To solve the problem, let's go through each part step by step:

1. Determine the Range of the Data Set:

   • The range is calculated by subtracting the smallest value in the data set from the largest value.
   • From the image, the smallest value is 3590, and the largest value is 8350.
   • Therefore, the range is: $\text{Range} = 8350 - 3590 = 4760$

2. Calculate the Optimal Class Width:

   • To find the class width for 10 classes, divide the range by the number of classes.
   • Using the formula: $\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}}$
   • Substituting the values: $\text{Class Width} = \frac{4760}{10} = 476$
   • To ensure that the class width is a "nice" value (usually rounded to a whole number that's convenient for grouping), we can round it to 500 for simplicity, making it easier to handle in a frequency distribution.

Summary:

• Range: 4760
• Optimal Class Width: 500 (rounded from 476 for simplicity)

Would you like more details on constructing the frequency distribution with this class width, or do you have any further questions?

Related Questions:

1. How do you construct a frequency distribution with a given class width?
2. What is the importance of choosing a "nice" class width in statistics?
3. How does the choice of class width affect the shape of a histogram?
4. Why is the range an important measure when constructing a frequency distribution?
5. What are some methods to determine the best number of classes for a data set?

Tip:

In constructing grouped frequency distributions, rounding the class width to a nearby convenient number (like 10, 50, 100, etc.) helps make the data easier to interpret and present visually.