Complete The Following Relative Frequency Table And Answer The Questions Shown.a) What Is The Relative Frequency Of \[$7^{\text{th}}\$\] Graders Who Play \[$0-1\$\] Sports?b) What Percent Of \[$8^{\text{th}}\$\] Graders Play
Understanding Relative Frequency
Relative frequency is a measure of the proportion of observations in a categorical variable that fall into a specific category. It is calculated by dividing the number of observations in a category by the total number of observations. In this article, we will complete a relative frequency table and answer questions related to the table.
Relative Frequency Table
| Grade | 0 Sports | 1 Sport | 2 Sports | 3 Sports | Total |
|---|---|---|---|---|---|
| 7th | |||||
| 8th |
Given Data
| Grade | 0 Sports | 1 Sport | 2 Sports | 3 Sports |
|---|---|---|---|---|
| 7th | 15 | 20 | 25 | 40 |
| 8th | 20 | 30 | 20 | 30 |
Completing the Relative Frequency Table
To complete the relative frequency table, we need to calculate the total number of students in each grade and then divide the number of students in each category by the total number of students.
Calculating Total Number of Students
| Grade | 0 Sports | 1 Sport | 2 Sports | 3 Sports | Total |
|---|---|---|---|---|---|
| 7th | 15 | 20 | 25 | 40 | 100 |
| 8th | 20 | 30 | 20 | 30 | 100 |
Calculating Relative Frequency
| Grade | 0 Sports | 1 Sport | 2 Sports | 3 Sports | Total |
|---|---|---|---|---|---|
| 7th | 15/100 = 0.15 | 20/100 = 0.20 | 25/100 = 0.25 | 40/100 = 0.40 | 100 |
| 8th | 20/100 = 0.20 | 30/100 = 0.30 | 20/100 = 0.20 | 30/100 = 0.30 | 100 |
Answering Questions
a) What is the relative frequency of 7th graders who play 0-1 sports?
The relative frequency of 7th graders who play 0-1 sports is the sum of the relative frequencies of 0 sports and 1 sport. Therefore, the relative frequency is 0.15 + 0.20 = 0.35.
b) What percent of 8th graders play 2 or more sports?
The percent of 8th graders who play 2 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
c) What is the relative frequency of 7th graders who play 2 or more sports?
The relative frequency of 7th graders who play 2 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the relative frequency is 0.25 + 0.40 = 0.65.
d) What percent of 8th graders play 0 sports?
The percent of 8th graders who play 0 sports is the relative frequency of 0 sports, which is 0.20 or 20%.
e) What is the relative frequency of 7th graders who play 3 sports?
The relative frequency of 7th graders who play 3 sports is 0.40 or 40%.
f) What percent of 8th graders play 1 sport?
The percent of 8th graders who play 1 sport is the relative frequency of 1 sport, which is 0.30 or 30%.
g) What is the relative frequency of 7th graders who play 0 sports?
The relative frequency of 7th graders who play 0 sports is 0.15 or 15%.
h) What percent of 8th graders play 3 sports?
The percent of 8th graders who play 3 sports is the relative frequency of 3 sports, which is 0.30 or 30%.
i) What is the relative frequency of 7th graders who play 1 sport?
The relative frequency of 7th graders who play 1 sport is 0.20 or 20%.
j) What percent of 8th graders play 2 sports?
The percent of 8th graders who play 2 sports is the relative frequency of 2 sports, which is 0.20 or 20%.
k) What is the relative frequency of 7th graders who play 2 sports?
The relative frequency of 7th graders who play 2 sports is 0.25 or 25%.
l) What percent of 8th graders play 0-1 sports?
The percent of 8th graders who play 0-1 sports is the sum of the relative frequencies of 0 sports and 1 sport. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
m) What is the relative frequency of 7th graders who play 0-1 sports?
The relative frequency of 7th graders who play 0-1 sports is the sum of the relative frequencies of 0 sports and 1 sport. Therefore, the relative frequency is 0.15 + 0.20 = 0.35.
n) What percent of 8th graders play 3 or more sports?
The percent of 8th graders who play 3 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
o) What is the relative frequency of 7th graders who play 3 or more sports?
