Draw the first graph to try to convince the reader that the trend is quite ominous. Draw the second graph to try to convince the reader that it is not. Make sure all of the other features of your graph meet the criteria for a good picture. b. Draw a scatterplot of population versus violent crime, making sure it meets all the criteria for a good picture. Comment on the scatterplot. Now explain why drawing a line graph of violent crime versus year, as in part (a) of this exercise, might be misleading. Answer \(t\) c. Rather than using number of violent crimes on the vertical axis, redraw the first line graph (from part [a]) using a measure that adjusts for the increase in population. Comment on the differences between the two graphs.

Global warming is a major concern because it implies that temperatures around the world are going up on a permanent basis. Suppose you were to examine a plot of monthly temperatures in one location for the past 50 years. Explain the role that the three time series components (trend, seasonal, cycles) would play in trying to determine whether global warming was taking place.

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