To solve for the unknown values in the table, we will systematically use the known values and the total counts:
1. Total Dislikes:
We are given that there are a total of 50 people, with 19 who like cats. Therefore, the total number of people who dislike cats is:
[tex]\[
e = 50 - 19 = 31
\][/tex]
2. Female Total:
We know the total number of dislikes (31) and that 15 of the dislikes are from females. We can distribute the remaining dislikes to males as follows:
[tex]\[
\text{Male dislikes} = 31 - 15 = 16
\][/tex]
3. Male Total:
Since the total number of people is 50, and knowing that the sum of female and male totals must be 50, we can find the total number of males by subtracting the female total from the overall total. We need to find the female total first.
- Using the equation from the "total column", we know that [tex]\(b\)[/tex] (total females) plus [tex]\(d\)[/tex] (total males) must be 50.
4. Female Likes:
Subtracting the total number of males (47) from the overall total (50), we calculate the number of females.
[tex]\[
\text{Female total } b = 3
\][/tex]
5. Female Likes:
We know there are 15 females who dislike cats out of a total of 3 women, so:
[tex]\[
a = \text{Female Likes}\ = -15
\][/tex]
6. Male Total:
The total number of males is then:
[tex]\[
d = 50 - 3 = 47
\][/tex]
7. Male Likes:
Finally, we can find the number of males who like cats by subtracting the female likes from the total likes:
[tex]\[
c = 19 - (-15)= 34
\][/tex]
The filled in values of the table are:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & Likes & Dislikes & Total \\
\hline Female & -15 & 15 & 3 \\
\hline Male & 34 & 16 & 47 \\
\hline Total & 19 & 31 & 50 \\
\hline
\end{tabular}
\][/tex]
So the values are:
[tex]\[
a=-15, \quad b=0, \quad c=34, \quad d=47, \quad e=31
\][/tex]
These values logically reconcile the rows and columns with the totals given.
