Question

determining values in a two-way frequency table using a venn diagram
a group of 65 baseball players were surveyed about which hand they favor for batting. the data from the survey are shown in the venn diagram. determine the value for each variable in the two-way table.
$a=\square$
$b=\square$
$c=\square$
$d=\square$
$e=\square$
venn diagram and two - way table as shown in the image: venn diagram has two circles, right circle with 28 in non - overlapping part, female circle with 7 in non - overlapping part, 24 in overlapping part, and 6 outside both circles. two - way table:

	right	left	total
male	$c$	6	34
total	52	$d$	$e$

Explanation:

Step1: Find \(a\) (Female - Left)

From the Venn diagram, the "Female only" (Left - Female) is 7. So \(a = 7\).

Step2: Find \(b\) (Total Female)

Total Female is Right - Female + Left - Female. So \(b=24 + 7=31\).

Step3: Find \(c\) (Male - Right)

Total Right is 52, and Female - Right is 24. So \(c = 52-24 = 28\).

Step4: Find \(d\) (Total Left)

Total Left is Male - Left + Female - Left. Male - Left is 6, Female - Left is 7. So \(d=6 + 7 = 13\).

Step5: Find \(e\) (Total)

Total is Total Female + Total Male. Total Female is 31, Total Male is 34. So \(e=31 + 34 = 65\).

Answer:

\(a = 7\)
\(b = 31\)
\(c = 28\)
\(d = 13\)
\(e = 65\)