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A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a twoway table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-fifties: \(^{37}\) $$ \begin{array}{lccc} \hline & \text { Elite } & \text { Non-Elite } & \text { Did not play } \\ \text { Arthritis } & 10 & 9 & 24 \\ \text { No arthritis } & 61 & 206 & 548 \\ \hline \end{array} $$ (a) What percent of the people in this study were elite soccer players? What percent had arthritis? (b) What percent of the elite soccer players had arthritis? What percent of those who had arthritis were elite soccer players?

Step by step solution

01

Calculate Total Number of Individuals

First, calculate the total number of individuals in the study by adding all the people in each category from the table. \[ Total = (10 + 61) + (9 + 206) + (24 + 548) = 858 \] Thus, there are 858 individuals in total.

02

Determine Percent of Elite Soccer Players

Next, find the total number of elite soccer players. This includes both with and without arthritis. \[ \text{Number of Elite Soccer Players} = 10 + 61 = 71 \] Calculate the percentage of elite soccer players: \[ \frac{71}{858} \times 100\% \approx 8.28\% \] Thus, about 8.28% of the people were elite soccer players.

03

Determine Percent of People with Arthritis

Calculate the total number of people who had arthritis by summing the arthritis row. \[ \text{Number with Arthritis} = 10 + 9 + 24 = 43 \] Calculate the percentage of individuals who had arthritis: \[ \frac{43}{858} \times 100\% \approx 5.01\% \] Therefore, about 5.01% of the people had arthritis.

04

Calculate Percent of Elite Players with Arthritis

Now find the percent of elite soccer players who had arthritis. The number of elite players with arthritis is 10. \[ \frac{10}{71} \times 100\% \approx 14.08\% \] Thus, about 14.08% of the elite soccer players had arthritis.

05

Determine Percent of Arthritis Patients Who are Elite Players

Calculate the percentage of those with arthritis who were elite soccer players. With 10 elite players having arthritis out of 43 total with arthritis: \[ \frac{10}{43} \times 100\% \approx 23.26\% \] Therefore, about 23.26% of those with arthritis were elite soccer players.

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Key Concepts

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

Percent Calculation

Calculating percentages is a useful skill for understanding how parts of a dataset relate to the whole. It can show what proportion of a large group a smaller group represents.

• To find a percentage, you divide the part by the whole and then multiply by 100 to convert to a percent. For example, to find what percent of the study participants were elite soccer players, you divide the number of elite soccer players by the total number of participants and multiply it by 100.
• Percentages make comparisons easier by showing how much of the total is represented by a subgroup.

In the exercise, we calculated different percentages from the data, such as what percent of the total were elite soccer players or how many of them had arthritis. Knowing how to do this kind of calculation helps you understand and interpret data more effectively.

Data Analysis

Analyzing data involves looking at it in a structured way to discover patterns or trends. The two-way table is a simple yet powerful tool to organize data, making it easier to analyze.

• In this specific exercise, each row and column of the table represent different categories of individuals and their arthritis status.
• A two-way table allows you to easily compare the number of individuals across different groups and identify relationships between categorized data.

By organizing data into tables, we simplify complex information and enable clearer analysis of relationships, such as how many soccer players had arthritis compared to those who did not play soccer.

Descriptive Statistics

Descriptive statistics involve summarizing and describing the features of a dataset.

• They provide a simple summary of the sample and the measures.
• In this exercise, we used descriptive statistics to understand the broader picture of arthritis occurrence among different groups.

Descriptive statistics provide insight through metrics such as percentages that describe the distribution of individuals with certain characteristics. They don't make conclusions beyond the data but give a lead to where deeper analysis might be needed. By summarizing data, descriptive statistics make complex datasets easier to understand at a glance.