Venn diagrams
- 1. VENN DIAGRAMS Creating and Using to Answer Questions
- 2. ➤ It is a way to organize information. Why Use Venn Diagrams? Adapted Thoughtful dog avatar by Schade is licensed by Public Domain.
- 3. ➤ It is a way to organize information. ➤ It shows the relationship between 2 or 3 sets of items. Why Use Venn Diagrams? Adapted Thoughtful dog avatar by Schade is licensed by Public Domain.
- 4. ➤ It is a way to organize information. ➤ It shows the relationship between 2 or 3 sets of items. ➤ It is easier to see similarities and differences between items. Why Use Venn Diagrams? Adapted Thoughtful dog avatar by Schade is licensed by Public Domain.
- 5. ➤ It’s a way to organize information. ➤ It shows the relationship between 2 or 3 sets of items. ➤ It is easier to see similarities and differences between items. ➤ It can be used to easily answer questions. Why Use Venn Diagrams? Adapted Thoughtful dog avatar by Schade is licensed by Public Domain.
- 6. The Problem ➤ A survey is conducted to find out who has visited Spain, Canada, and/or Germany. 27% of people visited Spain, 67% have been to Canada, and 36% to Germany. 13% of people have been to Spain and Germany, 21% of people have been to Canada and Germany, and 3% of people have been to Spain and Canada but not Germany. 4% of people have been to all 3 countries. Spain by mireille is licensed by Public Domain. Canada by tgm is licensed by Public Domain. Germany by GDJ is licensed by Public Domain.
- 7. Organize Known Information ➤ Visited all 3 countries
- 8. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada
- 9. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada ➤ Visited 2 Countries
- 10. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada ➤ Visited 2 Countries ➤ 13% visited Spain and Germany
- 11. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada ➤ Visited 2 Countries ➤ 13% visited Spain and Germany ➤ 21% visited Canada and Germany
- 12. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada ➤ Visited 2 Countries ➤ 13% visited Spain and Germany ➤ 21% visited Canada and Germany ➤ 3% visited Spain and Canada but not Germany
- 13. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada ➤ Visited 2 Countries ➤ 13% visited Spain and Germany ➤ 21% visited Canada and Germany ➤ 3% visited Spain and Canada but not Germany ➤ Visited each Country
- 14. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada ➤ Visited 2 Countries ➤ 13% visited Spain and Germany ➤ 21% visited Canada and Germany ➤ 3% visited Spain and Canada but not Germany ➤ Visited each Country ➤ 27% visited Spain
- 15. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada ➤ Visited 2 Countries ➤ 13% visited Spain and Germany ➤ 21% visited Canada and Germany ➤ 3% visited Spain and Canada but not Germany ➤ Visited each Country ➤ 27% visited Spain ➤ 67% visited Canada
- 16. Organize Known Information ➤ Visited all 3 countries ➤ 4% visited Spain, Germany and Canada ➤ Visited 2 Countries ➤ 13% visited Spain and Germany ➤ 21% visited Canada and Germany ➤ 3% visited Spain and Canada but not Germany ➤ Visited each Country ➤ 27% visited Spain ➤ 67% visited Canada ➤ 36% visited Germany
- 17. Draw A Circle For Each Country
- 18. Draw A Circle For Each Country Spain Spain by mireille is licensed by Public Domain.
- 19. Draw A Circle For Each Country Spain Canada Canada by tgm is licensed by Public Domain.
- 20. Draw A Circle For Each Country Spain Canada Germany Germany by GDJ is licensed by Public Domain.
