To find the mean, median, and mode of the rain intensity data, let's analyze the given information.

Given Data

• Inches of Rain: 1, 2, 3, 4, 5, 6
• Frequency: 1, 4, 5, 2, 2, 0

Step 1: Mean Calculation

The mean is calculated using the formula:

$\text{Mean} = \frac{\sum (x_i \cdot f_i)}{\sum f_i}$

Where:

• $x_i$ = inches of rain
• $f_i$ = frequency

Calculating the sums:

$\sum (x_i \cdot f_i) = (1 \cdot 1) + (2 \cdot 4) + (3 \cdot 5) + (4 \cdot 2) + (5 \cdot 2) + (6 \cdot 0)$ $= 1 + 8 + 15 + 8 + 10 + 0 = 42$

$\sum f_i = 1 + 4 + 5 + 2 + 2 + 0 = 14$

Now, calculate the mean:

$\text{Mean} = \frac{42}{14} = 3.0$

Step 2: Median Calculation

To find the median, we first list the data in order, considering the frequency:

• 1 inch: 1 time
• 2 inches: 4 times
• 3 inches: 5 times
• 4 inches: 2 times
• 5 inches: 2 times
• 6 inches: 0 times

The data set is:

• 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5

Since there are 14 data points (an even number), the median is the average of the 7th and 8th values:

• 7th value: 3
• 8th value: 3

$\text{Median} = \frac{3 + 3}{2} = 3.0$

Step 3: Mode Calculation

The mode is the number that appears most frequently.

• Frequencies:
  • 1 inch: 1
  • 2 inches: 4
  • 3 inches: 5
  • 4 inches: 2
  • 5 inches: 2
  • 6 inches: 0

The mode is 3 inches (most frequent, appearing 5 times).

Summary of Results

• Mean: 3.0 inches
• Median: 3.0 inches
• Mode: 3 inches

Final Answer

Mean: 3.0, Median: 3.0, Mode: 3

Would you like more details on any of the calculations? Here are some related questions to consider:

1. How do you calculate the range of this data set?
2. What is the impact of outliers on the mean and median?
3. How would you interpret these statistical results in relation to agriculture?
4. What are some other measures of central tendency?
5. How can you visualize this data to better understand rainfall distribution?

Tip: When working with frequency distributions, always ensure to accurately list out all data points for median calculations!