Scatter Plots & Association — Drills
Scatter Plots & Association has 12 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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.
Direction
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
As age of a car increases, its value decreases. This is
- a negative association
- a positive association
- no association
- a causal proof
Worked answer
a negative association
One rises while the other falls.
A negative association.
Note that this still says nothing about cause.
Problem 2
As rainfall increases, plant height increases. This is
- a causal proof
- a negative association
- a positive association
- no association
Worked answer
a positive association
Both rise together.
A positive association.
Note that this still says nothing about cause.
Axes
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
You want to see whether more fertiliser used gives more crop yield. Which variable belongs on the x-axis?
Worked answer
fertiliser used
Fertiliser used is the explanatory variable.
So it goes on x, and crop yield goes on y.
Problem 2
You want to see whether more rainfall gives more plant height. Which variable belongs on the x-axis?
Worked answer
rainfall
Rainfall is the explanatory variable.
So it goes on x, and plant height goes on y.
Outlier
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A point at the far right of a scatter plot lies exactly on the pattern. It is
- an outlier
- a cluster
- not an outlier
- the median
Worked answer
not an outlier
It follows the trend of the rest.
So it is not an outlier, however extreme its x value.
Problem 2
A point on a scatter plot sits far away from the pattern of the others. It is
- an outlier
- not an outlier
- the median
- a cluster
Worked answer
an outlier
It does not follow the trend.
So it is an outlier.
Form
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
The dots on a scatter plot lie close to a bending arc. The form is
- linear
- clustered
- curved
- random
Worked answer
curved
A straight line would miss the bend.
So the form is curved.
Problem 2
The dots on a scatter plot lie close to a straight band. The form is
- clustered
- linear
- curved
- random
Worked answer
linear
A straight line would follow them well.
So the form is linear.
Cause
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Number of firefighters sent and damage to the building rise together. The best explanation is
- number of firefighters sent causes damage to the building
- the size of the fire drives both
- the data must be wrong
- damage to the building causes number of firefighters sent
Worked answer
the size of the fire drives both
Neither one need act on the other.
Here, the size of the fire drives both.
That is a confounding variable.
Problem 2
Coffee cups drunk and hours worked rise together. The best explanation is
- a busy day drives both
- the data must be wrong
- coffee cups drunk causes hours worked
- hours worked causes coffee cups drunk
Worked answer
a busy day drives both
Neither one need act on the other.
Here, a busy day drives both.
That is a confounding variable.
Strength
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two plots show positive association. In plot A the dots hug the line; in plot B they are widely scattered. Which is stronger?
- A
- Cannot be determined
- B
- They are equally strong
Worked answer
A
Closeness to the pattern measures strength.
A is tighter, so A is stronger.
Counting
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A scatter plot of one class shows 27 dots. How many students are in the class?
Worked answer
27
One dot per student.
27 students
Problem 2
A scatter plot of one class shows 34 dots. How many students are in the class?
Worked answer
34
One dot per student.
34 students
Predicting
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
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 widely.
So no guarantee.
Cluster
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A scatter plot shows two separate clouds of dots. The likeliest reason is
- there is no association
- two different groups are mixed in one plot
- the data is random
- the sample is too small
Worked answer
two different groups are mixed in one plot
Each group follows its own pattern.
Splitting the plot by group would show two clean trends.
Reasoning it through
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A study finds that more firefighters sent goes with more damage. Should we send fewer firefighters? Answer yes or no.
Worked answer
no
The underlying severity drives both variables.
Acting on the association would attack the response, not the cause.
So no.
Problem 2
A study finds that more hospital visits goes with worse health. Should we avoid hospitals? Answer yes or no.
Worked answer
no
The underlying severity drives both variables.
Acting on the association would attack the response, not the cause.
So no.
Design
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which study design could establish that a treatment causes an effect?
- Surveying people about results
- Comparing two towns
- Observing who chooses the treatment
- Randomly assigning subjects to the treatment or a control
Worked answer
Randomly assigning subjects to the treatment or a control
Random assignment balances out other factors.
Observational studies cannot rule out confounders.
Describe
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A scatter plot has dots widely scattered along a straight band running down to the right. Describe the association in three words.
Worked answer
weak negative linear
Widely scattered: weak
Falling: negative
Straight band: linear
Problem 2
A scatter plot has dots tightly packed along a straight band running down to the right. Describe the association in three words.
Worked answer
strong negative linear
Tightly packed: strong
Falling: negative
Straight band: linear