Question

there are 18 students in a certain painting class. their ages are shown below.
complete the grouped relative frequency distribution for the data. (note that we are using a class width of 4.)
write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.
age
19 32 18 34 31
35 16 23 17 17
25 28 30 19 28
29 30 27
age relative frequency
16 to 19
20 to 23
24 to 27
28 to 31
32 to 35

Explanation:

Step1: Count the frequency of each class

• For the class \(16 - 19\): The ages \(16,17,17,18,19,19\) are in this range. So the frequency \(f_1=6\).
• For the class \(20 - 23\): The age \(23\) is in this range. So the frequency \(f_2 = 1\).
• For the class \(24 - 27\): The ages \(25,27\) are in this range. So the frequency \(f_3=2\).
• For the class \(28 - 31\): The ages \(28,28,29,30,30,31\) are in this range. So the frequency \(f_4 = 6\).
• For the class \(32 - 35\): The ages \(32,34,35\) are in this range. So the frequency \(f_5=3\).

Step2: Calculate the relative frequency

The formula for relative frequency \(RF=\frac{f}{n}\), where \(n = 18\) (total number of students).

• For the class \(16 - 19\): \(RF_1=\frac{6}{18}\approx0.33\)
• For the class \(20 - 23\): \(RF_2=\frac{1}{18}\approx0.06\)
• For the class \(24 - 27\): \(RF_3=\frac{2}{18}\approx0.11\)
• For the class \(28 - 31\): \(RF_4=\frac{6}{18}\approx0.33\)
• For the class \(32 - 35\): \(RF_5=\frac{3}{18}=0.17\)

Answer:

Age	Relative frequency
\(20\) to \(23\)	\(0.06\)
\(24\) to \(27\)	\(0.11\)
\(28\) to \(31\)	\(0.33\)
\(32\) to \(35\)	\(0.17\)