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AP Statistics Practice Quiz: Introducing Statistics: Do Those Points Align?

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

Test your understanding with short quizzes. This quiz has 7 questions to check your progress.

Question 1 of 7

When examining a scatter plot that displays the relationship between two quantitative variables, the observed variation of the data points around a potential trend line primarily prompts which of the following statistical questions?

All Questions (7)

When examining a scatter plot that displays the relationship between two quantitative variables, the observed variation of the data points around a potential trend line primarily prompts which of the following statistical questions?

A) What are the exact numerical values for the mean and median of each variable?

B) Is the observed pattern of association between the variables statistically significant, or could it have occurred by random chance?

C) How many individual data points were included in the dataset?

D) Were the data collected using a simple random sample or a stratified sample?

Correct Answer: B

The variation in a scatter plot forces us to question the nature of the relationship. We want to know if the pattern we see (the alignment of points) is strong enough to be considered a real association or if the variation is so large that the pattern could simply be a result of random noise.

A statistician notes that in a scatter plot, the points deviate from a fitted regression line in a systematic, U-shaped pattern. This deviation is best described as what type of variation?

A) Random variation

B) Non-random variation

C) Standard variation

D) Expected variation

Correct Answer: B

When the points' positions relative to a theoretical line follow a discernible pattern (like a curve), the variation is considered non-random. This suggests that the chosen linear model may not be the best fit for the data, as there is a systematic component to the error.

If the variation in the positions of points relative to a theoretical line is judged to be random, what is the most appropriate conclusion about the line?

A) The line is a poor model because it does not pass through every point.

B) The line may be a suitable model because it has captured the systematic relationship, leaving only random error.

C) No conclusion can be made without calculating the exact correlation coefficient.

D) The relationship between the variables must be non-linear.

Correct Answer: B

Random variation around a theoretical line is expected in statistical modeling. Its presence suggests that the line has accounted for the predictable, non-random part of the relationship, and the remaining variation is simply 'noise'. This indicates the line could be an appropriate model.

A researcher plots engine size against fuel efficiency. For small engines, the data points are all above the theoretical line; for medium engines, they are below the line; and for large engines, they are again above the line. This pattern of variation suggests which of the following questions is most relevant?

A) Should more data points be collected to confirm the linear trend?

B) Is there a lurking variable, such as vehicle weight, that should be considered?

C) Is a linear model appropriate, or would a curved model better represent the relationship?

D) Was there a calculation error when plotting the data points?

Correct Answer: C

The described pattern is a classic example of non-random variation. The systematic way the points deviate from the line (above, then below, then above) strongly suggests the underlying relationship is curved, not linear. This prompts the question of whether a different, non-linear model should be used.

Which of the following provides the clearest distinction between random and non-random variation in a scatter plot?

A) Random variation has fewer points far from the line, while non-random variation has more points far from the line.

B) Random variation is unpredictable, while non-random variation shows a systematic pattern in how points deviate from a theoretical line.

C) Random variation only occurs when the correlation is weak, while non-random variation occurs when the correlation is strong.

D) Random variation means the slope of the line is near zero, while non-random variation means the slope is large.

Correct Answer: B

The core difference lies in predictability. Random variation is the 'noise' or scatter that lacks a discernible pattern. Non-random variation implies there is a systematic, predictable pattern in the errors (residuals), suggesting the model can be improved.

The presence of non-random variation in the positions of points relative to a theoretical line is a critical finding because it suggests that:

A) The variables are not associated in any way.

B) The sample size is too small to draw a meaningful conclusion.

C) The theoretical line has failed to account for a systematic aspect of the relationship between the variables.

D) The data contains outliers that should be removed immediately.

Correct Answer: C

Non-random variation (e.g., a curve in the residuals) indicates that our model is missing something. The theoretical line represents our attempt to explain the variation in Y using X. If the errors show a pattern, it means there's a part of the relationship that our current model hasn't captured.

A scatter plot of student test scores versus hours spent studying shows points scattered above and below a line of best fit. The vertical spread of the points around the line is roughly consistent across all hours of study. This observation of consistent, patternless spread primarily addresses the question of whether the variation is:

A) Positive or negative

B) Strong or weak

C) Linear or non-linear

D) Random or non-random

Correct Answer: D

The description of a 'consistent, patternless spread' is the definition of random variation (specifically, homoscedasticity). This observation helps a statistician conclude that the errors are random, supporting the appropriateness of the linear model, as there is no evidence of a non-random pattern.