To construct a grouped frequency distribution table (GFDT) for this dataset, we need to determine the range, class width, and class limits.

Step-by-Step Solution:

1. Identify the Range of Data:

   • The minimum value is 438.
   • The maximum value is 615.
   • Range = Maximum - Minimum = $615 - 438 = 177$.

2. Determine the Class Width:

   • You need 10 classes.
   • Class Width = $\frac{\text{Range}}{\text{Number of Classes}} = \frac{177}{10} = 17.7$.
   • We round up to the next "nice" number, so let's use a class width of 18.

3. Define the Class Intervals:

   • Starting from the minimum value (438) and using a class width of 18, we can define the classes. Each class interval will be closed on both ends and will look like [lower limit, upper limit].

4. Create the Frequency Distribution:

   • Count the number of data points in each interval.

Here’s what the grouped frequency distribution table will look like:

I’ll now calculate the frequency for each interval based on your dataset.I have displayed the grouped frequency distribution table for you, showing the data ranges and frequencies.

Would you like more details on how this table was constructed, or do you have any questions?

Here are five related questions to deepen your understanding:

1. How is class width determined in grouped frequency distribution?
2. What are the advantages of using a grouped frequency distribution table?
3. How would the table change if we used a different class width?
4. Why might we round the class width up to a "nice" number?
5. How would you represent this data using a histogram?

Tip: Grouped frequency distribution tables are particularly useful for large datasets, as they help to organize data into intervals, making patterns easier to observe.