To determine the class width for constructing a frequency distribution with seven classes, we need to calculate the range of the data and then divide by the number of classes. Here's the step-by-step solution:

1. Identify the minimum and maximum values in the dataset:

   • Minimum value: $825$
   • Maximum value: $1,600$

2. Calculate the range of the data: $\text{Range} = \text{Maximum} - \text{Minimum} = 1600 - 825 = 775$

3. Determine the class width: $\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{775}{7} \approx 111$

4. Round the class width to the next whole number:

   • Rounded class width = 111

Therefore, the class width should be 111.

Would you like further details or have any questions?

Here are some related questions you might find useful:

1. How can we determine the class limits with the calculated class width?
2. How would the frequency distribution look for these values with seven classes?
3. What are the steps to calculate the mean and median of this dataset?
4. How does changing the number of classes affect the class width?
5. What is the purpose of constructing a frequency distribution?

Tip: Always remember to round the class width to a whole number if specified in the question, as it ensures proper intervals in your frequency distribution.