To create a grouped frequency distribution table (GFDT) for the data set, we need to follow these steps:

Steps:

1. Determine the Range: The range is the difference between the largest and smallest values in the data set.

   • Smallest value: 175
   • Largest value: 633
   • Range = Largest value - Smallest value = 633 - 175 = 458

2. Choose the Number of Classes: We are instructed to use 10 classes.

3. Determine the Class Width: The class width can be found by dividing the range by the number of classes: $\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{458}{10} = 45.8$ To keep it a "nice" number, we round the class width up to 50.

4. Set the First Class: The first class is provided: [150, 199]. The lower class limit should be a multiple of the class width (which is 50).

5. Construct the Classes: Since we are using closed intervals, the classes will look like this:

   • 1st class: [150, 199]
   • 2nd class: [200, 249]
   • 3rd class: [250, 299]
   • and so on...

Constructing the Frequency Distribution Table:

With a class width of 50, we can create the following 10 classes:

Now, let's count how many data points fall into each class:

• [150, 199]: 175, 161, 199 → 3 data points
• [200, 249]: 209, 241, 249 → 3 data points
• [250, 299]: 262, 251, 262 → 3 data points
• [300, 349]: 336, 332, 346 → 3 data points
• [350, 399]: 355, 371, 371, 396, 389, 399 → 6 data points
• [400, 449]: 421, 429, 450, 416, 401 → 5 data points
• [450, 499]: 486, 486 → 2 data points
• [500, 549]: 521, 532, 521 → 3 data points
• [550, 599]: 584 → 1 data point
• [600, 649]: 633 → 1 data point

Final Grouped Frequency Distribution Table (GFDT):

This is the grouped frequency distribution table for the given data set.

Do you need any further clarification or additional details on how the table was constructed?

Related questions:

1. How would you find the cumulative frequency for this table?
2. How would you calculate the class midpoints for this GFDT?
3. What is the total frequency and how is it calculated in this context?
4. How would you create a histogram for this distribution?
5. How can you calculate the mean and standard deviation for this data set?

Tip:

When creating frequency tables, always aim for a "nice" class width that makes the classes easy to interpret. A class width that is a multiple of 5 or 10 usually works well!