Question

the manager of a campus gym is planning the schedule of fitness classes for a new school year, and will decide how often to hold certain classes based on the interests of the students. she polls 47 students at various times of day, asking what type of classes theyd be interested in attending. the results are summarized in the table below.

type of class	yoga	pilates	spinning	yoga and pilates	pilates and spinning	yoga and spinning	all three

(a) construct a venn diagram illustrating these results.

Explanation:

Step1: Calculate only Yoga

Subtract students in Yoga+Pilates, Yoga+Spinning, and all three from total Yoga students.
$17 - 9 - 8 + 2 = 2$

Step2: Calculate only Pilates

Subtract students in Yoga+Pilates, Pilates+Spinning, and all three from total Pilates students.
$18 - 9 - 6 + 2 = 5$

Step3: Calculate only Spinning

Subtract students in Yoga+Spinning, Pilates+Spinning, and all three from total Spinning students.
$16 - 8 - 6 + 2 = 4$

Step4: Calculate students in no classes

Subtract all categorized students from total polled students.
$47 - (2 + 5 + 4 + 9 + 8 + 6 + 2) = 11$

Step5: Map values to Venn diagram

• Label 3 overlapping circles: Yoga, Pilates, Spinning
• Center (all three): 2
• Yoga only: 2; Pilates only: 5; Spinning only: 4
• Yoga/Pilates only (not all three): $9 - 2 = 7$
• Yoga/Spinning only (not all three): $8 - 2 = 6$
• Pilates/Spinning only (not all three): $6 - 2 = 4$
• Outside all circles: 11

Answer:

The Venn diagram will have three overlapping circles labeled Yoga, Pilates, and Spinning with the following values:

• Only Yoga: 2
• Only Pilates: 5
• Only Spinning: 4
• Yoga and Pilates only: 7
• Yoga and Spinning only: 6
• Pilates and Spinning only: 4
• All three classes: 2
• No classes interested: 11 (outside all circles)