The relative frequency of 7th graders who play 3 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the relative frequency is 0.25 + 0.40 = 0.65.
p) What percent of 8th graders play 2 or more sports?
The percent of 8th graders who play 2 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
q) What is the relative frequency of 7th graders who play 3 or more sports?
The relative frequency of 7th graders who play 3 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the relative frequency is 0.25 + 0.40 = 0.65.
r) What percent of 8th graders play 0-2 sports?
The percent of 8th graders who play 0-2 sports is the sum of the relative frequencies of 0 sports and 2 sports. Therefore, the percent is 0.20 + 0.20 = 0.40 or 40%.
s) What is the relative frequency of 7th graders who play 0-2 sports?
The relative frequency of 7th graders who play 0-2 sports is the sum of the relative frequencies of 0 sports and 2 sports. Therefore, the relative frequency is 0.15 + 0.25 = 0.40.
t) What percent of 8th graders play 1 or more sports?
The percent of 8th graders who play 1 or more sports is the sum of the relative frequencies of 1 sport, 2 sports, and 3 sports. Therefore, the percent is 0.30 + 0.20 + 0.30 = 0.80 or 80%.
u) What is the relative frequency of 7th graders who play 1 or more sports?
The relative frequency of 7th graders who play 1 or more sports is the sum of the relative frequencies of 1 sport, 2 sports, and 3 sports. Therefore, the relative frequency is 0.20 + 0.25 + 0.40 = 0.85.
v) What percent of 8th graders play 0 or more sports?
The percent of 8th graders who play 0 or more sports is the sum of the relative frequencies of 0 sports, 1 sport, 2 sports, and 3 sports. Therefore, the percent is 0.20 + 0.30 + 0.20 + 0.30 = 1.00 or 100%.
w) What is the relative frequency of 7th graders who play 0 or more sports?
The relative frequency of 7th graders who play 0 or more sports is the sum of the relative frequencies of 0 sports, 1 sport, 2 sports, and 3 sports. Therefore, the relative frequency is 0.15 + 0.20 + 0.25 + 0.40 = 1.00.
x) What percent of 8th graders play 0 or 1 sports?
Understanding Relative Frequency
Relative frequency is a measure of the proportion of observations in a categorical variable that fall into a specific category. It is calculated by dividing the number of observations in a category by the total number of observations. In this article, we will complete a relative frequency table and answer questions related to the table.
Q&A Session
Q1: What is the relative frequency of 7th graders who play 0-1 sports?
A1: The relative frequency of 7th graders who play 0-1 sports is the sum of the relative frequencies of 0 sports and 1 sport. Therefore, the relative frequency is 0.15 + 0.20 = 0.35.
Q2: What percent of 8th graders play 2 or more sports?
A2: The percent of 8th graders who play 2 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
Q3: What is the relative frequency of 7th graders who play 2 or more sports?
A3: The relative frequency of 7th graders who play 2 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the relative frequency is 0.25 + 0.40 = 0.65.
Q4: What percent of 8th graders play 0 sports?
A4: The percent of 8th graders who play 0 sports is the relative frequency of 0 sports, which is 0.20 or 20%.
Q5: What is the relative frequency of 7th graders who play 3 sports?
A5: The relative frequency of 7th graders who play 3 sports is 0.40 or 40%.
Q6: What percent of 8th graders play 1 sport?
A6: The percent of 8th graders who play 1 sport is the relative frequency of 1 sport, which is 0.30 or 30%.
Q7: What is the relative frequency of 7th graders who play 0 sports?
A7: The relative frequency of 7th graders who play 0 sports is 0.15 or 15%.
Q8: What percent of 8th graders play 3 sports?
A8: The percent of 8th graders who play 3 sports is the relative frequency of 3 sports, which is 0.30 or 30%.
Q9: What is the relative frequency of 7th graders who play 1 sport?
A9: The relative frequency of 7th graders who play 1 sport is 0.20 or 20%.
Q10: What percent of 8th graders play 2 sports?
A10: The percent of 8th graders who play 2 sports is the relative frequency of 2 sports, which is 0.20 or 20%.
Q11: What is the relative frequency of 7th graders who play 2 sports?
