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Use the table to answer the question.

\begin{tabular}{|l|l|l|}
\hline Preference & 7th Graders & 8th Graders \\
\hline Prefers Cats & 36 & 22 \\
\hline Prefers Dogs & 8 & 26 \\
\hline No Preference & 2 & 6 \\
\hline
\end{tabular}

What is the relative frequency of 7th graders who prefer dogs? Round to the nearest tenth.

A. 23.5%
B. 8%
C. 76.5%
D. 17.4%


Sagot :

To find the relative frequency of students who prefer dogs among the 7th graders, follow these steps:

1. Calculate the total number of 7th grade students:
You need to sum up all the categories of students in the 7th grade:
- Prefers Cats: 36
- Prefers Dogs: 8
- No Preference: 2

[tex]\[ \text{Total students in 7th grade} = 36 + 8 + 2 = 46 \][/tex]

2. Determine the number of 7th graders who prefer dogs:
According to the table, 8 students prefer dogs.

3. Calculate the relative frequency:
To find the relative frequency, divide the number of students who prefer dogs by the total number of students and then multiply by 100 to convert it to a percentage:

[tex]\[ \text{Relative frequency} = \left( \frac{\text{Number of students who prefer dogs}}{\text{Total number of students}} \right) \times 100 \][/tex]

Plugging in the numbers:

[tex]\[ \text{Relative frequency} = \left( \frac{8}{46} \right) \times 100 \approx 17.391304347826086 \% \][/tex]

4. Round the percentage to the nearest tenth:
When you round 17.391304347826086 to the nearest tenth, you get:

[tex]\[ \text{Rounded relative frequency} = 17.4\% \][/tex]

Therefore, the relative frequency of 7th graders who prefer dogs is 17.4%, which corresponds to the last option.

So, the correct answer is:
[tex]\[ \boxed{17.4\%} \][/tex]
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