To construct a grouped frequency distribution table (GFDT) and determine the class width, we first calculate the range and then choose a suitable class width for 10 classes.

1. Range Calculation

The range is the difference between the maximum and minimum values in the data set:

$\text{Range} = \text{Maximum value} - \text{Minimum value}$

From the data:

• Maximum value = $3.2$
• Minimum value = $0.78$

$\text{Range} = 3.2 - 0.78 = 2.42$

So, the range is 2.42.

2. Optimal Class Width

To determine the class width, we divide the range by the desired number of classes ($10$):

$\text{Class width (raw)} = \frac{\text{Range}}{\text{Number of classes}} = \frac{2.42}{10} = 0.242$

Since class widths should be "nice" numbers (e.g., rounded to convenient values like $0.1$, $0.2$, $0.25$, $0.5$, etc.), we round up $0.242$ to the next "nice" number.

The nicest class width in this case is:

$\text{Optimal class width} = 0.25$

Final Answers:

1. Range = 2.42
2. Optimal Class Width = 0.25

Would you like me to proceed with constructing the complete grouped frequency distribution table?

Related Questions:

1. How are class limits and boundaries determined in a frequency table?
2. How do you calculate the midpoint of each class in a GFDT?
3. How do you decide between different possible "nice" class widths (e.g., 0.2 vs. 0.25)?
4. What is the importance of rounding up for class widths?
5. How does changing the number of classes affect the GFDT?

Tip:

Always round up the raw class width to ensure all data points fit into the intervals properly!