The survey below represents data drawn from college students about their weight-control habits. Draw a Venn Diagram to represent the data from the survey. • 29 students play sports. • 32 students work out at the gym. • 7 students both play sports and diet. Of those, 2 do not work out at the gym. • 10 students are both working out at the gym and on a diet. • 27 students are dieting but do not work out at the gym nor play a sport. • 10 students both work out at the gym and play a sport but do not diet. • 24 students are neither working out at the gym, playing a sport, nor on a diet. • 97 students took the survey.
Answers
Given : 29 students play sports. • 32 students work out at the gym. • 7 students both play sports and diet. Of those, 2 do not work out at the gym. • 10 students are both working out at the gym and on a diet. • 27 students are dieting but do not work out at the gym nor play a sport. • 10 students both work out at the gym and play a sport but do not diet. • 24 students are neither working out at the gym, playing a sport, nor on a diet. • 97 students took the survey.
To Find : Draw a Venn Diagram to represent the data from the survey.
Solution:
Total = 97
Sports S = 29
Gym G = 32
Diet D =
S ∩ D = 7
2 do not work out at the gym.
S ∩ D ∩ G = 5
D ∩ G = 10
None = 24
27 students are dieting but do not work out at the gym nor play a sport
Diet only = 27
Venn Diagram attached
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