Question

$$ \begin{aligned} &\text { Use the table below to answer questions 12-14. }\\\ &\begin{array}{|c|c|} \hline \text { Eruption } & \begin{array}{c} \text { Volume Percent } \\ \text { Water Vapor } \end{array} \\ \hline 1 & 58.7 \\ \hline 2 & 60.1 \\ \hline 3 & 61.4 \\ \hline 4 & 59.3 \\ \hline 5 & 59.6 \\ \hline \end{array} \end{aligned} $$ Calculate the mean, median, and range of the water vapor data in the table? Describe how this information would be helpful to a volcanologist.

Short answer

Mean: 59.82, Median: 59.6, Range: 2.7. This data helps volcanologists understand typical and variable eruption conditions.

Step-by-step solution

Calculate the Mean

To find the mean (average) of the given percentages, sum all the water vapor percentages and divide by the number of eruptions. The data points are: 58.7, 60.1, 61.4, 59.3, and 59.6.Sum = 58.7 + 60.1 + 61.4 + 59.3 + 59.6 = 299.1Number of data points = 5Mean = \( \frac{299.1}{5} = 59.82 \)

Calculate the Median

To find the median, arrange the data in ascending order and identify the middle value. The data ordered: 58.7, 59.3, 59.6, 60.1, 61.4. The middle value (third data point) is 59.6. Median = 59.6.

Calculate the Range

The range is the difference between the highest and lowest values in the data set. Highest value = 61.4 Lowest value = 58.7 Range = 61.4 - 58.7 = 2.7

Explanation for Volcanologists

The mean offers an average water vapor percentage, giving volcanologists insight into typical eruption conditions. The median helps identify typical conditions unaffected by outliers. The range indicates the variability of water vapor content between eruptions, which might suggest differences in eruption intensity or type.

Key concepts

Water Vapor in Eruptions

Water vapor plays a crucial role in volcanic eruptions as it is one of the primary gases released during these events. This vapor is usually stored in magma under high pressure and can cause eruptions when it transitions from liquid to gas. Understanding the volume percent of water vapor is essential for predicting the behavior of volcanoes, as it directly impacts magma's explosivity.

When water vapor escapes, it expands rapidly, increasing the internal pressure of a volcano. This means a higher percentage of water vapor could lead to more explosive eruptions, capable of dispersing volcanic material over larger areas. Consequently, monitoring and analyzing water vapor in magmatic systems helps volcanologists predict eruption size and potential volcanic hazards.

By understanding the average and variability in water vapor content, experts can better assess the potential risks associated with specific volcanic activities.

Statistical Analysis in Earth Science

Statistical analysis plays a significant role in Earth science, including volcanology. In the context of volcanic eruptions, statistical tools help understand various eruption characteristics, such as gas emissions.

For example, calculating the mean, median, and range of water vapor percentages offers insights into typical eruption conditions and their variability.

• The mean provides an average, helpful in identifying general tendencies.
• The median identifies a central point, providing an indication of typical values unaffected by extreme outliers.
• The range highlights variability and can indicate shifts in eruption dynamics.

Statistical analyses equip scientists with reliable data to create models for predicting future eruptions and understanding geological phenomena.

Volcanic Eruption Study

Studying volcanic eruptions involves understanding and monitoring the various parameters that influence eruptive behavior. This includes analyzing gases like water vapor, sulfur dioxide, and carbon dioxide.

Volcanologists utilize different techniques to study these gases. These include direct sampling, satellite imagery, and remote sensing technologies, providing data necessary to understand eruption dynamics. By investigating the frequencies, compositions, and emission rates of volcanic gases, scientists can predict potential eruption scenarios.

Moreover, historical data and recent observations are combined to develop models that explain eruption patterns. These studies are essential for hazard assessment and developing mitigation strategies to protect communities living near volcanoes. By integrating a deep understanding of gases like water vapor with statistical analyses, volcanologists improve their ability to predict and respond to volcanic events effectively.