Let's begin by organizing and analyzing the given data to calculate the range, variance, and standard deviation.

Given Data:

12, 6, 8, 5, 20, 2, 10, 11, 7, 11, 20, 18, 3, 17

Step 1: Calculate the Range

The range is calculated as the difference between the maximum and minimum values in the dataset.

• Maximum value = 20
• Minimum value = 2

$\text{Range} = \text{Max} - \text{Min} = 20 - 2 = 18 \text{ hurricanes}$

Step 2: Calculate the Variance

Variance is a measure of how much the data points deviate from the mean.

First, we need the mean of the data. $\text{Mean} = \frac{12 + 6 + 8 + 5 + 20 + 2 + 10 + 11 + 7 + 11 + 20 + 18 + 3 + 17}{14} = \frac{150}{14} \approx 10.7 \text{ hurricanes}$

Now, for each data point, we compute the squared difference from the mean, then calculate the average of those squared differences.

$\text{Variance} (\sigma^2) = \frac{(12-10.7)^2 + (6-10.7)^2 + (8-10.7)^2 + \dots + (17-10.7)^2}{n - 1}$ Where $n = 14$ (the number of data points).

Let me compute the variance.### Results:

1. Range: The range of the sample data is 18 hurricanes.
2. Variance: The variance of the sample data is approximately 36.8 hurricanes².
3. Standard Deviation: The standard deviation of the sample data is approximately 6.1 hurricanes.

Important Feature Not Revealed:

These measures of variation (range, variance, standard deviation) do not reveal the shape of the data distribution, such as whether the data is skewed or if there are clusters or gaps.

Do you want further details or clarifications on any part?

Here are five follow-up questions you might find interesting:

1. How does skewness affect the interpretation of standard deviation?
2. Can you calculate the interquartile range (IQR) for this data?
3. What would be the effect of adding an extreme outlier to the data?
4. How do range and standard deviation complement each other in understanding data spread?
5. What are the differences between population and sample variance?

Tip: Always check for outliers in your data, as they can significantly impact the variance and standard deviation.