SOLUTION: I need a Venn diagram for there are 100 people in a company. 70 are married, 80 are college grads and 60 married and college grads

Question 1103738: I need a Venn diagram for there are 100 people in a company. 70 are married, 80 are college grads and 60 married and college grads
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!

10+60+20=90
10 are neither married nor in college
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let
U = universal set
M = set of people who are married
C = set of people who are college grads

Step 1) Draw a rectangle that is fairly large (say the width of your paper). This rectangle represents the entire universe U, basically the set of people we're restricting the survey to.

Step 2) Draw two overlapping circles inside the rectangle. Label them M and C for "married" and "college grad" respectively. Make sure you provide a key/legend for the reader to be able to determine what M and C stand for.

Step 3) In the overlapping region of the two circles, write the value 60. This represents the 60 married people who are also college grads

Step 4) Write the value 10 inside circle M but NOT in circle C. How am I getting the 10? There are 70 people who are married and 60 are both married and a college grad. So there are 70-60 = 10 people who are married only and not a college grad. Notice how the values in the M circle are 10 and 60 which add back up to 60+10 = 70; the proper total number of people who are married. This confirms we have the right number.

Step 5) Similarly, write the value 20 in circle C but outside of circle M. This represents those who are college grads but aren't married. It's computed by subtracting 80-60 = 20. As a check, add up everything in circle C and we get 20+60 = 80 people total who are college grads.

Step 6) Add up the values in the three regions so far: 10+60+20 = 90. There are 90 people who are either married only, a college grad only, or both. This is out of 100 people so there are 100-90 = 10 people who are neither married nor a college grad. Write this value (10) inside the rectangle but outside both circles

This is what the final result should look like. The numbers can move around but they must stay in the proper regions.

Summary of values

100 people overall (given)
70 are married (given). Some of these people are also college grads
80 are college grads (given). Some of these people are also married
10 people are married only and not a college grad. This is computed above and written inside circle M but not in circle C
20 people are a college grad but not married. This is computed above and written inside circle C but not in circle M
10 people are neither married nor a college grad (also computed above). This value is written outside the circles but inside the rectangle

Side Note: as a final check, you can add up all the values listed in the venn diagram to get: 10+10+60+20 = 20+80 = 100. This confirms we have the right answer as there are 100 people total.

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