- 21. Place Known Information For All Spain Canada Germany
- 22. Place Known Information For All ➤ Start with the inner most piece, which is who visited all 3 countries. Spain Canada Germany
- 23. Place Known Information For All ➤ Start with the inner most piece, which is who visited all 3 countries. ➤ From the known information, 4% visited all 3 countries. Spain Canada Germany
- 24. Place Known Information For All ➤ Start with the inner most piece, which is who visited all 3 countries. ➤ From the known information, 4% visited all 3 countries. ➤ Place 4% in the piece where all 3 circles overlap. Spain Canada Germany 4%
- 25. Place Known Information For 2 Pieces Spain Canada Germany 4%
- 26. Place Known Information For 2 Pieces ➤ Use the known information about those visiting 2 countries. It doesn’t matter which is done first. Spain Canada Germany 4%
- 27. Place Known Information For 2 Pieces ➤ Use the known information about those visiting 2 countries. It doesn’t matter which is done first. ➤ 13% visited Spain and Germany Spain Canada Germany 4%
- 28. Place Known Information For 2 Pieces ➤ Use the known information about those visiting 2 countries. It doesn’t matter which is done first. ➤ 13% visited Spain and Germany ➤ This is those who visited both countries. Notice it does not say if they visited Canada or not. Because this information isn’t given, it is assumed that some may have visited Canada as well. Spain Canada Germany 4%
- 29. Place Known Information For 2 Pieces ➤ Use the known information about those visiting 2 countries. It doesn’t matter which is done first. ➤ 13% visited Spain and Germany, ➤ This is those who visited both countries. Notice it does not say if they visited Canada or not. Because this information isn’t given, it is assumed that some may have visited Canada as well. ➤ Because 4% was already filled in to account for those who visited Canada, this needs subtracted from 13% to fill in the missing piece. Spain Canada Germany 4%
- 30. Place Known Information For 2 Pieces (Con’t) ➤ Identify the overlap. Spain Canada Germany 4%
- 31. Place Known Information For 2 Pieces (Con’t) ➤ Identify the overlap. Spain Canada Germany 4%
- 32. Place Known Information For 2 Pieces (Con’t) ➤ Identify the overlap. ➤ Because 4% was already filled in to account for those who visited Canada, this needs subtracted from 13% to fill in the missing piece. Spain Canada Germany 4%
- 33. Place Known Information For 2 Pieces (Con’t) ➤ Identify the overlap. ➤ Because 4% was already filled in to account for those who visited Canada, this needs subtracted from 13% to fill in the missing piece. ➤ Missing piece: 13% - 4% Spain Canada Germany 4% 13% - 4%
- 34. Place Known Information For 2 Pieces ➤ Identify the overlap. ➤ Because 4% was already filled in to account for those who visited Canada, this needs subtracted from 13% to fill in the missing piece. ➤ Missing piece: 13% - 4% ➤ = 9% Spain Canada Germany 4% 9%
- 35. Place Known Information For 2 Pieces (Con’t) ➤ 21% visited Canada and Germany Spain Canada Germany 9% 4%
- 36. Place Known Information For 2 Pieces (Con’t) ➤ 21% visited Canada and Germany ➤ Identify the overlap. Spain Canada Germany 9% 4%
- 37. Place Known Information For 2 Pieces (Con’t) ➤ 21% visited Canada and Germany ➤ Identify the overlap. ➤ Find the missing piece by subtracting 4% from the total who visited both countries. Spain Canada Germany 9% 4%
- 38. Place Known Information For 2 Pieces (Con’t) ➤ 21% visited Canada and Germany ➤ Identify the overlap. ➤ Find the missing piece by subtracting 4% from the total who visited both countries. ➤ Missing piece: 21% - 4% Spain Canada Germany 9% 4% 21% - 4%
- 39. Place Known Information For 2 Pieces (Con’t) ➤ 21% visited Canada and Germany ➤ Identify the overlap. ➤ Find the missing piece by subtracting 4% from the total who visited both countries. ➤ Missing piece: 21% - 4% ➤ = 17% Spain Canada Germany 9% 4% 17%
- 40. Place Known Information For 2 Pieces (Con’t) ➤ 3% visited Spain and Canada but not Germany Spain Canada Germany 17%9% 4%
