Questions: If we are studying the age of all students in Boston, then... The mean age of all students in Boston is a population parameter. The mean age of 200 randomly selected students in Boston is a sample statistic. The age of an individual student in Boston is a variable. The age of a specific student in the sample is an observation.

Solution Steps

It seems like the text provided is a mix of definitions and examples related to statistics. Since there is no specific math question to solve, I will outline the solution approach for the given definitions and examples.

1. Identify and define the key terms: population parameter, sample statistic, variable, and observation.
2. Provide examples to illustrate each term.

In statistics, we have several important concepts that help us understand data:

• Population Parameter (\( \mu \)): This is a characteristic or measure of a whole population. For example, the mean age of all students in Boston can be represented as \( \mu \).

• Sample Statistic (\( \bar{x} \)): This is a characteristic or measure of a sample taken from the population. For instance, the mean age of 200 randomly selected students in Boston can be denoted as \( \bar{x} \).

• Variable (\( X \)): This refers to a characteristic or attribute that can take on different values. In this context, the age of an individual student in Boston is a variable.

• Observation (\( x_i \)): This is a single data point or measurement. For example, the age of a specific student in the sample can be represented as \( x_i \).

Using the definitions from Step 1, we can illustrate each term with specific examples:

• Population Parameter: The mean age of all students in Boston is denoted as \( \mu \).

• Sample Statistic: The mean age of 200 randomly selected students in Boston is denoted as \( \bar{x} \).

• Variable: The age of an individual student in Boston is represented as \( X \).

• Observation: The age of a specific student in the sample is denoted as \( x_i \).

Final Answer