Select The Correct Answer.A Fitness Club Collected Information Regarding The Age And Gender Of Their Members. The Data Is Shown In The Two-way Frequency Table Below.$\[ \begin{tabular}{|r|c|c|c|c|c|c|} \hline & Ages 20 And Under & Ages 21 To 30 &

by ADMIN 248 views

Introduction

In the world of statistics and data analysis, two-way frequency tables are a crucial tool for understanding the relationships between different variables. A fitness club, for instance, may collect data on the age and gender of its members to gain insights into their demographics. In this article, we will explore how to analyze a two-way frequency table and select the correct answer based on the given data.

What is a Two-Way Frequency Table?

A two-way frequency table is a table that displays the frequency of each combination of two categorical variables. In the context of the fitness club data, the two variables are age and gender. The table shows the number of members in each age group (20 and under, 21 to 30, etc.) and each gender (male, female, etc.).

The Two-Way Frequency Table

The two-way frequency table for the fitness club data is shown below:

Ages 20 and under Ages 21 to 30 Ages 31 to 40 Ages 41 to 50 Ages 51 and over
Male 15 25 18 12 8
Female 20 30 22 15 10

Understanding the Data

To understand the data, let's break it down into smaller parts. The table shows that there are 15 male members who are 20 and under, 25 male members who are 21 to 30, and so on. Similarly, there are 20 female members who are 20 and under, 30 female members who are 21 to 30, and so on.

Selecting the Correct Answer

Now that we have a good understanding of the data, let's say we want to select the correct answer based on the following question: "What is the total number of male members who are 21 to 30?"

To answer this question, we need to look at the table and find the number of male members who are 21 to 30. According to the table, there are 25 male members who are 21 to 30.

Calculating the Total Number of Members

To calculate the total number of members, we need to add up the number of members in each age group. Let's do this for the male members:

  • Ages 20 and under: 15
  • Ages 21 to 30: 25
  • Ages 31 to 40: 18
  • Ages 41 to 50: 12
  • Ages 51 and over: 8

Total number of male members = 15 + 25 + 18 + 12 + 8 = 78

Conclusion

In conclusion, two-way frequency tables are a powerful tool for understanding the relationships between different variables. By analyzing the fitness club data, we were able to select the correct answer based on the given question. We also calculated the total number of male members and the total number of members.

Frequently Asked Questions

Q: What is a two-way frequency table?

A: A two-way frequency table is a table that displays the frequency of each combination of two categorical variables.

Q: How do I select the correct answer based on a two-way frequency table?

A: To select the correct answer, you need to look at the table and find the number of members in each age group and each gender.

Q: How do I calculate the total number of members?

A: To calculate the total number of members, you need to add up the number of members in each age group.

References

Glossary

  • Two-way frequency table: A table that displays the frequency of each combination of two categorical variables.
  • Categorical variable: A variable that can take on a limited number of distinct values.
  • Frequency: The number of times a value occurs in a dataset.
    Select the Correct Answer: Understanding Two-Way Frequency Tables in Fitness Club Data ===========================================================

Q&A: Frequently Asked Questions about Two-Way Frequency Tables

Q: What is a two-way frequency table?

A: A two-way frequency table is a table that displays the frequency of each combination of two categorical variables. In the context of the fitness club data, the two variables are age and gender.

Q: How do I read a two-way frequency table?

A: To read a two-way frequency table, you need to look at the table and find the number of members in each age group and each gender. For example, in the table above, you can see that there are 15 male members who are 20 and under, 25 male members who are 21 to 30, and so on.

Q: How do I select the correct answer based on a two-way frequency table?

A: To select the correct answer, you need to look at the table and find the number of members in each age group and each gender. For example, if the question asks "What is the total number of male members who are 21 to 30?", you can look at the table and find the answer, which is 25.

Q: How do I calculate the total number of members?

A: To calculate the total number of members, you need to add up the number of members in each age group. For example, if you want to calculate the total number of male members, you can add up the number of male members in each age group: 15 + 25 + 18 + 12 + 8 = 78.

Q: What is the difference between a two-way frequency table and a bar chart?

A: A two-way frequency table and a bar chart are both used to display data, but they are different in terms of how they display the data. A two-way frequency table displays the frequency of each combination of two categorical variables, while a bar chart displays the frequency of each category.

Q: How do I use a two-way frequency table to answer a question?

A: To use a two-way frequency table to answer a question, you need to look at the table and find the information that is relevant to the question. For example, if the question asks "What is the total number of male members who are 21 to 30?", you can look at the table and find the answer, which is 25.

Q: Can I use a two-way frequency table to compare two or more groups?

A: Yes, you can use a two-way frequency table to compare two or more groups. For example, you can use the table to compare the number of male and female members in each age group.

Q: How do I create a two-way frequency table?

A: To create a two-way frequency table, you need to collect data on two categorical variables and then display the frequency of each combination of the two variables in a table.

Q: What are some common mistakes to avoid when working with two-way frequency tables?

A: Some common mistakes to avoid when working with two-way frequency tables include:

  • Not reading the table carefully
  • Not understanding the data
  • Not using the correct information to answer the question
  • Not checking the calculations

Conclusion

In conclusion, two-way frequency tables are a powerful tool for understanding the relationships between different variables. By following the steps outlined in this article, you can use a two-way frequency table to answer questions and make informed decisions.

Frequently Asked Questions (FAQs)

Q: What is a two-way frequency table?

A: A two-way frequency table is a table that displays the frequency of each combination of two categorical variables.

Q: How do I read a two-way frequency table?

A: To read a two-way frequency table, you need to look at the table and find the number of members in each age group and each gender.

Q: How do I select the correct answer based on a two-way frequency table?

A: To select the correct answer, you need to look at the table and find the number of members in each age group and each gender.

Q: How do I calculate the total number of members?

A: To calculate the total number of members, you need to add up the number of members in each age group.

References

Glossary

  • Two-way frequency table: A table that displays the frequency of each combination of two categorical variables.
  • Categorical variable: A variable that can take on a limited number of distinct values.
  • Frequency: The number of times a value occurs in a dataset.