To determine the class width for constructing seven classes for the given data, we’ll follow these steps:

1. Find the Range of the Data:

   • Identify the smallest and largest values in the data set.
   • Subtract the smallest value from the largest to get the range.

2. Calculate the Class Width:

   • Divide the range by the number of classes (7 in this case).
   • Round up to the next whole number, as class width is generally rounded up to ensure all data points are covered.

Let’s apply this:

Step 1: Range

• Minimum Value: 825
• Maximum Value: 1600
• Range = $1600 - 825 = 775$

Step 2: Class Width Calculation

• Class Width = $\frac{\text{Range}}{\text{Number of Classes}} = \frac{775}{7} \approx 111$ (rounded up)

So, the class width should be 111.

Would you like further details on constructing the classes, or have any questions about frequency distributions?

Here are some additional questions for practice:

1. How would you determine the midpoint of each class in this distribution?
2. What are the advantages of rounding up the class width?
3. How would you organize the data into a frequency distribution table with these classes?
4. How would the class width change if you used a different number of classes?
5. How can frequency distributions help in visualizing data trends?

Tip: Always round up the class width to ensure that all values fit within the defined classes.