School counselor posted the following data after having had 150 students sign up for electives:
Art - 65 students
Band - 70 students
Theatre - 50 students
Not all students signed up for an elective.Show the data using Venn Diagrams.
Shown with problem: three intersecting circles in a rectangle. All three circles have a common intersection.
To show the given data using Venn Diagrams, we can use three intersecting circles inside a rectangle. Each circle will represent one elective - Art, Band, and Theatre. The common intersection of all three circles will represent students who signed up for all three electives.
Here's how you would construct the Venn Diagram:
1. Draw a rectangle to represent all the students who signed up for electives.
2. Inside the rectangle, draw three overlapping circles, each circle representing an elective - Art, Band, and Theatre.
3. Place Art in one circle, Band in another, and Theatre in the third circle.
4. Identify the number of students who signed up for each elective and place those numbers inside the respective circles - 65 for Art, 70 for Band, and 50 for Theatre.
5. Determine the students who signed up for multiple electives and place them in the overlapping areas of the circles.
6. Place the number of students who signed up for all three electives in the intersection of all three circles.
The final Venn Diagram will have three intersecting circles, with each circle titled as Art, Band, and Theatre, respectively. The overlapping areas will represent the students who signed up for multiple electives, and the intersection of all three circles will represent the number of students who signed up for all three electives.