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AP Statistics Practice Quiz: Correlation

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

What two characteristics of a linear association does the correlation coefficient, r, describe?

All Questions (16)

What two characteristics of a linear association does the correlation coefficient, r, describe?

A) Slope and y-intercept

B) Direction and strength

C) Cause and effect

D) Mean and standard deviation

Correct Answer: B

The correlation, r, gives the direction (positive or negative) and quantifies the strength (how close the points are to a line) of a linear association.

A researcher calculates a correlation coefficient of r = 1.25 between two variables. What can be concluded from this value?

A) There is a very strong, positive linear association.

B) There is a calculation error.

C) The association is non-linear.

D) One variable causes the other.

Correct Answer: B

The correlation coefficient, r, must always be between -1 and 1, inclusive. A value of 1.25 is outside this valid range, indicating a mistake was made in the calculation.

If the correlation coefficient between two variables is r = 0, what does this indicate?

A) There is no relationship of any kind between the variables.

B) There is a strong, negative association between the variables.

C) There is no linear association between the variables.

D) The relationship between the variables is perfectly linear.

Correct Answer: C

A correlation of r = 0 specifically means there is no linear association. It is possible that a non-linear relationship (e.g., a parabolic relationship) exists between the variables.

A study finds a strong, positive correlation (r = 0.85) between the number of ice cream cones sold and the number of drownings at a beach. Which of the following is the most appropriate conclusion?

A) Eating ice cream causes people to be more susceptible to drowning.

B) An increase in drownings causes people to buy more ice cream.

C) There is a linear association between ice cream sales and drownings, but a third variable, such as temperature, is likely influencing both.

D) The correlation value is not strong enough to suggest any relationship.

Correct Answer: C

This is a classic example of the principle that correlation does not necessarily imply causation. A lurking variable, in this case, the hot weather (temperature), leads to both more ice cream sales and more people swimming (and thus more drownings).

A researcher measures the height of students in inches and their weight in pounds and finds a correlation of r = 0.7. If the researcher converts the height to centimeters and the weight to kilograms, what will the new correlation coefficient be?

A) It will be less than 0.7.

B) It will be greater than 0.7.

C) It will remain 0.7.

D) It will become negative.

Correct Answer: C

The correlation coefficient, r, is a unit-free measure. Changing the units of the variables (e.g., from inches to centimeters or pounds to kilograms) does not change the value of the correlation.

A scatterplot of data results in a correlation coefficient of r = 0.98. Which of the following statements is true?

A) The relationship between the variables must be linear.

B) A linear model is guaranteed to be the best fit for the data.

C) There is a strong, positive linear association, but a visual inspection of the data is needed to confirm if a linear model is appropriate.

D) The relationship is weak.

Correct Answer: C

While a correlation of 0.98 indicates a very strong, positive linear association, it does not guarantee that a linear model is the most appropriate. The data could have a slight curve that is not captured by the correlation coefficient alone. A correlation coefficient close to 1 or -1 does not necessarily mean a linear model is appropriate.

A study on the relationship between hours spent studying and exam scores is expected to show what kind of correlation?

A) A correlation close to -1.

B) A correlation close to 0.

C) A positive correlation.

D) A correlation with units of 'score-hours'.

Correct Answer: C

It is generally expected that as the number of hours spent studying increases, exam scores will also increase. This describes a positive association, which would be represented by a positive correlation coefficient (r > 0).

Which of the following correlation coefficients represents the strongest linear association?

A) r = 0.75

B) r = -0.85

C) r = 0.10

D) r = -0.50

Correct Answer: B

The strength of a linear association is determined by the absolute value of the correlation coefficient. The value closest to 1 or -1 indicates the strongest relationship. |-0.85| = 0.85, which is greater than the absolute values of the other options.

In a typical AP Statistics course or real-world data analysis, how is the correlation coefficient, r, for a dataset most often calculated?

A) By estimating from a hand-drawn line of best fit.

B) By using a complex formula calculated by hand.

C) By using statistical software or a graphing calculator.

D) By averaging the x and y values.

Correct Answer: C

The correlation coefficient is most commonly determined using technology. While a formula for r exists, it is complex and tedious to calculate by hand for any reasonably sized dataset.

