To solve this problem, we need to calculate two things:

1. Range of the dataset
2. Optimal class width for a grouped frequency distribution table (GFDT) with 10 classes.

Step 1: Calculate the Range

The range of a dataset is calculated as: $\text{Range} = \text{Maximum Value} - \text{Minimum Value}$

Let's identify the maximum and minimum values in the dataset provided:

• Maximum value: 29480
• Minimum value: 11000

Therefore, $\text{Range} = 29480 - 11000 = 18480$

Step 2: Calculate the Optimal Class Width

To find the class width for 10 classes, we divide the range by the desired number of classes and round up to the nearest "nice" number (which typically means a round number for easier interpretation).

$\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{18480}{10} = 1848$

Since 1848 is not a round number, let's round it up to a more "nice" number, such as 1900 or 2000.

Final Answer:

• Range = 18480
• Optimal Class Width = 1900 (or 2000 for simplicity)

Would you like more details on the steps or have any questions?

Here are some related questions that might expand your understanding:

1. How can we determine a "nice" number for class width?
2. What would the class limits look like if we used a width of 1900 versus 2000?
3. How would the range change if an outlier was added to the dataset?
4. Why is it important for the class width to be consistent in a GFDT?
5. How would using fewer classes affect the class width and frequency distribution?

Tip: When constructing grouped frequency tables, rounding the class width to a simple number makes interpretation easier for analysis.