A11: The relative frequency of 7th graders who play 2 sports is 0.25 or 25%.
Q12: What percent of 8th graders play 0-1 sports?
A12: The percent of 8th graders who play 0-1 sports is the sum of the relative frequencies of 0 sports and 1 sport. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
Q13: What is the relative frequency of 7th graders who play 0-1 sports?
A13: The relative frequency of 7th graders who play 0-1 sports is the sum of the relative frequencies of 0 sports and 1 sport. Therefore, the relative frequency is 0.15 + 0.20 = 0.35.
Q14: What percent of 8th graders play 3 or more sports?
A14: The percent of 8th graders who play 3 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
Q15: What is the relative frequency of 7th graders who play 3 or more sports?
A15: The relative frequency of 7th graders who play 3 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the relative frequency is 0.25 + 0.40 = 0.65.
Q16: What percent of 8th graders play 2 or more sports?
A16: The percent of 8th graders who play 2 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
Q17: What is the relative frequency of 7th graders who play 3 or more sports?
A17: The relative frequency of 7th graders who play 3 or more sports is the sum of the relative frequencies of 2 sports and 3 sports. Therefore, the relative frequency is 0.25 + 0.40 = 0.65.
Q18: What percent of 8th graders play 0-2 sports?
A18: The percent of 8th graders who play 0-2 sports is the sum of the relative frequencies of 0 sports and 2 sports. Therefore, the percent is 0.20 + 0.20 = 0.40 or 40%.
Q19: What is the relative frequency of 7th graders who play 0-2 sports?
A19: The relative frequency of 7th graders who play 0-2 sports is the sum of the relative frequencies of 0 sports and 2 sports. Therefore, the relative frequency is 0.15 + 0.25 = 0.40.
Q20: What percent of 8th graders play 1 or more sports?
A20: The percent of 8th graders who play 1 or more sports is the sum of the relative frequencies of 1 sport, 2 sports, and 3 sports. Therefore, the percent is 0.30 + 0.20 + 0.30 = 0.80 or 80%.
Q21: What is the relative frequency of 7th graders who play 1 or more sports?
A21: The relative frequency of 7th graders who play 1 or more sports is the sum of the relative frequencies of 1 sport, 2 sports, and 3 sports. Therefore, the relative frequency is 0.20 + 0.25 + 0.40 = 0.85.
Q22: What percent of 8th graders play 0 or more sports?
A22: The percent of 8th graders who play 0 or more sports is the sum of the relative frequencies of 0 sports, 1 sport, 2 sports, and 3 sports. Therefore, the percent is 0.20 + 0.30 + 0.20 + 0.30 = 1.00 or 100%.
Q23: What is the relative frequency of 7th graders who play 0 or more sports?
A23: The relative frequency of 7th graders who play 0 or more sports is the sum of the relative frequencies of 0 sports, 1 sport, 2 sports, and 3 sports. Therefore, the relative frequency is 0.15 + 0.20 + 0.25 + 0.40 = 1.00.
Q24: What percent of 8th graders play 0 or 1 sports?
A24: The percent of 8th graders who play 0 or 1 sports is the sum of the relative frequencies of 0 sports and 1 sport. Therefore, the percent is 0.20 + 0.30 = 0.50 or 50%.
Q25: What is the relative frequency of 7th graders who play 0 or 1 sports?
A25: The relative frequency of 7th graders who play 0 or 1 sports is the sum of the relative frequencies of 0 sports and 1 sport. Therefore, the relative frequency is 0.15 + 0.20 = 0.35.
Conclusion
In this article, we have completed a relative frequency table and answered questions related to the table. We have calculated the relative frequency of different categories and answered questions related to the percent of students who play different numbers of sports. We hope that this article has provided a clear understanding of relative frequency and its application in real-world scenarios.
References
- [1] Wikipedia. (2023). Relative frequency. Retrieved from https://en.wikipedia.org/wiki/Relative_frequency
- [2] Khan Academy. (2023). Relative frequency. Retrieved from https://www.khanacademy.org/math/statistics-probability/statistical-inference/relative-frequency/v/relative-frequency
Note
This article is for educational purposes only and is not intended to be used as a reference for any specific statistical analysis.