Step 1 :Given the ages of the students in the class, we are asked to find the relative frequency of the age groups. The relative frequency is calculated by dividing the frequency of a data point by the total number of data points.
Step 2 :The ages of the students are: 37, 27, 23, 29, 28, 22, 21, 34, 35, 18, 33, 35, 19, 35, 32, 37, 24, 25, 20. The total number of students is 19.
Step 3 :The age groups are defined as follows: 18 to 22, 23 to 27, 28 to 32, and 33 to 37.
Step 4 :Counting the number of students in each age group, we get: 5 students in the age group 18 to 22, 4 students in the age group 23 to 27, 3 students in the age group 28 to 32, and 7 students in the age group 33 to 37.
Step 5 :Calculating the relative frequencies for each age group, we get: \( \frac{5}{19} \approx 0.26 \) for the age group 18 to 22, \( \frac{4}{19} \approx 0.21 \) for the age group 23 to 27, \( \frac{3}{19} \approx 0.16 \) for the age group 28 to 32, and \( \frac{7}{19} \approx 0.37 \) for the age group 33 to 37.
Step 6 :\(\boxed{\text{Final Answer:}}\) The relative frequencies for the age groups 18 to 22, 23 to 27, 28 to 32, and 33 to 37 are 0.26, 0.21, 0.16, and 0.37 respectively.