Question

Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Use the ranges listed in the table:

Range Number of Values Relative Frequency
1 – 5
6 – 10
11 – 15
16 – 20
21 – 25


What is the relative frequency for the range 16 – 20?

0.33

0.2

.27

0.4

Answer 1

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**.