- A researcher records each student's weekly study time (hours) and their score on a unit test (points). The scatterplot shows a clear upward trend with moderate scatter around a roughly straight-line pattern. Which statement about correlation is correct?
Answer: The correlation is positive and likely moderate to strong, since the pattern is roughly linear and increasing.
This question tests understanding of correlation as a measure of linear association strength. The scatterplot shows an upward trend with moderate scatter, indicating a positive correlation that is not perfect (r=1 would require all points to fall exactly on a line). Choice B correctly identifies this as a positive correlation that is moderate to strong. Choice A incorrectly assumes any upward pattern must have r=1, while choice D confuses correlation with causation. Correlation measures how closely points follow a linear pattern, not the steepness of the trend (choice E is wrong).
- A student collects data on 10 phones: battery capacity (mAh) and battery life (hours). The scatterplot shows a positive linear association. Which statement about correlation is correct?
Answer: The correlation would stay the same if battery capacity were converted from mAh to Ah (a positive linear rescaling).
AP Statistics teaches that correlation is invariant under linear transformations of variables, like unit conversions. Choice B correctly explains that converting mAh to Ah (dividing by 1000) won't change the correlation, as it's a positive linear rescaling. The positive linear association remains, unaffected by units. Distractor A wrongly suggests units alter correlation, but it's standardized. Time units like minutes vs. hours wouldn't flip the sign, countering C. Correlation indicates association strength, not causation or slope equality.
- A company tracks advertising spending (thousands of dollars) and weekly sales (thousands of dollars). The scatterplot shows two distinct clusters (one for small stores and one for large stores), and within each cluster the association is weak. Overall, the points appear to have a positive trend. Which statement about correlation is correct?
Answer: The overall correlation could be positive even if the within-group correlations are weak, because combining groups can create an apparent linear association.
This question explores Simpson's paradox in correlation. When data contains distinct groups (clusters), the overall correlation can differ dramatically from within-group correlations. Combining small and large stores creates an overall positive trend even if each group shows weak association internally, making choice A correct. Choice B wrongly claims correlation can't be computed with clusters, while choice E incorrectly assumes weak within-group correlations guarantee weak overall correlation. Correlation measures association, not causation (choice C), and having same units doesn't force r=1 (choice D).
- A lab group measures the concentration of a solution (mol/L) and the reaction rate (mL/min). The scatterplot shows a strong positive linear association. One student suggests converting concentration from mol/L to mmol/L (multiplying by 1000). Which statement about correlation is correct?
Answer: Changing units by multiplying one variable by a positive constant does not change the correlation (it stays the same).
This question tests understanding that correlation is invariant under linear transformations. Multiplying one variable by a positive constant (like converting mol/L to mmol/L by multiplying by 1000) doesn't change the correlation coefficient - it remains exactly the same. Choice B correctly states this property. Choice A wrongly assumes correlation scales with the variable, while choice C incorrectly claims the sign changes. The correlation doesn't become zero (choice D) or change based on slope considerations (choice E). This invariance property makes correlation a standardized measure of linear association.
- An engineer compares outside temperature (°C) and daily electricity use (kWh) for a building. The scatterplot shows a strong downward linear pattern. Which statement about correlation is correct?
Answer: The correlation is negative and likely strong because the points follow a fairly straight decreasing pattern.
This question examines negative correlation in a real-world context. When temperature increases, electricity use decreases (likely due to less heating needed), creating a downward linear pattern. Choice A correctly identifies this as a negative correlation that is likely strong due to the fairly straight pattern. Choice B incorrectly claims different units prevent correlation calculation, while choice C misunderstands that correlation sign depends on the relationship direction, not variable values. Correlation measures association strength and direction, not causation (choice D) or slope steepness (choice E).
- A student investigates whether screen time (hours per day) is related to sleep duration (hours per night). The scatterplot shows a fairly tight downward linear pattern. Which statement about correlation is correct?
Answer: The correlation is negative and likely strong because the points cluster around a decreasing line.
This question tests recognizing strong negative correlation. A fairly tight downward linear pattern indicates negative correlation with high magnitude (close to -1 but not exactly -1), making choice B correct. Choice A incorrectly links correlation sign to unit similarity, while choice C wrongly assumes any downward trend must have r=-1. Strong correlation describes association strength, not causation (choice D). Correlation and slope are different concepts - correlation is standardized and unitless while slope has units (choice E).
- A researcher records, for 12 runners, weekly training time (hours per week) and 5K race time (minutes). The scatterplot shows a clear downward linear trend with moderate strength and one possible high-leverage point at very high training time. Which statement about correlation is correct?
Answer: The correlation is negative because larger training times tend to be associated with smaller 5K times.