- 41. Place Known Information For 2 Pieces (Con’t) ➤ 3% visited Spain and Canada but not Germany ➤ Because this amount has excluded the people who visited Germany, it is just placed into the piece where only Spain and Canada overlap. Spain Canada Germany 17%9% 4%
- 42. Place Known Information For 2 Pieces (Con’t) ➤ 3% visited Spain and Canada but not Germany ➤ Because this amount has excluded the people who visited Germany, it is just placed into the piece where only Spain and Canada overlap. Spain Canada Germany 4% 17%9% 3%
- 43. Place Known Information For Each Country Spain Canada Germany 4% 17% 3% 9%
- 44. Place Known Information For Each Country ➤ The only pieces remaining are those who visited only one country. Spain Canada Germany 4% 17% 3% 9%
- 45. Place Known Information For Each Country ➤ The only pieces remaining are those who visited only one country. ➤ The totals for each country are known. Spain Canada Germany 4% 17% 3% 9%
- 46. Place Known Information For Each Country ➤ The only pieces remaining are those who visited only one country. ➤ The totals for each country are known. ➤ To find the missing pieces, subtract the pieces previously filled in from the total to find those who visited only one country. Spain Canada Germany 4% 17% 3% 9%
- 47. Place Known Information For Each Country ➤ The only pieces remaining are those who visited only one country. ➤ The totals for each country are known. ➤ To find the missing pieces, subtract the pieces previously filled in from the total to find those who visited only one country. ➤ It doesn’t matter which you find first. Spain Canada Germany 4% 17% 3% 9%
- 48. Place Known Information For Spain Spain Canada Germany 4% 17% 3% 9%
- 49. Place Known Information For Spain ➤ 27% visited Spain Spain Canada Germany 4% 17% 3% 9%
- 50. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain Spain Canada Germany 4% 17% 3% 9%
- 51. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain Spain Canada Germany 4% 17% 3% 9%
- 52. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain Spain Canada Germany 4% 17%9% 3%
- 53. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain Spain Canada Germany 4% 17% 3% 9%
- 54. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain Spain Canada Germany 17% 3% 9% 4%
- 55. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain ➤ Subtract the known pieces from 27% to find the missing piece. Spain Canada Germany 17% 3% 9% 4%
- 56. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain ➤ Subtract the known pieces from 27% to find the missing piece. ➤ 27% - 3% Spain Canada Germany 17% 3% 9% 4%
- 57. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain ➤ Subtract the known pieces from 27% to find the missing piece. ➤ 27% - 3% - 4% Spain Canada Germany 17% 3% 9% 4%
- 58. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain ➤ Subtract the known pieces from 27% to find the missing piece. ➤ 27% - 3% - 4% - 9% Spain Canada Germany 17% 3% 9% 4%
- 59. Place Known Information For Spain ➤ 27% visited Spain ➤ 4 pieces make up Spain ➤ Subtract the known pieces from 27% to find the missing piece. ➤ 27% - 3% - 4% - 9% ➤ = 11% Spain Canada Germany 17% 3% 9% 4% 11%
- 60. Place Known Information For Canada Spain Canada Germany 11% 9% 3% 4% 17%
- 61. Place Known Information For Canada ➤ 67% visited Canada Spain Canada Germany 11% 9% 3% 4% 17%
- 62. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada Spain Canada Germany 11% 9% 3% 4% 17%
- 63. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada Spain Canada Germany 11% 9% 3% 4% 17%
- 64. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada Spain Canada Germany 11% 9% 3% 4% 17%
- 65. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada Spain Canada Germany 11% 9% 3% 4% 17%
- 66. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada Spain Canada Germany 11% 9% 3% 4% 17%
- 67. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada ➤ Subtract the known pieces from 67% to find the missing piece. Spain Canada Germany 11% 9% 3% 4% 17%
