We are given the data on rain intensity (in inches) and their respective frequencies:

Inches of Rain	1	2	3	4	5	6
Frequency	4	0	2	3	4	3

1. Mean Rain Intensity

To calculate the mean, we need to use the formula:

$\text{Mean} = \frac{\sum (x \cdot f)}{\sum f}$

Where $x$ is the rain intensity (in inches), and $f$ is the frequency.

Let's compute the mean.

2. Median Rain Intensity

The median is the middle value of the dataset when arranged in ascending order. Since the data is given in a frequency table, we will list out the total number of data points and determine the middle value based on the cumulative frequency.

3. Mode Rain Intensity

The mode is the value(s) that occur most frequently. We will identify the value with the highest frequency.

Let's compute these values.### Results:

1. Mean rain intensity: 3.8 inches (rounded to 1 decimal place)
2. Median rain intensity: 4.0 inches
3. Mode rain intensity: 1, 5 inches (bimodal)

Would you like further details or clarifications?

Here are 5 related questions to deepen your understanding:

1. How is the mean affected by extreme values or outliers in a dataset?
2. What is the significance of the median in skewed distributions compared to the mean?
3. Can a dataset have no mode? Under what conditions does that happen?
4. How would the mean change if we increased the frequency for higher rain intensities?
5. How can the shape of the data distribution (e.g., symmetrical, skewed) affect the mean, median, and mode?

Tip: In statistics, the mean is sensitive to outliers, whereas the median provides a better measure of central tendency for skewed data.