A scatterplot reveals a distinct U-shaped (parabolic) pattern. Which of the following is a possible value for the correlation coefficient, r?

A) r = 0.95

B) r = -0.95

C) r is approximately 0.

D) r is undefined for non-linear data.

Correct Answer: C

The correlation coefficient, r, measures the strength and direction of a linear association. For a symmetric U-shaped pattern, the negative linear trend on one side would be cancelled out by the positive linear trend on the other side, resulting in a correlation coefficient close to 0, which indicates no linear association, even though a strong non-linear relationship exists.

A researcher finds that the correlation between a car's age and its resale value is r = -0.92. What is the best interpretation of this value?

A) There is a strong, positive linear relationship between a car's age and its value.

B) There is a strong, negative linear relationship; as a car gets older, its value tends to decrease.

C) There is a weak, negative linear relationship between a car's age and its value.

D) A car's age causes its value to decrease.

Correct Answer: B

The negative sign indicates a negative association (as one variable increases, the other decreases). The value of -0.92 is close to -1, which indicates a strong linear relationship. The statement about causation in option D is not justified by correlation alone.

Which of the following statements about the correlation coefficient, r, is FALSE?

A) A correlation of r = 0.9 indicates a stronger linear association than r = -0.8.

B) If r = 0.99, the data must follow a perfectly straight line.

C) The value of r is not affected by changing the units of measurement of the variables.

D) A correlation of r = 0.5 means that as the explanatory variable increases, the response variable tends to increase.

Correct Answer: B

A correlation coefficient close to 1 or -1 does not necessarily mean a linear model is appropriate or that the data is perfectly linear. There could still be a slight curve in the data. Only a value of exactly 1 or -1 would indicate a perfect linear relationship.

A city's data shows a strong negative correlation between the number of public parks and the crime rate. A council member argues that building more parks will directly cause the crime rate to decrease. Why is this conclusion potentially flawed?

A) The correlation is negative, so it implies that more parks cause more crime.

B) A strong correlation is not sufficient evidence to establish a causal link; other factors, like neighborhood wealth, could be influencing both variables.

C) The relationship is likely non-linear, so correlation is not a valid measure.

D) The correlation should have been calculated using technology to be valid.

Correct Answer: B

The principle that 'correlation does not necessarily imply causation' applies here. While there is an association, it is not proof that one variable causes the other. A lurking variable, such as the socioeconomic status of the neighborhoods, could be the true underlying cause for the observed relationship.

A scatterplot shows that as the value of the explanatory variable increases, the value of the response variable consistently decreases. Which of the following is a possible value for the correlation coefficient?

A) 0.88

B) 0.02

C) -0.79

D) 1.15

Correct Answer: C

The description indicates a negative association, where one variable increases as the other decreases. Therefore, the correlation coefficient, r, must be negative. Of the options provided, only -0.79 is a possible value for a negative correlation.

A researcher is studying the relationship between a person's IQ and their phone number. What would be the expected correlation coefficient, r, and why?

A) Close to 1, because both are numerical values.

B) Close to -1, because there is no logical connection.

C) Close to 0, because there is no expected linear association between the two variables.

D) Undefined, because phone numbers are not quantitative.

Correct Answer: C

There is no logical or theoretical reason to believe that a person's IQ and their phone number would have a linear relationship. When there is no discernible linear pattern or association between two variables, the correlation coefficient is expected to be close to 0.

An analyst reports a correlation of r = -0.95 between the amount of time a user spends on a social media app and their self-reported happiness score. The analyst concludes that reducing time on the app will cause an increase in happiness. Which of the following is the most significant flaw in the analyst's reasoning based on the principles of correlation?

A) The correlation is negative, which is impossible for time-based data.

B) The strength of the correlation (r = -0.95) is too weak to draw any conclusions.

C) The analyst has assumed a causal relationship from a correlation and has not considered that the data may have a non-linear pattern despite the strong r-value.

D) The correlation was likely calculated incorrectly, as this type of relationship should be positive.

Correct Answer: C

This reasoning has two key flaws covered by the provided content. First, correlation does not imply causation. It's possible that less happy people tend to spend more time on social media. Second, even with a strong r-value, a linear model may not be appropriate. Option C correctly combines these critical limitations.