### All Common Core: 8th Grade Math Resources

## Example Questions

### Example Question #1 : Statistics & Probability

Which of the following would most likely represent an outlier on a scatterplot which relates height (in inches) to shoe size for men?

**Possible Answers:**

**Correct answer:**

An outlier is defined as a point that does not fit within the general pattern of the data. Thus, we are looking for a height that is not within the normal range for an adult male, and shoe size which is outside of the range for an adult male. Typically, an adult male would be between 65 and 77 inches tall (5 feet 5 inches and 6 feet 5 inches). Typically, an adult male's shoe size would be around a 10. Thus, the outlier would have height and shoe size drastically different from these, .

### Example Question #1 : Scatter Plots

Which of the following represents a positive association in a scatterplot?

**Possible Answers:**

As increases, decreases.

As decreases, increases.

As increases, stays constant.

As increases, also increases.

There is no pattern amongst the data.

**Correct answer:**

As increases, also increases.

A positive association is defined as a scatterplot on which the best fit line has a positive slope.

This pattern is identified because on the graph, looking from left to right, the vast majority of the points goes up.

This can also be described by saying, "as increases, increases".

### Example Question #1 : Scatter Plots

A scatterplot correlates adult males' height vs. shoe size. What does the point on the scatterplot represent?

**Possible Answers:**

The median adult male height and shoe size.

All adult males that were surveyed were the same height and weight.

That 72 inches and 13 shoe size are outliers compared to the rest of the adult male population.

The mean adult male height and shoe size.

One adult male who is 72 inches tall and with a shoe size of 13.

**Correct answer:**

One adult male who is 72 inches tall and with a shoe size of 13.

When creating a scatterplot, data is collected. This data is formulated into ordered pairs. Each of these ordered pairs, which are later graphed, represent one person's data. Thus, this particular piece of data would represent one man's height of inches and that same man's shoe size of .

### Example Question #1 : Construct And Interpret Scatter Plots: Ccss.Math.Content.8.Sp.A.1

What type of correlation does this data have?

**Possible Answers:**

No correlation

Linear correlation

Negative correlation

Positive correlation

**Correct answer:**

Positive correlation

It has a positive correlation because the points all trend upward. In other words, as the independent variable on the x-axis increases, the dependent variable on the y-axis also increases. Therefore, the line of best fit that is drawn through the data represents a positive line as it has a positive slope. This verifies that our data has a positive correlation.

### Example Question #1 : Construct And Interpret Scatter Plots: Ccss.Math.Content.8.Sp.A.1

This scatter plot represents data about snack quality (-axis) vs. price (-axis). Which statements are a correct interpretation of the data?

I. The price of a higher quality snack tends to be higher.

II. Points below the line represent snacks whose price is higher than their quality.

III. Points above the line represent snacks whose quality is higher than their price.

**Possible Answers:**

I only

I and III

II only

I and II

**Correct answer:**

I only

I. is a true statement about the scatter plot: as quality increases, price tends to increase.

II. is not true - the points under the line have a relatively low price compared to their quality.

III. is also not true - the points above the line have relatively low quality compared to their price.

### Example Question #1 : Construct And Interpret Scatter Plots: Ccss.Math.Content.8.Sp.A.1

The scatter plot provided displays a group of students' test scores versus the length of time the students spent studying for a test. Based on plot, are there any outliers in the data?

**Possible Answers:**

No

Yes, point

Yes, point

Yes, point

**Correct answer:**

No

To answer this question correctly, we need to recall what "outlier" means. An outlier is a value that is much smaller or larger than the rest of the values in a set of data. Also, a data point that does follow the same pattern as the rest of the set could be described as an outlier. In this case, if we had a student that studied hours, but received a test score of that data point would be considered an outlier because it doesn't follow the same pattern as the rest of the set. However, there are no data points in this set that don't follow the pattern; thus, there are no outliers in this set.

### Example Question #1 : Statistics & Probability

The scatter plot provided displays a group of students' test scores versus the length of time the students spent studying for a test. Based on plot, which of the following patterns does the relationship between number of hours spent studying and the corresponding test score represent?