- 68. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada ➤ Subtract the known pieces from 67% to find the missing piece. ➤ 67% - 3% Spain Canada Germany 11% 9% 3% 4% 17%
- 69. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada ➤ Subtract the known pieces from 67% to find the missing piece. ➤ 67% - 3% - 4% Spain Canada Germany 11% 9% 3% 4% 17%
- 70. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada ➤ Subtract the known pieces from 67% to find the missing piece. ➤ 67% - 3% - 4% - 17% Spain Canada Germany 11% 9% 3% 4% 17%
- 71. Place Known Information For Canada ➤ 67% visited Canada ➤ 4 pieces make up Canada ➤ Subtract the known pieces from 67% to find the missing piece. ➤ 67% - 3% - 4% - 17% ➤ = 43% Spain Canada Germany 11% 9% 3% 4% 17% 43%
- 72. Place Known Information For Germany Spain Canada Germany 4% 17% 3%11% 43% 9%
- 73. Place Known Information For Germany ➤ 36% visited Germany Spain Canada Germany 4% 17% 3%11% 43% 9%
- 74. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany Spain Canada Germany 4% 17% 3%11% 43% 9%
- 75. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany Spain Canada Germany 3%11% 43% 4% 17%9%
- 76. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany Spain Canada Germany 3%11% 43% 4% 17%9%
- 77. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany Spain Canada Germany 3%11% 43% 4% 17%9%
- 78. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany Spain Canada Germany 3%11% 4% 17%9% 43%
- 79. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany ➤ Subtract the known pieces from 36%. Spain Canada Germany 3%11% 4% 17%9% 43%
- 80. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany ➤ Subtract the known pieces from 36%. ➤ 36% - 9% Spain Canada Germany 3%11% 43% 4% 17%9%
- 81. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany ➤ Subtract the known pieces from 36%. ➤ 36% - 9% - 4% Spain Canada Germany 3%11% 43% 4% 17%9%
- 82. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany ➤ Subtract the known pieces from 36%. ➤ 36% - 9% - 4% - 17% Spain Canada Germany 3%11% 43% 4% 17%9%
- 83. Place Known Information For Germany ➤ 36% visited Germany ➤ 4 pieces make up Germany ➤ Subtract the known pieces from 36%. ➤ 36% - 9% - 4% - 17% ➤ = 6% Spain Canada Germany 3%11% 43% 4% 17%9% 6%
- 84. None Of The Countries ➤ All the information is filled in for the 3 countries but what about those who have not visited any of the 3 countries? Spain Canada Germany 4% 17% 3%11% 43% 6% 9%
- 85. None Of The Countries ➤ All the information is filled in for the 3 countries but what about those who have not visited any of the 3 countries? ➤ Because this is based on a percent, all those surveyed must equal 100%. To find those who did not visited any of these countries, subtract all who did from 100%. Spain Canada Germany 6% 4% 17%9% 3% 43%11%
- 86. None Of The Countries (Con’t) ➤ 100 -11% Spain Canada Germany 6% 4% 17%9% 3% 43%11%
- 87. None Of The Countries (Con’t) ➤ 100 -11% -3% Spain Canada Germany 6% 4% 17%9% 3% 43%11%
- 88. None Of The Countries (Con’t) ➤ 100 -11% -3% -43% Spain Canada Germany 6% 4% 17%9% 3% 43%11%
- 89. None Of The Countries (Con’t) ➤ 100 -11% -3% -43% -9% Spain Canada Germany 6% 4% 17%9% 3% 43%11%
- 90. None Of The Countries (Con’t) ➤ 100 -11% -3% -43% -9% -4% Spain Canada Germany 6% 4% 17%9% 3% 43%11%
- 91. None Of The Countries (Con’t) ➤ 100 -11% -3% -43% -9% -4% -17% Spain Canada Germany 6% 4% 17%9% 3% 43%11%
- 92. None Of The Countries (Con’t) ➤ 100 -11% -3% -43% -9% -4% -17% -6% Spain Canada Germany 6% 4% 17%9% 3% 43%11%
- 93. None Of The Countries (Con’t) ➤ 100 -11% -3% -43% -9% -4% -17% -6% ➤ = 7% Spain Canada Germany 4% 17% 3%11% 43% 6% 9% None = 7%
- 94. None Of The Countries (Con’t) ➤ 100 -11% -3% -43% -9% -4% -17% -6% ➤ = 7% ➤ Thus, 7% of those surveyed visited none of these countries. Spain Canada Germany 4% 17% 3%11% 43% 6% 9% None = 7%
- 95. Spain Canada Germany 4% 17% 3%11% 43% 6% None = 7% 9% Now the Venn Diagram is ready to use to answer questions.
