Here is a data set:
3.54	4.99	4.51	4.68
3.47	2.21	4.26	6.29
3.52	3.16	3.48	4.68
3.94	4.69	3.51	4.22
6.29	4.25	4.79	4.99
2.08	1.66	3.6	2.63
5.18	3.72	3.82	4.5


The goal is to construct a grouped frequency distribution table (GFDT) for this data set. The GFDT should have 10 classes with a "nice" class width. Each class should contain its lower class limit, and the lower class limits should all be multiples of the class width.

This problem is to determine what the class width should be.

What is the range of this data set?
range = 
4.63


Using this value, if the goal is to have 10 classes, what is the nicest class width?
optimal class width = 


To construct a grouped frequency distribution table (GFDT) with 10 classes, we first need to determine the class width. The "nicest" class width typically means one that is easy to work with (e.g., a simple number like 0.1, 0.5, 1, etc.).

### Step 1: Calculate the Range of the Data Set
You have provided the range as 4.63, but I'll calculate it again for clarity:

- **Minimum Value:** \( \min = 1.66 \)
- **Maximum Value:** \( \max = 6.29 \)

\[ \text{Range} = \max - \min = 6.29 - 1.66 = 4.63 \]

### Step 2: Determine the Class Width
We want 10 classes, so the class width can be calculated as:

\[
\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{4.63}{10} = 0.463
\]

### Step 3: Choose the "Nicest" Class Width
0.463 is not a very "nice" number. A nicer class width would be a simple, rounded number close to 0.463. Commonly used class widths are numbers like 0.5, 1, etc.

Given that we need a width close to 0.463, the nicest class width to use would be **0.5**. This width is simple and will divide the range well while keeping the number of classes close to 10.

### Summary
- **Range:** 4.63
- **Optimal Class Width:** 0.5

This class width of 0.5 will allow us to create a GFDT with approximately 10 classes where the lower class limits are multiples of 0.5.

Would you like to see the complete grouped frequency distribution table with this class width, or do you have any other questions?

Here are some questions related to this topic:

1. How would you determine the class limits for each class interval?
2. How does changing the number of classes affect the class width?
3. Can you explain how to find the midpoint of a class in a GFDT?
4. What are the advantages of choosing a "nice" class width?
5. How would you construct a histogram from the GFDT?

**Tip:** When creating a frequency distribution table, ensure that all class intervals are of equal width to maintain consistency in data interpretation.

Learn how to construct a grouped frequency distribution table (GFDT) with an optimal class width for a given dataset. Calculate the range and determine the nicest class width for 10 classes. Suitable for advanced high school students studying statistics and data analysis.

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