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Math Coach Amy
Amy Ferguson Moncure

Algebra 1 · Unit 10

Read a Scatterplot

Describe form, direction, and strength of an association between two numerical variables, and notice outliers.

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Key Ideas Easy Medium Hard Super Challenge
What to Remember

Form

Linear: cloud follows a line. Curved: quadratic, exponential, or something else. None: a blob.

Direction

Positive: larger x tends to go with larger y. Negative: larger x tends to go with smaller y.

Strength

Tight around a pattern is strong. Spread out is weak. Strength is not the same as slope.

Outliers

A point far from the cloud is worth naming. It can be a mistake, a special case, or a real extreme.

Level 1

Easy

Read direction and a rough form from a scatterplot.

Example
Describe the association.

Form: roughly linear.

Direction: positive.

Strength: moderately tight.

Answer: positive, roughly linear

1
Describe the association.
Show Answer

Negative, roughly linear.

Answer: negative linear

2
Describe the association.
Show Answer

No clear linear or curved trend. A blob.

Answer: no clear trend

3
Hours studied vs quiz score: the cloud rises to the right. Direction?
Show Answer

Positive association.

Answer: positive

4
Temperature vs heating-bill dollars: the cloud falls to the right. Direction?
Show Answer

Negative association.

Answer: negative

5
A point sits far above the rest of a tight linear cloud. What do you call it?
Show Answer

An outlier (in the y-direction).

Answer: outlier

Level 2

Medium

Strength versus slope, and a context sentence.

Example
Two plots both have positive linear form. Plot A is tight; plot B is spread out with the same slope. Which association is stronger?

Plot A. Strength is tightness, not how steep the line is.

Answer: the tighter plot

1
A scatterplot of practice minutes vs free-throw percent is positive and linear but weak. Write one sentence in context.
Show Answer

Students who practiced more minutes tended to have slightly higher free-throw percents, but the points are spread out.

Answer: weak positive in context

2
Could a steep line with lots of scatter still be a weak association?
Show Answer

Yes. Steep is slope. Weak is spread around the pattern.

Answer: yes

3
The plot of day number vs height of one plant is curved, rising fast then leveling. Form?
Show Answer

Nonlinear (a curve, maybe leveling off). Not a single straight line.

Answer: curved

4
x = class size, y = average score. The cloud is negative and moderately tight. Interpret.
Show Answer

Larger classes tended to have lower average scores in this data. That is an association, not by itself a cause.

Answer: negative association

5
A scatterplot has two clusters, each internally tight, with a gap. Why is “one linear trend” a poor summary?
Show Answer

The gap may be two groups (two grades, two sports). Describe each cluster, or the grouping, not one fake line through empty space.

Answer: two groups

Level 3

Hard

An outlier’s effect, or a curve vs a line.

Example
A mostly linear positive cloud has one point at very large x and very small y. What happens if you keep it when you draw a line?

That outlier can pull a fitted line down on the right.

Report the pattern with and without it, and check whether the point is an error.

Answer: it can pull the line

1
Second differences of binned y-values are roughly constant. The scatterplot looks U-shaped. Which form?
Show Answer

Quadratic-like curve, not linear.

Answer: curved / quadratic-like

2
A plot of speed vs stopping distance fans out (more spread at larger x). What does that say about strength?
Show Answer

The association may be positive but weaker at large speeds. Strength is not uniform.

Answer: spread grows with x

3
All points lie exactly on y = 2x + 1 except one typing error (3, 100). Describe form, direction, strength if you ignore the error.
Show Answer

Perfect positive linear, aside from the error.

Answer: perfect linear plus an error

4
Why is “the line is steep, so the relationship is strong” a mix-up of two ideas?
Show Answer

Steep is slope (rate). Strong is how close the points sit to the pattern.

Answer: slope ≠ strength

5
A scatterplot of month number vs ice-cream sales is curved (up in summer). Why might a single linear description fail?
Show Answer

Sales rise then fall with the seasons. A line cannot capture a peak in the middle.

Answer: seasonal curve

Super Challenge

Super Challenge

1
Sketch (in words) two scatterplots with the same slope of a fitted line but different strengths.
Show Answer

Both clouds tilt up at about the same rate.

One is a thin tube around the line (strong). One is a wide band (weak).

Answer: same tilt, different spread

2
Give a context where a negative linear association is expected, and one where a blob is expected.
Show Answer

Negative: outside temperature vs heating bill.

Blob: locker number vs quiz score.

Answer: temp vs bill; ID vs score

3
A classmate says any curved scatterplot is quadratic. Give a counterexample form from this course.
Show Answer

Exponential growth (ratios) also curves up.

A leveling-off curve or a piecewise drop can be neither a parabola nor a line.

Answer: exponential or piecewise

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