To construct a grouped frequency distribution table (GFDT) for this data set with 10 classes, we'll follow these steps:

Step 1: Determine the Range of the Data Set

First, we calculate the range:

• Minimum Value: $\min = 301$
• Maximum Value: $\max = 396$

$\text{Range} = \max - \min = 396 - 301 = 95$

Step 2: Choose a Suitable Class Width

To have approximately 10 classes, we divide the range by the desired number of classes:

$\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{95}{10} = 9.5$

Since 9.5 is not a convenient class width, we'll round it up to the next "nice" number. The closest nice class width would be 10.

Step 3: Determine the Class Limits

Given a class width of 10, we start from the minimum value (or a convenient lower limit close to it that is a multiple of 10) and create intervals of width 10.

Step 4: Create the Grouped Frequency Distribution Table

The classes will be:

• [300, 309]
• [310, 319]
• [320, 329]
• [330, 339]
• [340, 349]
• [350, 359]
• [360, 369]
• [370, 379]
• [380, 389]
• [390, 399]

Now, we count the frequency of data points falling into each class.

Grouped Frequency Distribution Table

Summary

• Class Width: 10
• Classes: [300, 309], [310, 319], ..., [390, 399]
• Frequencies: As shown in the table above

Would you like any further details on this, or do you have any other questions?

Here are some questions related to this topic:

1. How can you create a histogram based on this frequency distribution?
2. How does the choice of class width affect the appearance of the GFDT?
3. What are some alternative methods for determining class width?
4. How do you handle outliers when constructing a GFDT?
5. Can you explain how cumulative frequency is calculated from the GFDT?

Tip: When constructing a GFDT, ensure that each data point falls into one and only one class interval, and that the intervals are mutually exclusive.