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

Question

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.