### All Common Core: High School - Statistics and Probability Resources

## Example Questions

### Example Question #181 : Interpreting Categorical & Quantitative Data

Violent crime has a strong positive correlation with ice cream sales. What can be inferred from this?

**Possible Answers:**

The two events are causally related.

The correlation between ice cream sales and violent crime is the result of some error in the statistical study.

While the two events are correlated, more evidence is needed to determine whether or not this correlation is coincidental.

The increase in ice cream sales causes the increase in violent crime.

The increase in violent crime causes the increase in ice cream sales.

**Correct answer:**

While the two events are correlated, more evidence is needed to determine whether or not this correlation is coincidental.

### Example Question #1 : Correlation Vs. Causation: Ccss.Math.Content.Hss Id.C.9

Which choice best describes the relationship between the variables in the following scatterplot?

**Possible Answers:**

Shark attacks induce ice cream consumption

Ice cream consumption causes shark attacks

The variables possess a correlation due to a lurking or linking variable

None of these

**Correct answer:**

The variables possess a correlation due to a lurking or linking variable

In order to properly solve this question, we need to understand the differences between what is meant by correlation and causation. A correlation refers to the strength of the linear association between two quantitative variables. On the other hand, causation indicates that the change in one variable is the cause of change in another.

Correlation can be used as an indicator of causal relationships; however, experimentation is needed to properly identify which variable is actually causing the observed change. Scientific experimentation identifies causality through he implementation of laboratory procedures in a controlled setting. When variables are controlled, causation can be determined through observation and repeated tests.

Several logical fallacies explain why correlation does not directly imply causation. First, cause-and-effect is not determined by two events occurring simultaneously. In other words, events that occur together do not necessarily cause one another. Second, causality is not determined by an event preceding another temporally. In other words, this means that event B is not always a consequence of event A simply because event A occurs before event B.

Lurking or linking variables can cause events that are highly correlated to one another appear to have a casual relationship. This is because a third separate factor may be inducing change in the two variables.

Now, let's solve this problem. It asks us to describe the relationship in the scatterplot. We know that there is a positive relationship between the two variables; however, if we think critically we know that shark attacks and ice cream sales are independent of one another. The answers that suggest causality are incorrect. A linking or lurking variable—in this case warm temperatures—is causing change in both of the variables. In other words, warmer temperatures cause individuals to purchase ice cream and frequent the beach. Greater populations of beach goers increase the probability of shark attacks.

### Example Question #3 : Correlation Vs. Causation: Ccss.Math.Content.Hss Id.C.9

Which choice best describes the relationship between the variables in the following scatterplot?

**Possible Answers:**

Beach attendance is positively correlated with shark attacks

Beach attendance is negatively correlated with shark attacks

Beach attendance causes shark attacks

Shark attacks cause beach attendance

**Correct answer:**

Beach attendance is positively correlated with shark attacks

In order to properly solve this question, we need to understand the differences between what is meant by correlation and causation. A correlation refers to the strength of the linear association between two quantitative variables. On the other hand, causation indicates that the change in one variable is the cause of change in another.

Correlation can be used as an indicator of causal relationships; however, experimentation is needed to properly identify which variable is actually causing the observed change. Scientific experimentation identifies causality through he implementation of laboratory procedures in a controlled setting. When variables are controlled, causation can be determined through observation and repeated tests.

Several logical fallacies explain why correlation does not directly imply causation. First, cause-and-effect is not determined by two events occurring simultaneously. In other words, events that occur together do not necessarily cause one another. Second, causality is not determined by an event preceding another temporally. In other words, this means that event B is not always a consequence of event A simply because event A occurs before event B.

Lurking or linking variables can cause events that are highly correlated to one another appear to have a casual relationship. This is because a third separate factor may be inducing change in the two variables.

Now, let's solve this problem. It asks us to describe the relationship in the scatterplot. We know that there is a positive relationship between the two variables; however, if we think critically we know that beach attendance and shark attacks do not cause one another. The answers that suggest causality are incorrect. There are many factors that influence shark attacks on beaches—beach attendance is one of them. For example, if no one goes to the beach, then a shark located at the beach can attack no one. Increased beach attendance is positively correlated with shark attacks but further investigation is needed to determine if this causes the attacks. A mating cycle, global warming, or changes in food sources could all induce a shark attack. Beach attendance is only one factor correlated with this phenomenon.