**Possible Answers:**

A negative association, a lower number of hour spent studying correlated to a higher test score

A positive association, a higher number of hours spent studying correlated to a higher test score

A positive association, a higher number of hours spent studying correlated to a lower test score

The results shown do not show any sort of pattern

**Correct answer:**

A positive association, a higher number of hours spent studying correlated to a higher test score

In the provided scatter plot, we can pick out data points and organize them from least to greatest, based on hours spent studying:

Based on the results, we can see that as the number of hours spent studying increased, the test grade also increased; thus, a positive association, a higher number of hours spent studying correlated to a higher test score.

### Example Question #1 : Construct And Interpret Scatter Plots: Ccss.Math.Content.8.Sp.A.1

The scatter plot provided displays a group of students' test scores versus the number of missing assignments the students have. Based on plot, are there any outliers in the data?

**Possible Answers:**

Yes, point

Yes, point

Yes, point

No

**Correct answer:**

No

To answer this question correctly, we need to recall what "outlier" means. An outlier is a value that is much smaller or larger than the rest of the values in a set of data. Also, a data point that does follow the same pattern as the rest of the set could be described as an outlier. In this case, if we had a student that had missing assignments, but received a test score of that data point would be considered an outlier because it doesn't follow the same pattern as the rest of the set. However, there are no data points in this set that don't follow the pattern; thus, there are no outliers in this set.

### Example Question #1 : Statistics & Probability

The scatter plot provided displays a group of students' test scores versus the length of time the students spent studying for a test. Based on plot, select the answer choice with the data point that if added to the graph, would be an outlier.

**Possible Answers:**

**Correct answer:**

To answer this question correctly, we need to recall what "outlier" means. An outlier is a value that is much smaller or larger than the rest of the values in a set of data. Also, a data point that does not follow the same pattern as the rest of the set could be described as an outlier.

Let's look at our answer choices:

This point is showing that a student who studied for hours received a on the test. If we look at our graph, we can see that the two students that spent hours studying received scores of and . A score of fits in with that data; thus, is not an outlier.

This point is showing that a student who studied for hour received a on the test. If we look at our graph, we can see that the two students that spent hour studying received scores of and . A score of fits in with that data; thus, is not an outlier.

This point is showing that a student who studied for hours received a on the test. If we look at our graph, we can see that the two students that spent hours studying received scores of and . A score of fits in with that data; thus, is not an outlier.

This point is showing that a student who studied for hours received a on the test. If we look at our graph, we can see that the student who spent hours studying received a score of . Also, if we look at the student who studied for hours, that student received an . Based on this results, would be an outlier.

### Example Question #3 : Construct And Interpret Scatter Plots: Ccss.Math.Content.8.Sp.A.1

The scatter plot provided displays a group of students' test scores versus the number of missing assignments the students have. Based on plot, select the answer choice with the data point that if added to the graph, would be an outlier.

**Possible Answers:**

**Correct answer:**

To answer this question correctly, we need to recall what "outlier" means. An outlier is a value that is much smaller or larger than the rest of the values in a set of data. Also, a data point that does not follow the same pattern as the rest of the set could be described as an outlier.

Let's look at our answer choices:

This point is showing that a student had missing assignments received a on the test. If we look at our graph, we can see that the student that had missing assignments received a score of . A score of fits in with that data; thus, is not an outlier.

This point is showing that a student who had missing assignments received an on the test. If we look at our graph, we can see that the student that had missing assignments received score of . A score of fits in with that data; thus, is not an outlier.

This point is showing that a student who had missing assignments received a on the test. If we look at our graph, we can see that the two students that had missing assignments received scores of and . A score of fits in with that data; thus, is not an outlier.

This point is showing that a student who had assignments missing received a on the test. If we look at our graph, we can see that the student who had missing assignments received a score of . Also, if we look at the student who had missing assignments, that student received a . Based on this results, would be an outlier.