- 96. Use Venn Diagram To Answer Questions ➤ What percent visited Canada and Germany but not Spain? Spain Canada Germany 4% 17% 3%11% 43% 6% None = 7% 9%
- 97. Use Venn Diagram To Answer Questions ➤ What percent visited Canada and Germany but not Spain? ➤ 17% visited only Canada and Germany Spain Canada Germany 4% 3%11% 43% 6% None = 7% 9% 17%
- 98. Use Venn Diagram To Answer Questions ➤ What percent visited Canada and Germany but not Spain? ➤ 17% visited only Canada and Germany ➤ What percent visited only 2 countries? Spain Canada Germany 4% 9% 17% 3%11% 43% 6% None = 7%
- 99. Use Venn Diagram To Answer Questions ➤ What percent visited Canada and Germany but not Spain? ➤ 17% visited only Canada and Germany ➤ What percent visited only 2 countries? ➤ 9% Spain Canada Germany 4% 11% 43% 6% None = 7% 17%9% 3%
- 100. Use Venn Diagram To Answer Questions ➤ What percent visited Canada and Germany but not Spain? ➤ 17% visited only Canada and Germany ➤ What percent visited only 2 countries? ➤ 9% + 3% Spain Canada Germany 4% 11% 43% 6% None = 7% 17%9% 3%
- 101. Use Venn Diagram To Answer Questions ➤ What percent visited Canada and Germany but not Spain? ➤ 17% visited only Canada and Germany ➤ What percent visited only 2 countries? ➤ 9% + 3% + 17% Spain Canada Germany 4% 11% 43% 6% None = 7% 17%9% 3%
- 102. Use Venn Diagram To Answer Questions ➤ What percent visited Canada and Germany but not Spain? ➤ 17% visited only Canada and Germany ➤ What percent visited only 2 countries? ➤ 9% + 3% + 17% ➤ = 29% visited only 2 countries Spain Canada Germany 4% 11% 43% 6% None = 7% 17%9% 3%
- 103. Use Venn Diagram To Answer Questions (Con’t) Suppose 500 people were surveyed. Spain Canada Germany 4% 9% 17% 3%11% 43% 6% None = 7%
- 104. Use Venn Diagram To Answer Questions (Con’t) Suppose 500 people were surveyed. ➤ How many visited both Spain and Germany? Spain Canada Germany 4% 9% 17% 3%11% 43% 6% None = 7%
- 105. Use Venn Diagram To Answer Questions (Con’t) Suppose 500 people were surveyed. ➤ How many visited both Spain and Germany? ➤ The Venn Diagram gives percents. Find the percent who visited both. Spain Canada Germany 17% 3%11% 43% 6% None = 7% 4% 9%
- 106. Use Venn Diagram To Answer Questions (Con’t) Suppose 500 people were surveyed. ➤ How many visited both Spain and Germany? ➤ The Venn Diagram gives percents. Find the percent who visited both. ➤ 9% + 4% = 13% Spain Canada Germany 4% 9% 17% 3%11% 43% 6% None = 7%
- 107. Use Venn Diagram To Answer Questions (Con’t) Suppose 500 people were surveyed. ➤ How many visited both Spain and Germany? ➤ The Venn Diagram gives percents. Find the percent who visited both. ➤ 9% + 4% = 13% ➤ Use multiplication to find how many people visited Spain and Germany Spain Canada Germany 4% 9% 17% 3%11% 43% 6% None = 7%
- 108. Use Venn Diagram To Answer Questions (Con’t) Suppose 500 people were surveyed. ➤ How many visited both Spain and Germany? ➤ The Venn Diagram gives percents. Find the percent who visited both. ➤ 9% + 4% = 13% ➤ Use multiplication to find how many people visited Spain and Germany ➤ 500 * 13% = 500 * 0.13 = Spain Canada Germany 4% 9% 17% 3%11% 43% 6% None = 7%
- 109. Use Venn Diagram To Answer Questions (Con’t) Suppose 500 people were surveyed. ➤ How many visited both Spain and Germany? ➤ The Venn Diagram gives percents. Find the percent who visited both. ➤ 9% + 4% = 13% ➤ Use multiplication to find how many people visited Spain and Germany ➤ 500 * 13% = 500 * 0.13 = ➤ 65 people visited Spain and Germany Spain Canada Germany 4% 9% 17% 3%11% 43% 6% None = 7%
- 110. Venn Diagram Recap ➤ Venn Diagrams are useful for organizing information. ➤ Always start at the inner most piece and work your way out to fill in the pieces. ➤ To answer questions, identify all pieces that fit the situation. ➤ Remember that addition, subtraction, and/or multiplication may be needed to answer questions. Happy Venning!