Cracking Ap Statistics: 2021 FRQs

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Topic: 2021FRQ真题详解

Questions：

https://apcentral.collegeboard.org/media/pdf/ap21-frq-statistics.pdf

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官方解析

https://apcentral.collegeboard.org/media/pdf/ap21-sg-statistics.pdf

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重要考点：

1. the random variable of interest in statistics

In statistics, a random variable is the key element that ties outcomes of a random event to numerical values. It's basically a variable whose exact value we can't predict beforehand, but it can take on specific values depending on the outcome of the event.

Here's a breakdown of the concept:

Unknown but Measurable: Random variables represent something we can't know for sure (like the next roll of a dice), but we can assign numbers to the possible outcomes (1, 2, 3, etc. for the dice).

Types of Random Variables: There are two main categories:

Discrete: These variables can only take on specific, separate values. Examples include the number of customers in a store (1, 2, 3, ...) or the results of a coin toss (heads, tails).
Continuous: These variables can take on any value within a certain range. Examples include weight, height, or time it takes to complete a task.

Understanding Probabilities: By using random variables, we can analyze the probability of different outcomes occurring. This allows us to understand the likelihood of certain events and make predictions based on statistical models.

Overall, the random variable of interest is the specific characteristic or outcome we're focusing on in a statistical study. It's the foundation for assigning numerical values to events and analyzing their probabilities.

2.confounding variable

A confounding variable is a factor other than the independent variable that might produce an effect in an experimental study, potentially leading to a misleading association between the independent and dependent variables. Confounding variables can suggest there is causation when in fact there is not, or they can mask a real causal relationship. The presence of confounding variables can lead to erroneous conclusions about the relationship between variables of interest. To accurately interpret the results of a study, it's crucial to identify and control for confounding variables through various statistical methods or experimental design adjustments. Here are a few examples to illustrate the concept:

Effect of Exercise on Weight Loss: In a study examining the relationship between exercise and weight loss, diet can act as a confounding variable. If not controlled for, differences in diet could influence weight loss, making it seem as though exercise had a greater or lesser effect than it truly does.

Smoking and Lung Cancer: In early studies investigating the link between smoking and lung cancer, air pollution could be considered a confounding variable. If air pollution levels were not taken into account, the study might not accurately reflect the risk of lung cancer associated with smoking alone, as both smoking and high levels of air pollution are risk factors for lung cancer.

Medication and Recovery Time from Illness: Suppose a study aims to determine whether a new medication reduces recovery time from a certain illness. The overall health status of participants could serve as a confounding variable. Healthier individuals might recover more quickly regardless of the medication, suggesting that the medication is more effective than it actually is if the health status is not controlled for.

Education and Income: In exploring the relationship between education level and income, work experience could act as a confounding variable. Without accounting for work experience, it might appear that higher education directly leads to higher income, when in reality, those with more work experience (which often correlates with age) might naturally have higher incomes.

In each of these examples, failing to control for the confounding variable could lead to incorrect conclusions about the relationships between the variables being studied. Researchers often use techniques such as stratification, matching, multivariable analysis, or randomized controlled trials to minimize or adjust for the effects of confounding variables.