To calculate the relative frequency of students who participate in band and do not play a sport, you first need to find the number of students who do not play a sport and participate in band.
From the table:
- Students who do not play a sport and participate in band: 22
- Students who do not play a sport and do not participate in band: 8
The total number of students who do not play a sport is: \[ 22 + 8 = 30 \]
Now, the relative frequency of students who participate in band among those who do not play a sport is calculated by dividing the number of students who do participate in band by the total number of students who do not play a sport:
\[ \text{Relative Frequency} = \frac{\text{Number of students who participate in band and do not play a sport}}{\text{Total number of students who do not play a sport}} = \frac{22}{30} \]
Now, simplifying the fraction:
\[ \frac{22}{30} = \frac{11}{15} \approx 0.7333 \]
Therefore, the relative frequency of students who participate in band and do not play a sport is \( \frac{11}{15} \) or approximately \( 0.7333 \) (73.33%).
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