To solve the question regarding "greater relative variability" for the variables given:

1. Steps for determining relative variability:

The relative variability is often measured using the Coefficient of Variation (CV), which is calculated as: $CV = \frac{\text{Standard Deviation (SD)}}{\text{Mean}} \times 100$

For the temperatures (in Fahrenheit):

The data is: $50, 37, 29, 54, 30, 61, 47, 38, 34, 61, 25, 28, 39, 57, 60$

For the precipitation (in inches):

The data is: $4.8, 2.6, 1.5, 1.8, 1.9, 3.3, 5.1, 1.1, 1.8, 2.5, 3.6, 1.7, 1.9, 2.2, 3.5$

I will calculate the mean, standard deviation, and coefficient of variation (CV) for both datasets to determine which has greater relative variability.

Let as np import pandas as pd

Data for temperatures and precipitation

temperatures = np.array([50, 37, 29, 54, 30, 61, 47, 38, 34, 61, 25, 28, 39, 57, 60]) precipitation = np.array([4.8, 2.6, 1.5, 1.8, 1.9, 3.3, 5.1, 1.1, 1.8, 2.5, 3.6, 1.7, 1.9, 2.2, 3.5])

Calculating mean and standard deviation for temperatures

temp_mean = np.mean(temperatures) temp_std = np.std(temperatures)

Calculating mean and standard deviation for precipitation

prec_mean = np.mean(precipitation) prec_std = np.std(precipitation)

Calculating Coefficient of Variation (CV)

temp_cv = (temp_std / temp_mean) * 100 prec_cv = (prec_std / prec_mean) * 100

Results in a dataframe for clarity

results = pd.DataFrame({ "Variable": ["Temperature (°F)", "Precipitation (inches)"], "Mean": [temp_mean, prec_mean], "Standard Deviation": [temp_std, prec_std], "Coefficient of Variation (CV %)": [temp_cv, prec_cv] })

import ace_tools as tools; tools.display_dataframe_to_user(name="Relative VariI have calculated the mean, standard deviation, and coefficient of variation (CV) for both the temperature and precipitation data. The results are displayed for your review.

Based on the coefficient of variation (CV%), precipitation exhibits greater relative variability compared to temperature. Let me know if you have questions or would like further clarification.

Here are some related questions to consider:

1. How is relative variability applied in real-world decision-making scenarios?
2. Why might precipitation have greater relative variability compared to temperature?
3. What other measures of variability could be used besides the coefficient of variation?
4. How would these results change if we analyzed a different set of cities or data?
5. Can this analysis be extended to explore correlations between temperature and precipitation?

Tip: Always visualize data distributions alongside statistical metrics