To create a frequency table, we first need to count how many values fall into each specified range. Let's analyze the given data:
Data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Counting the values in each range:
- 1 – 5: 3, 2, 3 → 3 values
- 6 – 10: 6 → 1 value
- 11 – 15: 12, 12, 15, 13 → 4 values
- 16 – 20: 17, 17, 18, 19, 20 → 5 values
- 21 – 25: 25, 21 → 2 values
Now, let's fill in the frequency table:
| Range | Number of Values | Relative Frequency | |------------|------------------|--------------------| | 1 – 5 | 3 | | | 6 – 10 | 1 | | | 11 – 15 | 4 | | | 16 – 20 | 5 | | | 21 – 25 | 2 | |
Total Number of Values: 3 + 1 + 4 + 5 + 2 = 15.
Relative Frequency Calculation: Relative Frequency = \( \frac{\text{Number of Values in the Range}}{\text{Total Number of Values}} \)
- For range 1 – 5: \( \frac{3}{15} = 0.2 \)
- For range 6 – 10: \( \frac{1}{15} \approx 0.067 \)
- For range 11 – 15: \( \frac{4}{15} \approx 0.267 \)
- For range 16 – 20: \( \frac{5}{15} = \frac{1}{3} \approx 0.333 \)
- For range 21 – 25: \( \frac{2}{15} \approx 0.133 \)
Now, let's fill in the relative frequencies in the table:
| Range | Number of Values | Relative Frequency | |------------|------------------|--------------------| | 1 – 5 | 3 | 0.2 | | 6 – 10 | 1 | 0.067 | | 11 – 15 | 4 | 0.267 | | 16 – 20 | 5 | 0.333 | | 21 – 25 | 2 | 0.133 |
Relative Frequency for the Range 16 – 20:
The relative frequency for the range 16 – 20 is \( \frac{5}{15} = 0.333 \) or approximately 0.33.
From the provided options:
- 0.33
- 0.2
- 0.27
- 0.4
The correct answer is 0.33.
1 answer