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Table 1.38 contains data on hurricanes that have made direct hits on the U.S. Between 1851 and 2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm. $$\begin{array}{|l|l|l|}\hline \text { Category } & {\text { Number of Direct Hits }} & {\text { Relative Frequency }} & {\text { Cumulative Frequency }} \\\ \hline 1 & {109} & {0.3993} & {0.3993} \\ \hline 2 & {72} & {0.2637} & {0.6630} \\ \hline 3 & {71} & {0.2601} & {} \\ \hline 4 & {18} & {} & {0.9890} \\ \hline 5 & {3} & {0.0110} & {1.0000} \\ \hline & {\text { Total }=273} & {} & {} \\ \hline \end{array}$$ Table 1.38 Frequency of Hurricane Direct Hits What is the relative frequency of direct hits that were AT MOST a category 3 storm? a. 0.3480 b. 0.9231 c. 0.2601 d. 0.3370

Step by step solution

01

Understand Relative Frequency

Relative frequency is the proportion of each category relative to the total number of observations. It is calculated for each category.

02

Identify Hurricanes AT MOST Category 3

Hurricanes AT MOST Category 3 include those from Category 1, 2, and 3. We need to consider their cumulative effect.

03

Add Relative Frequencies for Categories 1 to 3

To find the relative frequency for AT MOST Category 3, we add the relative frequencies of Category 1 (0.3993), Category 2 (0.2637), and Category 3 (0.2601): \[ 0.3993 + 0.2637 + 0.2601 \]

04

Calculate Total Relative Frequency

By performing the addition: \[ 0.3993 + 0.2637 + 0.2601 = 0.9231 \]

05

Verify Answer with Choice

This calculated relative frequency of 0.9231 matches option (b) 0.9231 in the given choices.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Relative Frequency

Relative frequency is a fundamental concept in statistics education, offering insight into data proportions. It measures how often a specific event occurs relative to the total number of observations. In the context of hurricanes, we determine the relative frequency by dividing the number of hurricanes in a category by the total number of hurricanes recorded.
If, for instance, Category 1 hurricanes have had 109 hits out of 273 total hurricanes, the relative frequency is calculated as follows:
\[ \text{Relative Frequency} = \frac{109}{273} = 0.3993 \]
This example illustrates the fraction that represents the portion of hurricanes in Category 1. Knowing this fraction helps understand the likelihood of a hurricane hitting at that particular intensity when it does occur.

Cumulative Frequency

Cumulative frequency is another valuable tool in data interpretation. It helps us see data progressively, adding up frequencies as we go from one category to the next.
In the hurricane example, the cumulative frequency tells us how many hurricanes there have been that are within Category 1 up to a given category. Starting from Category 1 through to Category 3 hurricanes, the cumulative frequency amounts to 0.6630.
To find this value, you add the relative frequencies sequentially, providing an overall view up to that point. For Category 2, it would include the frequency of Category 1 and Category 2 hurricanes together:
\[ \text{Cumulative Frequency} = 0.3993 + 0.2637 = 0.6630 \]
This gives insight into the total impact of hurricanes "at most" of a particular category.

Data Interpretation

Data interpretation is crucial in assessing and understanding statistical information in a meaningful way. When examining hurricane data, proper interpretation helps identify patterns and predict future events.
By calculating both relative and cumulative frequencies, one can draw informed conclusions about the likelihood and trending nature of hurricane strengths. The interpretation process involves:

• Recognizing patterns in the data, like how frequent certain categories of hurricanes are.
• Understanding the relative intensity and impact, depicted by cumulative frequencies.
• Using these insights to prioritize preparedness measures in areas frequently hit.

This depth of understanding empowers decision-making processes, critical especially in natural disaster planning and response.

Hurricane Frequency Analysis

Analyzing the frequency of hurricanes provides insights into patterns that may affect strategic decisions regarding preparation and response. By understanding these frequencies, meteorologists and related agencies can predict and mitigate risks better.
From the analysis recorded, hurricanes in Categories 1 to 3 appear most often, shown by their combined relative frequency of 0.9231. Such patterns underscore areas that may need more robust resistance plans or infrastructure reinforcements.
In hurricane frequency analysis, several points are paramount:

• Identifying temporal changes in hurricane patterns.
• Assessing the trends for increasing or decreasing frequencies in certain categories.
• Considering the effects of climate change on altering these patterns.

The more accurately frequencies are analyzed, the better the resource allocation and strategic responses coordinated become, proving the significance of clear and detailed hurricane frequency analysis.