This list of 16 random numbers has been sorted:

21
21
21
24
25
30
35
38
41
41
42
43
47
47
53
54

Fill in this table with the frequencies as whole numbers and the relative frequencies
as decimals with 4 decimal places for the relative frequencies.
(This problem does not accept fractions.)
Remember: relative frequencies are between 0.0 and 1.0

Class	Frequency	Rel.Freq
20-29
5
Correct
0.3125
Correct
30-39
2
Incorrect
0.1250
Incorrect
40-49
7
Incorrect
0.4375
Incorrect
50-59
2
Correct
0.1250
Correct

Let's go through the problem step by step and ensure all frequencies and relative frequencies are correct.

### Data Set:
- 21, 21, 21, 24, 25, 30, 35, 38, 41, 41, 42, 43, 47, 47, 53, 54

### Step 1: Frequency Count for Each Class

- **Class 20-29**: The numbers in this class are 21, 21, 21, 24, 25.
    - Frequency: 5 (already correct)
    
- **Class 30-39**: The numbers in this class are 30, 35, 38.
    - Frequency: 3 (the previous entry of 2 is incorrect)

- **Class 40-49**: The numbers in this class are 41, 41, 42, 43, 47, 47.
    - Frequency: 6 (the previous entry of 7 is incorrect)

- **Class 50-59**: The numbers in this class are 53, 54.
    - Frequency: 2 (already correct)

### Step 2: Total Frequency
Sum of frequencies:  
\( 5 + 3 + 6 + 2 = 16 \)

### Step 3: Calculating Relative Frequencies
To find the relative frequency, divide each class's frequency by the total frequency (16) and round to four decimal places.

- **Class 20-29**:  
  \( \text{Rel. Freq} = \frac{5}{16} = 0.3125 \) (correct)
  
- **Class 30-39**:  
  \( \text{Rel. Freq} = \frac{3}{16} = 0.1875 \) (previous answer of 0.1250 was incorrect)

- **Class 40-49**:  
  \( \text{Rel. Freq} = \frac{6}{16} = 0.3750 \) (previous answer of 0.4375 was incorrect)

- **Class 50-59**:  
  \( \text{Rel. Freq} = \frac{2}{16} = 0.1250 \) (correct)

### Final Table:

| Class   | Frequency | Rel. Freq |
|---------|-----------|-----------|
| 20-29   | 5         | 0.3125    |
| 30-39   | 3         | 0.1875    |
| 40-49   | 6         | 0.3750    |
| 50-59   | 2         | 0.1250    |

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:
1. How do you calculate cumulative frequency?
2. What is the sum of all relative frequencies in this table?
3. What is the mode of the original data set?
4. How would the frequency distribution change if the classes were in intervals of 10?
5. How would you find the median of the data set?

**Tip:** Relative frequencies are a great way to compare data distributions of different sizes, as they normalize the frequencies into proportions.

This list of 16 random numbers has been sorted:

21
21
21
24
25
30
35
38
41
41
42
43
47
47
53
54

Fill in this table with the frequencies as whole numbers and the relative frequencies as decimals with 4 decimal places for the relative frequencies.

Class	Frequency	Rel.Freq
20-29
5
Correct
0.3125
Correct
30-39
2
Incorrect
0.1250
Incorrect
40-49
7
Incorrect
0.4375
Incorrect
50-59
2
Correct
0.1250
Correct

Understand how to calculate frequency and relative frequency for a sorted data set of 16 numbers, with step-by-step guidance on creating a frequency table. This problem explores statistical concepts and relative frequency calculations, suitable for students in Grades 6-8.

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