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

## Example Questions

### Example Question #101 : Interpreting Categorical & Quantitative Data

A social scientist measures the correlation between an individual's socio-economic status and highest level of education obtained. The scientists plots these points and creates the following graph.

Which of the following best describes how the variables in the graph are related to one another?

**Possible Answers:**

Weak or moderately negative

Strong positive

No relationship

Weak or moderately positive

Strong negative

**Correct answer:**

Weak or moderately negative

In order to solve this problem, we need to understand the common associations between variables with linear relationships. Scatter plots are used to plot data points with two variables. A correlation exists when there is an observable relationship between points. There are several common relationships between correlations. They include the following: weak positive, strong positive, weak negative, strong negative, and random relationships.

Let's first look at whether a relationship is positive or negative. Positive relationships flow upward vertically from the left to the right of the horizontal axis, while negative relationships flow downward. Next, let's discuss how to tell if a relationship is strong or weak/moderate. A strong relationship exists when the plotted points are clustered close together to one another; whereas, a weak relationship is characterized by a greater amount of spread between points. Last, a random relationship occurs when there is no discernible pattern of association between points.

Before we solve this question, let's look at each of these relationships in turn.

**Weak or moderately positive **

A weak or moderately positive relationship exists when points increase from the left to the right but possess a large spread between points away from the trend line.

**Strong positive**

A strong positive relationship exists when points increase from the left to the right and are clustered tightly around the trend line.

**Weak or moderately negative **

A weak or moderately negative relationship exists when points decrease from the left to the right but possess a large spread between points away from the trend line.

**Strong negative**

A strong negative relationship exists when points decrease from the left to the right and are clustered tightly around the trend line.

**No or random relationship**

A random relationship or spread exists when the data does not increase or decrease from the left to the right; furthermore, a nearly horizontal trend line characterizes these graphs. They possess a great spread and appear random in nature of associations between points.

Now, let's focus on our question. The question states that several variables were plotted against one another and the following graph was produced:

We can see that the trend line decreases from the left to the right; therefore, there is a negative relationship between points. Also, we can see that the points are not closely clustered together. This graph depicts a weak or moderately negative relationship.

### Example Question #102 : Interpreting Categorical & Quantitative Data

A social scientist measures the correlation between an individual's socio-economic status and highest level of education obtained. The scientists plots these points and creates the following graph.

Which of the following best describes how the variables in the graph are related to one another?

**Possible Answers:**

Weak or moderately positive

Strong positive

Weak or moderately negative

No relationship

Strong negative

**Correct answer:**

Weak or moderately negative

In order to solve this problem, we need to understand the common associations between variables with linear relationships. Scatter plots are used to plot data points with two variables. A correlation exists when there is an observable relationship between points. There are several common relationships between correlations. They include the following: weak positive, strong positive, weak negative, strong negative, and random relationships.

Let's first look at whether a relationship is positive or negative. Positive relationships flow upward vertically from the left to the right of the horizontal axis, while negative relationships flow downward. Next, let's discuss how to tell if a relationship is strong or weak/moderate. A strong relationship exists when the plotted points are clustered close together to one another; whereas, a weak relationship is characterized by a greater amount of spread between points. Last, a random relationship occurs when there is no discernible pattern of association between points.

Before we solve this question, let's look at each of these relationships in turn.

**Weak or moderately positive **

A weak or moderately positive relationship exists when points increase from the left to the right but possess a large spread between points away from the trend line.

**Strong positive**

A strong positive relationship exists when points increase from the left to the right and are clustered tightly around the trend line.

**Weak or moderately negative **

A weak or moderately negative relationship exists when points decrease from the left to the right but possess a large spread between points away from the trend line.

**Strong negative**

A strong negative relationship exists when points decrease from the left to the right and are clustered tightly around the trend line.

**No or random relationship**

A random relationship or spread exists when the data does not increase or decrease from the left to the right; furthermore, a nearly horizontal trend line characterizes these graphs. They possess a great spread and appear random in nature of associations between points.

Now, let's focus on our question. The question states that several variables were plotted against one another and the following graph was produced:

We can see that the trend line decreases from the left to the right; therefore, there is a negative relationship between points. Also, we can see that the points are not closely clustered together. This graph depicts a weak or moderately negative relationship.

### Example Question #103 : Interpreting Categorical & Quantitative Data

A social scientist measures the correlation between an individual's socio-economic status and highest level of education obtained. The scientists plots these points and creates the following graph.

Which of the following best describes how the variables in the graph are related to one another?

**Possible Answers:**

Weak or moderately negative

Weak or moderately positive

Strong positive

No relationship

Strong negative

**Correct answer:**

Weak or moderately positive

In order to solve this problem, we need to understand the common associations between variables with linear relationships. Scatter plots are used to plot data points with two variables. A correlation exists when there is an observable relationship between points. There are several common relationships between correlations. They include the following: weak positive, strong positive, weak negative, strong negative, and random relationships.

Let's first look at whether a relationship is positive or negative. Positive relationships flow upward vertically from the left to the right of the horizontal axis, while negative relationships flow downward. Next, let's discuss how to tell if a relationship is strong or weak/moderate. A strong relationship exists when the plotted points are clustered close together to one another; whereas, a weak relationship is characterized by a greater amount of spread between points. Last, a random relationship occurs when there is no discernible pattern of association between points.

Before we solve this question, let's look at each of these relationships in turn.

**Weak or moderately positive **

A weak or moderately positive relationship exists when points increase from the left to the right but possess a large spread between points away from the trend line.

**Strong positive**

A strong positive relationship exists when points increase from the left to the right and are clustered tightly around the trend line.

**Weak or moderately negative **

A weak or moderately negative relationship exists when points decrease from the left to the right but possess a large spread between points away from the trend line.

**Strong negative**

A strong negative relationship exists when points decrease from the left to the right and are clustered tightly around the trend line.

**No or random relationship**

A random relationship or spread exists when the data does not increase or decrease from the left to the right; furthermore, a nearly horizontal trend line characterizes these graphs. They possess a great spread and appear random in nature of associations between points.

Now, let's focus on our question. The question states that several variables were plotted against one another and the following graph was produced:

We can see that the trend line increases from the left to the right; therefore, there is a positive relationship between points. Also, we can see that the points are not closely clustered together. This graph depicts a weak or moderately positive relationship.

### Example Question #104 : Interpreting Categorical & Quantitative Data

Which of the following best describes how the variables in the graph are related to one another?

**Possible Answers:**

Weak or moderately negative

Strong negative

No relationship

Weak or moderately positive

Strong positive

**Correct answer:**

No relationship

Before we solve this question, let's look at each of these relationships in turn.

**Weak or moderately positive **

**Strong positive**

**Weak or moderately negative **

**Strong negative**

**No or random relationship**

We can see that the trend line is horizontal from the left to the right; therefore, there is no relationship between points. Also, we can see that the points are not closely clustered together. This graph depicts no relationship.