Scatter Plots & Association — Practice

Two measurements per person, one dot each. The shape of the cloud is the finding.

What these questions cover

These questions use 10 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

As study time increases, test scores increase. This is

  1. a positive association
  2. a negative association
  3. no association
  4. a causal proof
Worked answer

a positive association

Up together means positive

Nothing here proves cause

Problem 2

As the age of a car increases, its value decreases. This is

  1. a negative association
  2. a positive association
  3. no association
  4. a cluster
Worked answer

a negative association

Opposite directions means negative

Problem 3

You want to see whether more rainfall gives taller plants. Which variable belongs on the x-axis?

Worked answer

rainfall

Rainfall is the explanatory variable

So rainfall goes on x and height on y

Problem 4

On a plot of height against weight, one point is far above the pattern. It is

  1. an outlier
  2. a cluster
  3. the median
  4. impossible
Worked answer

an outlier

It does not follow the trend of the rest

So it is an outlier

Problem 5

The dots on a scatter plot lie close to a straight band. The form is

  1. linear
  2. curved
  3. clustered
  4. random
Worked answer

linear

Close to a straight line means linear form

Problem 6

Ice cream sales and sunburn cases rise together. The best explanation is

  1. hot weather drives both
  2. ice cream causes sunburn
  3. sunburn causes ice cream sales
  4. the data must be wrong
Worked answer

hot weather drives both

Hot weather increases both independently

That is a confounding variable

Association is not causation

Problem 7

A scatter plot has dots falling steeply from upper left to lower right, tightly packed. Describe the association in three words.

Worked answer

strong negative linear

Tightly packed: strong

Falling: negative

Straight band: linear

Problem 8

Two plots both show positive association. In plot A the dots are tight to the line; in plot B they are widely scattered. Which is stronger?

  1. A
  2. B
  3. They are equally strong
  4. Cannot be determined
Worked answer

A

Closeness to the pattern measures strength

A is tighter, so A is stronger

Problem 9

A scatter plot of a class shows 24 dots. How many students are in the class?

Worked answer

24

One dot per student

24 students

Problem 10

A point at the far right of a scatter plot lies exactly on the pattern. It is

  1. not an outlier
  2. an outlier
  3. the mean
  4. a cluster
Worked answer

not an outlier

This point follows the trend

So it is not an outlier, however extreme its x value

Problem 11

A scatter plot of shoe size against height shows a positive association. Does a large shoe size guarantee a tall person? Answer yes or no.

Worked answer

no

Positive means taller on average

Individual cases still vary

So no guarantee

Problem 12

A scatter plot of price against size for houses shows two separate clouds. The likeliest reason is

  1. two different neighbourhoods are mixed together
  2. houses have two prices
  3. the data is random
  4. there is no association
Worked answer

two different neighbourhoods are mixed together

Each group follows its own pattern

Splitting the plot would show two clean trends

Problem 13

A study finds a strong positive association between number of firefighters sent and damage done to a building. Should fewer firefighters be sent? Answer yes or no.

Worked answer

no

Bigger fires get more firefighters

Bigger fires also cause more damage

Fire size is the confounder

Sending fewer would make things worse

Problem 14

Two variables have a perfect V-shaped relationship. Is the linear association strong or weak?

Worked answer

weak

One arm rises, the other falls

The rises and falls cancel

So the linear association is weak, even though the pattern is perfect

Problem 15

Which study could establish that a new fertiliser causes taller plants?

  1. Randomly assigning plants to fertiliser or none
  2. Observing which gardeners use it
  3. Comparing two neighbourhoods
  4. Surveying gardeners about yields
Worked answer

Randomly assigning plants to fertiliser or none

Random assignment balances out other factors

Observational studies cannot rule out confounders

Problem 16

A plot of hours of television against grade shows a moderate negative linear association with two outliers. Write one sentence a statistician would accept about cause.

Worked answer

no cause can be concluded from this association

The data shows an association only

A third factor could drive both

So no causal claim is justified

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