Question

try it venn diagram a group of 50 people were asked their gender and if they liked cats. the data from the survey are shown in the venn diagram. determine the value for each variable in the two - way table. a = b = c = d = e =

	likes	dislikes	total
male	c	16	d
total	19	e	50

Explanation:

Step1: Find \( a \) and \( c \)

From the Venn diagram, the "Likes" circle has 13 (only likes) and 6 (likes and male). So total who like: \( 13 + 6 = 19 \) (matches total likes in table). For males who like, \( c = 6 \) (overlap). Then \( a = 19 - c = 19 - 6 = 13 \).

Step2: Find \( d \) (male total)

Male dislikes is 16, male likes is 6, so \( d = 6 + 16 = 22 \).

Step3: Find \( b \) (female total)

Total people is 50, male total \( d = 22 \), so \( b = 50 - d = 50 - 22 = 28 \).

Step4: Find \( e \) (total dislikes)

Female dislikes 15, male dislikes 16, so \( e = 15 + 16 = 31 \).

Answer:

\( a = 13 \)
\( b = 28 \)
\( c = 6 \)
\( d = 22 \)
\( e = 31 \)