To arrange the given data into a frequency distribution table with exclusive class intervals, we will follow these steps:

Step 1: Find the Range

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

• Minimum value = 14
• Maximum value = 36

Range = Maximum value - Minimum value = $36 - 14 = 22$

Step 2: Decide the Number of Classes

A general rule for the number of classes ($k$) is to use Sturges' formula:

$k = 1 + 3.322 \log n$ where $n$ is the number of observations.

Given that there are 50 observations,

$k = 1 + 3.322 \log(50) \approx 1 + 3.322 \times 1.6990 \approx 6.64 \approx 7 \text{ classes}$

We will create 7 classes.

Step 3: Determine Class Width

The class width ($W$) can be calculated as:

$W = \frac{\text{Range}}{\text{Number of Classes}} = \frac{22}{7} \approx 3.14$

We round up the class width to 4.

Step 4: Set Up the Class Intervals

Starting from the minimum value (14), we create the class intervals with a width of 4.

The exclusive intervals would be:

• 14 - 17
• 18 - 21
• 22 - 25
• 26 - 29
• 30 - 33
• 34 - 37

Step 5: Tally the Frequency

Class Interval	Frequency
14 - 17	6
18 - 21	13
22 - 25	15
26 - 29	7
30 - 33	4
34 - 37	5

Frequency Distribution Table:

Class Interval	Frequency
14 - 17	6
18 - 21	13
22 - 25	15
26 - 29	7
30 - 33	4
34 - 37	5

This table shows the frequency distribution of the data using exclusive class intervals.

Do you want more details or have any questions?

Here are 5 relative questions to explore further:

1. How do you determine the best number of classes for a distribution?
2. What are inclusive and exclusive class intervals, and how are they different?
3. How would the distribution change with different class widths?
4. How can you create a histogram from this frequency distribution?
5. What are the advantages of frequency distributions in data analysis?

Tip: When rounding class widths, always round up to ensure that all data points are included in the intervals.