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Guns in School. Researchers surveyed 14,765 American high school students (grades 9-12) and found that \(27.3 \%\) of those surveyed were in grade 9 . The percentage of all American high school students who are are in grade 9 is \(\mathbf{2 6 . 5} \%\). The percentage of those surveyed who were in grade 9 and had carried a gun to school was \(\mathbf{4 . 4 \%}\). Is each of the boldface numbers a parameter or a statistic?

Short Answer

Expert verified
**26.5%** is a parameter; both **27.3%** and **4.4%** are statistics.

Step by step solution

01

Understanding Parameters and Statistics

Parameters are numerical values that summarize data from an entire population, while statistics are numerical values that summarize data from a sample taken from the population.
02

Identify the Population Percentage

The percentage of all American high school students who are in grade 9 is stated as **26.5%**. Since this value comes from the entire population of American high school students, it is a **parameter**.
03

Identify the Sample Percentage

The percentage of the surveyed students (a sample) who were in grade 9 is **27.3%**. This value is derived from the sample of 14,765 students surveyed, so it is a **statistic**.
04

Identify the Percentage with Behavioral Aspect

The percentage of surveyed students who were in grade 9 and had carried a gun to school is **4.4%**. This also comes from the sample rather than the entire population, making it a **statistic**.

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Key Concepts

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

Population
In the vast field of statistics, "population" refers to the entire group that you want to draw conclusions about. In the context of the original exercise, the population consists of all American high school students, across grades 9-12. A population encompasses every individual that falls under the category being studied or surveyed.
Think of the population as the whole pie, where each slice represents a subsection of students, but together, they make up the entirety of American high school students. It's important because when a parameter is stated, it's reflecting a measurement from this complete group.
Knowing the makeup of the population helps ensure that surveys and studies represent the group you are interested in accurately. Researchers use this concept to determine who they need to study and see what data is missing.
Sample
A "sample" is a smaller, manageable version of the entire population. Instead of attempting to study an entire population, which is often impractical, researchers select a sample. In the original exercise, 14,765 students represent a sample of American high school students.
Sampling is crucial because it allows researchers to gather and analyze data efficiently, saving time and resources. It's like tasting a spoonful of soup to understand its flavor without eating the whole pot.
The key to a successful sample is that it needs to be representative of the population. This means it should reflect the various characteristics of the full group to draw accurate inferences. Samples provide insights about the population, helping in making predictions and understanding trends.
Survey Methods
Survey methods are the techniques used to gather data from a sample. They include a range of tools and techniques, from online questionnaires to face-to-face interviews. In the context of high school students, surveys might be conducted in classrooms or through online platforms to reach a broad audience.
Good survey methods ensure the data collected is unbiased and accurate. The choice of which method to use depends on the research question, population size, and resources available.
Effective survey methods for high school students often require consideration of their accessibility. For instance, online surveys can be effective due to the digital proficiency of most students. The goal is to ensure the sample reflects the population accurately to provide valid statistics.
High School Students
High school students, in the context of this exercise, form the primary focus of the study. They are at a stage in life filled with diverse experiences and varying challenges. This makes them an interesting group for educational and sociological studies.
Surveying high school students can provide insights into behavioral patterns and educational trends. As they grow into their identities, understanding their choices and experiences can inform policy and educational improvements.
It is crucial to recognize their perspectives because the life experiences of high school students today are drastically different from those of past generations. Studies like these help keep educational approaches and policies relevant and effective.
Data Analysis
Data analysis is the process of making sense out of the collected data. Once researchers gather data, they analyze it to draw conclusions and answer the research question. For instance, comparing the statistic of 27.3% of surveyed grade 9 students to the parameter of 26.5% gives insights into how representative the sample is.
Analyzing data from high school students involves looking at trends, patterns, and possibly correlations. It requires using statistical tools to ensure the results are valid and reliable.
The ultimate aim of data analysis is to convert raw data into actionable insights. By interpreting the survey results correctly, researchers can provide valuable information to policymakers, educators, and other stakeholders.

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