This question tests understanding of correlation in AP Statistics, which measures the strength and direction of the linear association between two quantitative variables, ranging from -1 to +1. The scatterplot shows a downward linear trend, indicating that as training time increases, 5K race time decreases, resulting in a negative correlation. Choice B correctly identifies this negative association without implying causation. A common distractor, like choice A, confuses correlation with causation by suggesting training time 'causes' faster times, but correlation does not prove causality. Remember, correlation quantifies how closely points follow a straight line, with the sign reflecting the slope's direction and the magnitude indicating the tightness of the fit. The presence of a high-leverage point might influence the correlation value, but it doesn't change the overall negative direction here.
- A sports scientist records, for 13 cyclists, average speed (miles per hour) and heart rate (beats per minute) during a steady ride. The scatterplot shows an upward trend, but two points are far from the pattern (possible outliers). Which statement about correlation is correct?
Answer: The correlation describes the strength and direction of the linear association, and outliers can change it substantially.
This AP Statistics question explores how outliers affect correlation, which measures linear association's strength and direction. Choice B correctly notes that outliers, especially influential ones, can substantially alter the correlation coefficient. The upward trend suggests positive correlation, but the two outliers could skew it. Distractor A assumes removal always weakens correlation, but it depends on the outliers' position. Correlation doesn't prove causation, countering E. In essence, correlation calculates average product of z-scores, sensitive to extreme points disrupting the linear pattern.
- An analyst studies, for 16 apartments, distance to downtown (miles) and monthly rent (dollars). The scatterplot shows a clear downward linear association. Which statement about correlation is correct?
Answer: The correlation is negative because larger distances tend to be associated with lower rents.
AP Statistics correlation evaluates the direction and strength of linear relationships, negative when variables move oppositely. The downward association means higher distances link to lower rents, yielding negative correlation per choice B. This pattern shows inverse movement, not requiring causation as in distractor C. Choice A wrongly ties positivity to positive measurements, but correlation depends on association, not scales. A negative slope doesn't mean zero correlation, debunking D. Correlation is a standardized measure, focusing on relative deviations, not absolute values or units.
- A teacher compares students' number of absences (days) and final course grade (percent). The scatterplot shows a negative linear trend, but one student has many absences and still earned a very high grade. Which statement about correlation is correct?
Answer: The outlier likely weakens the magnitude of the negative correlation compared with the rest of the pattern.
This question explores how outliers affect correlation. The single student with many absences but high grades goes against the overall negative trend, which will pull the correlation coefficient closer to zero, weakening its magnitude. Choice A correctly identifies this effect. Choice B wrongly assumes correlation is unaffected by outliers, while choice C overestimates the outlier's impact. Correlation measures association, not causation (choice D), and it's not the same as slope (choice E). Outliers can substantially influence correlation values.
- A city planner records, for 20 neighborhoods, average commute time (minutes) and average home price (thousands of dollars). The scatterplot appears to have a curved (nonlinear) pattern: home prices are highest for moderate commute times and lower for very short or very long commutes. Which statement about correlation is correct?
Answer: The correlation could be close to 0 even though there is a strong nonlinear association.
Correlation in AP Statistics is specifically for linear associations, so nonlinear patterns like curves can yield correlations near 0 despite strong relationships. Choice A accurately states this, referencing the curved pattern where prices peak at moderate commutes. The eventual downward part doesn't force negative correlation, as in distractor C. Correlation near 0 doesn't prove no relationship, just no linear one, countering E. It's not the slope of any curve, debunking D. Thus, correlation measures linear predictability, potentially missing curved associations. - A nutritionist compares daily sodium intake (mg) and systolic blood pressure (mmHg) for adults. The scatterplot shows a weak positive linear trend with substantial scatter. Which statement about correlation is correct?
Answer: The correlation is probably small and positive because there is an upward tendency but lots of scatter.
This question examines weak positive correlation. With an upward tendency but substantial scatter, the correlation will be positive but small in magnitude, making choice B correct. Choice A overestimates correlation strength based solely on direction, while choice C misinterprets individual exceptions as determining the overall correlation sign. Weak correlation doesn't imply no effect (choice D) - it just means the linear relationship isn't strong. Correlation is unitless and can be calculated regardless of different measurement units (choice E).
- A business owner tracks, for 11 months, advertising spending (thousands of dollars) and monthly revenue (thousands of dollars). The scatterplot shows a strong positive linear association, but one month has unusually high advertising and unusually low revenue (an influential point). Which statement about correlation is correct?
Answer: The correlation could change noticeably if the unusual month were removed, because influential points can affect r.
