15	23	17	13	3	9	7	6	8	11
16	32	27	4	20	3	28	5	6	11
20	12	8	10	25	10	8	15	11	9
Construct a grouped frequency table with six classes, showing class limit, class boundaries, class midpoints, frequencies, relative frequencies, and cumulative frequencies. 

To create a grouped frequency table with six classes, we'll follow these steps:

### Step 1: Organize the Data
First, let's combine and organize all the dataTo create a grouped frequency table with six classes, we'll follow these steps:

### Step 1: Organize the Data
First, let's combine and organize all the 

**Data Set:**

15, 23, 17, 13, 3, 9, 7, 6, 8, 11,  
16, 32, 27, 4, 20, 3, 28, 5, 6, 11,  
20, 12, 8, 10, 25, 10, 8, 15, 11, 9.

### Step 2: Determine the Range of Data
- Minimum value: 3
- Maximum value: 32

**Range** = Maximum value - Minimum value = 32 - 3 = 29

### Step 3: Determine the Class Width
We will divide the data into **6 classes**. To find the class width, we divide the range by the number of classes and round up if necessary.

Class width \( = \frac{\text{Range}}{\text{Number of classes}} = \frac{29}{6} \approx 4.83 \)

We round this up to **5**.

### Step 4: Set Class Limits
We will create six classes with width 5, starting from the minimum value 3.

| Class Limits | Class Boundaries | Midpoint |
|--------------|------------------|----------|
| 3 - 7        | 2.5 - 7.5        | 5        |
| 8 - 12       | 7.5 - 12.5       | 10       |
| 13 - 17      | 12.5 - 17.5       | 15       |
| 18 - 22      | 17.5 - 22.5       | 20       |
| 23 - 27      | 22.5 - 27.5       | 25       |
| 28 - 32      | 27.5 - 32.5       | 30       |

### Step 5: Calculate Frequencies
Now we will count how many data points fall within each class:

- Class 3 - 7: \( 3, 3, 7, 6, 6, 5 \) → Frequency = 6
- Class 8 - 12: \( 9, 8, 11, 11, 10, 

Construct a grouped frequency table with six classes, showing class limit, class boundaries, class midpoints, frequencies, relative frequencies, and cumulative frequencies.

Learn how to construct a grouped frequency table with six classes, including class limits, boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. This problem demonstrates key statistical concepts suitable for students in Grades 10-12.

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