Question 1
Comment on the correlation of the following scatter graph
Select the correct answer from the list below:
A: No correlation
B: Strong positive
C: Weak negative
D: Weak positive
CORRECT ANSWER: B: Strong positive
WORKED SOLUTION:
We can see that as one variable increases the other does as well, so the correlation is positive. Secondly, we can see that the points are quite tightly grouped, so it must be a strong correlation. Therefore, we have a strong positive correlation.
Level 3
Question 2
Comment on the correlation of the following scatter graph
Select the correct answer from the list below:
A: No correlation
B: Strong positive
C: Weak negative
D: Weak positive
CORRECT ANSWER: A: No correlation
WORKED SOLUTION:
Because there doesn’t appear to be any sort of relationship between the variables increasing or decreasing with each other, then there is no correlation.
Level 3
Question 3
Plot the following data as a scatter graph and comment on the correlation, if any.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: C
WORKED SOLUTION:
To plot our scatter graph, we will use the first row (Shoe Size) on the x-axis and the second row (Height (cm)) on the y-axis. For example:
Would be plotted as
If we do this for all of our data, the scatter graph will look a little something like this:
From this we can see that as one variable increases, so does the other.
So, this shows that there is a positive correlation between shoe size and height. The points are also pretty close together, so there is going to be a strong positive correlation.
Level 3
Question 4
A teacher uses a scatter graph to plot students’ respective maths and physics exam marks. Use the scatter graph to predict the physics mark of somebody who got 60 in their maths exam.
Select the correct answer from the list below:
A: 84-86
B: 47- 49
C: 60 - 62
D: 73-75
CORRECT ANSWER:
WORKED SOLUTION:
To make a prediction or approximation using a scatter graph we need to first draw a line of best fit. We can tell that there is a positive correlation between maths and physics marks, so the line of best fit will be going from the bottom left to the top right. We need to try and split the points evenly.
After drawing our line of best fit, we read up to our line from a mark of 60 in maths, and then across to find our physics score.
From this, we can predict that a student who gets a mark of 60 in maths will get a mark of approximately 61 in physics.
Level 3
Question 5
A scientist is studying plants in the rain-forest, looking at the relationship between their height and the number of leaves they have. Their data is presented in the scatter graph below. Use this data to find a prediction for the height of a plant with 40 leaves to the nearest half of a cm.
Select the correct answer from the list below:
A: 15.5 cm – 16.5 cm
B: 17.5 cm – 18.5 cm
C: 21.5 cm – 22.5 cm
D: 19.5 cm – 20.5 cm
CORRECT ANSWER: D
WORKED SOLUTION:
To make a prediction or approximation using a scatter graph we need to first draw a line of best fit. We can tell that there is a negative correlation between plant height and the number of leaves, so the line of best fit will be going from the top left to the bottom right.
We need to try and split the points evenly.
After drawing our line of best fit, we need to read across from 40 (Number of Leaves) and then down to find its height.
From this, we can predict that a plant with 40 leaves will be about 20cm tall.
Level 3