Consider the following data. Click on the datafile logo to reference the data.

14	21	23	21	16
19	22	25	16	16
24	24	25	19	16
19	18	19	21	12
16	17	18	23	25
20	23	16	20	19
24	26	15	22	24
20	22	24	22	20
Summarize the data by filling in the frequency, the relative frequency (3 decimals), and the percent frequency (1 decimal) values below.

Class	Frequency	Relative Frequency	Percent Frequency

Total

To calculate the **frequency**, **relative frequency**, and **percent frequency**, we first need to organize the given data into "classes" or intervals.

### Step 1: Organize the data into classes
Let’s assume the classes represent specific intervals of numbers, which will help in calculating the frequency distributions. From the data, the smallest number is 12, and the largest is 26. A reasonable way to divide these numbers is into 5 equal classes.

We can define the classes like this:

- Class 1: 12–14
- Class 2: 15–17
- Class 3: 18–20
- Class 4: 21–23
- Class 5: 24–26

### Step 2: Calculate the Frequency for each class
Go through the dataset and count how many numbers fall within each class.

- Class 1 (12–14): {12}
  - Frequency = 1
- Class 2 (15–17): {16, 16, 16, 16, 15, 16}
  - Frequency = 6
- Class 3 (18–20): {19, 19, 19, 18, 19, 19, 20, 19, 20}
  - Frequency = 9
- Class 4 (21–23): {21, 23, 21, 22, 23, 22, 22}
  - Frequency = 7
- Class 5 (24–26): {24, 24, 25, 25, 24, 24, 26, 25, 24}
  - Frequency = 9

### Step 3: Calculate the Relative Frequency
Relative frequency is the frequency of each class divided by the total number of data points. The total number of data points is:

\[
1 + 6 + 9 + 7 + 9 = 32
\]

Now calculate the relative frequency for each class:

- Class 1: \( \frac{1}{32} = 0.031 \)
- Class 2: \( \frac{6}{32} = 0.188 \)
- Class 3: \( \frac{9}{32} = 0.281 \)
- Class 4: \( \frac{7}{32} = 0.219 \)
- Class 5: \( \frac{9}{32} = 0.281 \)

### Step 4: Calculate the Percent Frequency
Percent frequency is the relative frequency multiplied by 100. Round to one decimal place:

- Class 1: \( 0.031 \times 100 = 3.1\% \)
- Class 2: \( 0.188 \times 100 = 18.8\% \)
- Class 3: \( 0.281 \times 100 = 28.1\% \)
- Class 4: \( 0.219 \times 100 = 21.9\% \)
- Class 5: \( 0.281 \times 100 = 28.1\% \)

### Summary Table

| Class  | Frequency | Relative Frequency | Percent Frequency |
|--------|-----------|--------------------|-------------------|
| 12–14  | 1         | 0.031              | 3.1%              |
| 15–17  | 6         | 0.188              | 18.8%             |
| 18–20  | 9         | 0.281              | 28.1%             |
| 21–23  | 7         | 0.219              | 21.9%             |
| 24–26  | 9         | 0.281              | 28.1%             |
| **Total** | 32        | **1.000**          | **100%**            |

Would you like more details on how these values were computed or help with another part of the data? 

Here are five related questions:
1. How do you decide the number of classes in frequency distribution?
2. What is the difference between relative and cumulative frequency?
3. How does the choice of class intervals affect the shape of a frequency distribution?
4. Can this frequency table be visualized using a histogram?
5. What is the significance of relative frequency in data analysis?

**Tip**: When defining class intervals, ensure that the range includes the smallest and largest data values to avoid missing any data points.

Consider the following data. Click on the datafile logo to reference the data.

14 21 23 21 16
19 22 25 16 16
24 24 25 19 16
19 18 19 21 12
16 17 18 23 25
20 23 16 20 19
24 26 15 22 24
20 22 24 22 20
Summarize the data by filling in the frequency, the relative frequency (3 decimals), and the percent frequency (1 decimal) values below.

Class Frequency Relative Frequency Percent Frequency

Total

Learn how to summarize a data set by calculating frequency, relative frequency (3 decimals), and percent frequency (1 decimal). This guide provides a step-by-step approach to organizing data into classes, counting frequencies, and converting them into relative and percent frequencies. Ideal for students in Grades 9-12.

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