To construct a grouped frequency distribution table (GFDT) for this dataset, we need to analyze the data and determine the appropriate class intervals and frequencies based on the instructions provided. Here's a breakdown of how we could approach it:

1. Identify the Range of the Data:

   • The data values in the table range from a minimum of 455 to a maximum of 649.

2. Determine the Number of Classes:

   • According to the problem, we need 10 classes.

3. Calculate Class Width:

   • The class width can be calculated as follows: $\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{649 - 455}{10} = 19.4 \approx 20$
   • Rounding to 20 gives us a “nice” class width, as requested.

4. Construct Class Intervals:

   • Starting from the lowest value, 450, and using a class width of 20, the intervals will be:
     • $450, 469$, $470, 489$, $490, 509$, etc.

5. Count Frequencies:

   • For each interval, count how many data values fall within it.

Let me create this table for you and ensure the frequency calculations match your provided image.

Would you like me to proceed with generating a detailed table based on this explanation, or do you need assistance with another aspect of this problem?

Follow-up Questions:

1. Would you like a deeper explanation of frequency distribution tables?
2. Do you need help understanding how to determine class intervals?
3. Are you interested in learning how to calculate class width with other methods?
4. Would you like guidance on different data grouping methods?
5. Do you want to know how to interpret grouped frequency distribution tables?

Tip:

When constructing frequency tables, always check the range and round the class width appropriately for simplicity and consistency.