Completing the Venn Diagram

Oct 13, 2025 by magicalceylontours.com 114 views

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Introduction

In this article, we will explore the data collected from a survey of 167 students. The survey revealed that 83 students study music, 105 students play a sport, and 56 students do both. Our goal is to complete the Venn diagram to illustrate the data collected and calculate the values A, B, C, and D.

The Venn Diagram

A Venn diagram is a visual representation of the relationships between sets. In this case, we have two sets: students who study music and students who play a sport. The Venn diagram is divided into four regions: A, B, C, and D.

The Regions of the Venn Diagram

A: The number of students who study music but do not play a sport.
B: The number of students who play a sport but do not study music.
C: The number of students who both study music and play a sport.
D: The number of students who do neither.

Calculating the Values A, B, C, and D

To calculate the values A, B, C, and D, we need to use the information provided in the survey.

Calculating A

The number of students who study music is 83. Since 56 students do both, the number of students who study music but do not play a sport is:

A = 83 - 56 A = 27

Calculating B

The number of students who play a sport is 105. Since 56 students do both, the number of students who play a sport but do not study music is:

B = 105 - 56 B = 49

Calculating C

We already know that 56 students do both.

Calculating D

The total number of students is 167. We can calculate the number of students who do neither by subtracting the number of students who study music, play a sport, and those who do both from the total number of students.

D = 167 - (83 + 105 - 56) D = 167 - 132 D = 35

Completing the Venn Diagram

Now that we have calculated the values A, B, C, and D, we can complete the Venn diagram.

The Completed Venn Diagram

	Study Music	Do Not Study Music	Total
Play a Sport	56	49	105
Do Not Play a Sport	27	35	62
Total	83	84	167

Conclusion

In this article, we completed the Venn diagram to illustrate the data collected from a survey of 167 students. We calculated the values A, B, C, and D, which represent the number of students who study music but do not play a sport, the number of students who play a sport but do not study music, the number of students who both study music and play a sport, and the number of students who do neither. The completed Venn diagram provides a visual representation of the relationships between the sets of students who study music and those who play a sport.

Final Answer

	Study Music	Do Not Study Music	Total
Play a Sport	56	49	105
Do Not Play a Sport	27	35	62
Total	83	84	167

References

The data from a survey of 167 students showed that 83 study music, 105 play a sport, and 56 do both.

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Introduction

In our previous article, we explored the data collected from a survey of 167 students. The survey revealed that 83 students study music, 105 students play a sport, and 56 students do both. We completed the Venn diagram to illustrate the data collected and calculated the values A, B, C, and D. In this article, we will answer some frequently asked questions related to the data.

Q&A

Q1: What is the total number of students who study music?

A1: The total number of students who study music is 83.

Q2: What is the total number of students who play a sport?

A2: The total number of students who play a sport is 105.

Q3: How many students do both study music and play a sport?

A3: 56 students do both study music and play a sport.

Q4: What is the number of students who study music but do not play a sport?

A4: The number of students who study music but do not play a sport is 27.

Q5: What is the number of students who play a sport but do not study music?

A5: The number of students who play a sport but do not study music is 49.

Q6: What is the number of students who do neither study music nor play a sport?

A6: The number of students who do neither study music nor play a sport is 35.

Q7: What is the total number of students who study music or play a sport?

A7: The total number of students who study music or play a sport is 83 + 105 - 56 = 132.

Q8: What is the percentage of students who study music?

A8: The percentage of students who study music is (83 / 167) x 100% ≈ 49.7%.

Q9: What is the percentage of students who play a sport?

A9: The percentage of students who play a sport is (105 / 167) x 100% ≈ 62.9%.

Q10: What is the percentage of students who do both study music and play a sport?

A10: The percentage of students who do both study music and play a sport is (56 / 167) x 100% ≈ 33.5%.

Conclusion

In this article, we answered some frequently asked questions related to the data collected from a survey of 167 students. We provided the answers to questions such as the total number of students who study music, the total number of students who play a sport, and the number of students who do both. We also calculated the percentages of students who study music, play a sport, and do both.

Final Answer

	Study Music	Do Not Study Music	Total
Play a Sport	56	49	105
Do Not Play a Sport	27	35	62
Total	83	84	167

References

The data from a survey of 167 students showed that 83 study music, 105 play a sport, and 56 do both.