In AP Statistics, influential points can significantly affect correlation by altering the linear fit. Choice B correctly notes that removing the unusual month could change the correlation noticeably. The strong positive association might weaken or strengthen without it. Correlation depends on all points, not just slope, countering A. One low-revenue point doesn't force negativity, debunking C. Correlation proves association, not causation, and units don't affect its sign or value. - A city planner records distance from downtown (miles) and monthly rent (dollars) for apartments. The scatterplot shows a fairly strong negative linear association. Which statement about correlation is correct?
Answer: The correlation is negative because higher distance values tend to be paired with lower rent values.
This question tests understanding correlation's sign and interpretation. As distance from downtown increases, rent tends to decrease, creating a negative linear association. Choice B correctly identifies this negative correlation. Choice A misunderstands that correlation is always between -1 and +1 regardless of variable units. Choice C incorrectly assumes both variables increasing means positive correlation - it's about how they vary together. Correlation describes association, not causation (choice D), and unlike slope, correlation is unitless (choice E).
- A meteorologist records, over 18 days, humidity (percent) and high temperature (°F). The scatterplot shows a fairly strong downward linear association. Which statement about correlation is correct?
Answer: The correlation is negative because higher humidity tends to be associated with lower high temperatures in this data set.
Correlation in AP Statistics is negative when higher values of one variable pair with lower values of the other, as in choice B's description of humidity and temperature. The strong downward pattern supports this inverse association. Units differ but don't impact correlation, debunking C. It's not exactly -1 unless perfect linearity, countering D. Positivity isn't from measurement types, as in distractor A. Correlation shows association, not causation, so it doesn't prove humidity causes temperature drops.
- An ecologist measures daily sunlight (hours per day) and plant growth (centimeters per week) for 15 plants. The scatterplot shows a strong positive linear association with little scatter. Which statement about correlation is correct?
Answer: The correlation is close to +1 because the points follow a strong upward linear pattern.
In AP Statistics, correlation assesses the linear relationship between variables, with positive values indicating that as one variable increases, the other tends to increase. The strong upward linear pattern with little scatter suggests a correlation close to +1, as described in choice A. This references the pattern of increasing plant growth with more sunlight, showing a tight positive association. A distractor like choice B incorrectly assumes a negative correlation based on the direction of increase, but positive means both rise together. Correlation is unitless and unaffected by different units, debunking choice E. Overall, correlation measures linear strength and direction, not causation, so even a strong positive r doesn't prove sunlight causes growth. - A teacher compares, for 14 students, number of absences (days) and final exam score (points out of 100). The scatterplot shows a weak downward trend with substantial scatter. Which statement about correlation is correct?
Answer: The correlation is near 0 because the points are widely scattered even though there is a slight downward trend.
Correlation in AP Statistics quantifies linear association, and a value near 0 indicates weak or no linear relationship, even if a trend exists amid scatter. The weak downward trend with substantial scatter points to a correlation near 0, as choice B states. This references the pattern where more absences loosely associate with lower scores, but the wide scatter weakens the linear strength. Choice A is a distractor, overstating the negativity by ignoring the scatter's impact on magnitude. Units don't affect correlation, countering choice E. Fundamentally, correlation measures how predictably one variable changes with another in a linear fashion, with scatter reducing its absolute value. - A psychologist studies, for 25 adults, hours of sleep per night (hours) and stress score (on a 0–50 scale). The scatterplot shows a moderate negative linear association. Which statement about correlation is correct?
Answer: A negative correlation means higher sleep tends to be associated with lower stress scores, but it does not by itself establish causation.
This AP Statistics question addresses correlation's interpretation, emphasizing it shows association but not causation. Choice B rightly states the negative correlation means higher sleep associates with lower stress, without proving cause. The moderate strength implies not -1, countering D. Negative doesn't mean independence, debunking C. Slope sign matches correlation sign, so negative r means negative slope, not positive as in A. Correlation isn't zero due to scales, countering E; it's about linear linkage.
- A biologist measures the length of a lizard (cm) and its sprint speed (m/s). The scatterplot shows an increasing pattern that curves upward (not well-approximated by a straight line). Which statement about correlation is correct?
Answer: Correlation describes linear association, so a strong curved pattern can still have a correlation that is not close to 1.
This question highlights that correlation specifically measures linear association. A curved pattern, even if consistently increasing, will not produce a correlation close to +1 because correlation only captures straight-line relationships. Choice B correctly explains this limitation. Choice A wrongly assumes any increasing pattern yields high positive correlation, while choice C incorrectly links curved patterns to negative correlation. Correlation is about association strength, not causation (choice D), and it's unitless - changing measurement units doesn't affect r (choice E).
