Describe association in a scatterplot (direction, strength, form, outliers).
核心知识
Describing a scatterplot means stating four things: direction (positive or negative), strength (strong or weak), form (linear or nonlinear), and whether outliers exist.
深入理解
When the SAT asks you to "describe the association," it wants specific vocabulary, not vague impressions.
Direction — Do the points go up-right (positive) or down-right (negative)? If
Strength — How tightly do the points cluster around an imaginary line or curve? If they hug it closely, the association is strong. If they're spread out, it's weak.
Form — Is the overall shape a straight line (linear) or a curve (nonlinear)? A set of points that bends is nonlinear even if the general direction is upward.
Outliers — Look for any point that sits far from the rest of the data. One isolated point in the upper-left corner when everything else trends down-right is an outlier.
A complete description sounds like: "There is a strong, positive, linear association with no apparent outliers." That single sentence covers all four elements.
The most common mistake is confusing strength with direction. A scatterplot can have a strong negative association — the points go downhill but stick tightly to a line. Strong doesn't mean positive.
分步讲解
- Look at the overall trend: are points rising or falling left to right? That's direction.
- Judge how tightly the points cluster around the trend. Tight = strong, spread = weak.
- Decide if the pattern is a straight line (linear) or a curve (nonlinear).
- Scan for any points far removed from the general pattern — those are outliers.
常见误解
- Confusing a strong association with a positive one. A scatterplot can show a strong negative trend.
- Thinking that outliers invalidate the association. One outlier doesn't change the overall direction or form — it's just noted separately.
- Calling a curved pattern 'no association' because it isn't a straight line. A clear curve is a nonlinear association, not the absence of one.
示例解析
A researcher collected data on the number of hours students studied and their scores on a standardized test. The scatterplot shows that as hours increase, scores generally increase, but the points are widely spread around any potential trend line. Which of the following best describes the association shown in the scatterplot?
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