To help you find the best class width and first lower class limit, let's go through the steps:

1. Identify the Range:

   • First, we need to find the minimum and maximum values in the dataset to calculate the range.

2. Calculate the Range:

   • $\text{Range} = \text{Maximum Value} - \text{Minimum Value}$

3. Determine Optimal Class Width:

   • Since the goal is to create 10 classes, we can calculate the class width as: $\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}}$
   • Round up to the nearest "nice" number if necessary (like 20, 25, etc.).

4. Set the First Lower Class Limit:

   • Choose a lower bound that is a multiple of the class width and just below or around the minimum value in the dataset.

Let me analyze these steps for you based on the values in the table.Based on the calculations:

• Minimum Value: 199
• Maximum Value: 370
• Range: 171
• Optimal Class Width: 18 (rounded to the nearest "nice" number that works for 10 classes)
• First Lower Class Limit: 198 (a multiple of the class width just below the minimum value)

Thus, you should try setting:

• Optimal Class Width = 18
• First Lower Class Limit = 198

Would you like further details on any of these steps or have other questions? Here are some related questions for deeper understanding:

1. How can you determine the number of classes for a different dataset?
2. What happens if you choose a larger class width?
3. Why is it beneficial to round the class width to a "nice" number?
4. How do you adjust the class intervals if the dataset range changes?
5. How is the first lower class limit chosen if the minimum value is very low?

Tip: When setting class intervals, make sure each class limit includes values only up to but not including the next class limit for clarity in a frequency table.