Analyze the fundamental components of Data Science: data management, statistical modeling. Expound on each component by providing a detailed analysis, including the important concepts and key ideas related to each component and its significance in the broader context of Data Science. Additionally, support your argument with specific examples from within the component to illustrate how it is applied in practice. After describing an example, stop. I will then say "continue" and you will generate your response for the next component. Use the following format and be concise in your response for each component in turn:

Component: Begin by identifying the first component (then the next component until you cover them all) of Data Science and its important concepts. 
Analysis: Provide a detailed analysis of the component 
Key Concepts: Briefly discuss the key concepts related to the component and in support of the analysis of the component
Example: Use specific examples to illustrate how the component is applied in practice and how it helps to address key challenges in Data Science. 
Significance: Highlight the significance of the component in the broader context of Data Science.