The annual precipitation in inches per year during the past 30 years in Tucson, Arizona, is as follows: 11.60, 7.19, 12.69, 11.86, 14.81, 8.07, 11.15, 8.00, 9.55, 11.02, 19.54, 8.63, 12.33, 8.53, 16.55, 19.74, 18.40, 11.37, 10.55, 8.68, 9.62, 6.93, 14.80, 10.64, 14.76, 15.19, 14.56, 9.68, 11.13, and 4.35.

(a) Draw the histogram for the data.

(b) Draw the frequency diagram for the data.

(c) Calculate the mean, variance, standard deviation, coefficient of variation, skewness, and skewness coefficient for the precipitation.

(d) Using the frequency diagram, calculate the probability that the annual precipitation in Tucson will exceed 12 in./yr using the actual data and using the frequency diagram

Here are the results of the calculations:

### (a) & (b) Histogram and Frequency Diagram
- The histogram and frequency diagram of annual precipitation in Tucson were generated based on the data. The histogram shows the distribution of precipitation values across 6 bins, while the frequency diagram presents the same information in a different visual format.

### (c) Descriptive Statistics:
1. **Mean Precipitation**: \( \mu = 11.73 \) inches/year
2. **Variance**: \( \sigma^2 = 13.81 \) (inches/year)²
3. **Standard Deviation**: \( \sigma = 3.72 \) inches/year
4. **Coefficient of Variation**: \( CV = 0.317 \) (dimensionless)
5. **Skewness**: \( \text{Skewness} = 0.467 \) (indicating a moderate right skew)
6. **Skewness Coefficient**: \( \text{Skewness Coefficient} = 0.0156 \) (skewness per data point)

### (d) Probability Calculation
To calculate the probability that the annual precipitation in Tucson will exceed 12 inches/year, I will analyze the frequency diagram and the actual data next.### (d) Probability Calculation:
- **Using Actual Data**: The probability that the annual precipitation in Tucson will exceed 12 inches per year is approximately **36.67%**.
- **Using the Frequency Diagram**: The probability is also approximately **36.67%**.

Both methods yield the same probability, reflecting consistency in the data representation.

Would you like more details on any of these calculations or explanations?

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Here are some related questions to deepen your understanding:
1. How would the probability change if we used a different bin size in the histogram?
2. What does the coefficient of variation tell us about the variability of precipitation in Tucson?
3. How would you interpret a skewness coefficient close to zero?
4. How might the results differ if we used a sample from a different climate period?
5. How can skewness influence decision-making based on this data?

**Tip:** When analyzing real-world data, visualizations like histograms can reveal important insights about the distribution and variability of the data, making it easier to understand and communicate results.

Explore the analysis of annual precipitation data in Tucson, Arizona, over the past 30 years. Includes calculations of mean, variance, standard deviation, coefficient of variation, skewness, skewness coefficient, and probability of exceeding 12 inches/year using both actual data and frequency diagram.

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