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

To construct a grouped frequency table with six classes, we need data, or at least an assumption about the dataset's range and structure. I'll guide you through how to do this with hypothetical data.

Let’s assume the following dataset with 30 values:

```
12, 14, 19, 23, 25, 27, 31, 35, 36, 37, 41, 43, 45, 47, 50, 
52, 53, 55, 57, 60, 61, 63, 65, 66, 67, 69, 72, 75, 78, 80
```

### Step 1: Determine the range and class width

- **Range** = Maximum value - Minimum value = 80 - 12 = 68
- **Number of classes** = 6
- **Class width** = \( \frac{\text{Range}}{\text{Number of classes}} = \frac{68}{6} \approx 11.33 \). Round up to 12 for simplicity.

### Step 2: Construct the classes and boundaries

| **Class** | **Class Limits** |

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 using hypothetical data. This guide covers key statistical concepts such as class limits, boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. Ideal for students in Grades 9-12 studying statistics.

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