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.
- Mean — Two kinds of centre: the balance point, and the middle value.
- Median — Two kinds of centre: the balance point, and the middle value.
- Factor — A number that divides evenly into another.
- Scatter plot — A graph of paired data, one dot per case.
- Association — A pattern linking the two variables.
- Cluster — A group of dots bunched together.
- Outlier — A dot far away from the rest of the pattern.
- Linear association — The dots roughly follow a straight line.
- Prove — The statement you must arrive at. Always the last line.
- Height — The perpendicular distance from the base to the opposite corner.
Problem 1
As study time increases, test scores increase. This is
- a positive association
- a negative association
- no association
- 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
- a negative association
- a positive association
- no association
- 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
- an outlier
- a cluster
- the median
- 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
- linear
- curved
- clustered
- 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
- hot weather drives both
- ice cream causes sunburn
- sunburn causes ice cream sales
- 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?
- A
- B
- They are equally strong
- 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
- not an outlier
- an outlier
- the mean
- 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
- two different neighbourhoods are mixed together
- houses have two prices
- the data is random
- 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?
- Randomly assigning plants to fertiliser or none
- Observing which gardeners use it
- Comparing two neighbourhoods
- 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