To determine the relative frequency of preference for Alternative music, we need to follow these steps:
1. Calculate the total number of surveyed students:
We add together the frequencies of all the music types: [tex]\( 10 + 7 + 8 + 5 + 6 + 4 \)[/tex].
[tex]\[
\text{Total students} = 40
\][/tex]
2. Identify the frequency of preference for Alternative music:
According to the frequency table, the frequency for Alternative music is [tex]\( 6 \)[/tex].
3. Calculate the relative frequency:
The relative frequency is found by dividing the number of students who prefer Alternative music by the total number of students.
[tex]\[
\text{Relative Frequency} = \frac{\text{Frequency of Alternative}}{\text{Total Number of Students}} = \frac{6}{40}
\][/tex]
4. Simplify the fraction:
Simplifying the fraction [tex]\( \frac{6}{40} \)[/tex]:
[tex]\[
\frac{6}{40} = \frac{3}{20} = 0.15
\][/tex]
Thus, the correct answer representing the relative frequency of preference for Alternative music is:
D. [tex]\( \frac{3}{20} \)[/tex]
