To construct a frequency distribution table with 6 classes for the given data set, we'll follow these steps:

1. Determine the range: Find the difference between the maximum and minimum values.
2. Determine the class width: Divide the range by the number of classes and round up.
3. Create the classes: Start with the minimum value and add the class width to determine the upper limit of each class.
4. Tally the data into classes: Count how many data points fall into each class.
5. Calculate midpoints: For each class, find the midpoint by averaging the lower and upper limits.
6. Calculate relative frequencies: Divide the frequency of each class by the total number of data points.
7. Calculate cumulative frequencies: Add the frequencies of the current class and all previous classes.

Step 1: Determine the Range

• Minimum value = 30
• Maximum value = 532

$\text{Range} = 532 - 30 = 502$

Step 2: Determine the Class Width

$\text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{502}{6} \approx 83.67 \Rightarrow \text{Round up to 84}$

Step 3: Create the Classes

Starting with the minimum value (30), we'll create 6 classes with a width of 84.

Step 4: Tally the Data

Count how many data points fall into each class.

Step 5: Calculate Midpoints

$\text{Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$

Step 6: Calculate Relative Frequencies

$\text{Relative Frequency} = \frac{\text{Class Frequency}}{\text{Total Data Points}}$

Step 7: Calculate Cumulative Frequencies

Now let's build the table:

• Total Data Points = 35

Final Results:

• Class with the Greatest Frequency: 114 - 197 (Frequency = 10)
• Class with the Least Frequency: 450 - 533 (Frequency = 2)

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How do you interpret the relative frequency of a class?
2. What is the significance of cumulative frequency in data analysis?
3. Can you describe how the midpoint of a class is used in data analysis?
4. How does increasing the number of classes affect the frequency distribution?
5. What might cause the frequency of a class to be particularly high or low?

Tip: Always ensure the total of relative frequencies equals 1 (or 100%) to check your calculations.