To solve the problem, let's go through the following steps:
1. Calculate Total Numbers:
- Males who enjoyed the movie: 47
- Males who did not enjoy the movie: 13
- Females who enjoyed the movie: 53
- Females who did not enjoy the movie: 3
Total number of males = 47 (enjoyed) + 13 (did not enjoy) = 60
Total number of females = 53 (enjoyed) + 3 (did not enjoy) = 56
Total number of people surveyed = 60 (total males) + 56 (total females) = 116
2. Calculate the Relative Frequency:
- Relative frequency of males who enjoyed the movie [tex]\( a \)[/tex]:
[tex]\[
a = \left( \frac{\text{males who enjoyed}}{\text{total people}} \right) \times 100 = \left( \frac{47}{116} \right) \times 100
\][/tex]
When calculated and rounded to the nearest percent, [tex]\( a \approx 41\% \)[/tex].
- Relative frequency of females who did not enjoy the movie [tex]\( b \)[/tex]:
[tex]\[
b = \left( \frac{\text{females who did not enjoy}}{\text{total people}} \right) \times 100 = \left( \frac{3}{116} \right) \times 100
\][/tex]
When calculated and rounded to the nearest percent, [tex]\( b \approx 3\% \)[/tex].
So, the values in the relative frequency table for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are:
[tex]\[
a = 41\%, \quad b = 3\%
\][/tex]
The correct answer is:
[tex]\[ \boxed{a=41\% , b=3\%} \][/tex]
