Let's analyze and solve the problem step-by-step.
1. We are provided with the survey data showing the favorite pets of first-grade students:
- Dogs: 17 respondents
- Cats: 19 respondents
- Fish: 6 respondents
- Guinea Pigs: 8 respondents
2. First, let's calculate the total number of respondents. Adding up all the frequencies:
[tex]\[
17 \, (\text{dogs}) + 19 \, (\text{cats}) + 6 \, (\text{fish}) + 8 \, (\text{guinea pigs}) = 50
\][/tex]
The total number of respondents is 50.
3. Now, let's calculate the relative frequencies (in percentage) for each pet choice. We do this by dividing the frequency of each pet by the total number of respondents and then multiplying by 100 to get the percentage.
[tex]\[
\text{Relative frequency of dogs} = \left( \frac{17}{50} \right) \times 100 = 34.0\%
\][/tex]
[tex]\[
\text{Relative frequency of cats} = \left( \frac{19}{50} \right) \times 100 = 38.0\%
\][/tex]
[tex]\[
\text{Relative frequency of fish} = \left( \frac{6}{50} \right) \times 100 = 12.0\%
\][/tex]
[tex]\[
\text{Relative frequency of guinea pigs} = \left( \frac{8}{50} \right) \times 100 = 16.0\%
\][/tex]
Thus, the relative frequencies in percentage are:
- Dogs: 34.0%
- Cats: 38.0%
- Fish: 12.0%
- Guinea Pigs: 16.0%
4. To find the third most popular answer, we need to rank the choices by their frequencies:
- Cats: 19
- Dogs: 17
- Guinea Pigs: 8
- Fish: 6
From the ranking, the first most popular is 'Cats' (19), the second most popular is 'Dogs' (17), and the third most popular is 'Guinea Pigs' (8).
5. The percentage of respondents who liked guinea pigs is the relative frequency calculated above for guinea pigs.
Therefore, the third most popular answer was given by [tex]\( \boxed{16.0} \% \)[/tex] of respondents.
