The scatter diagram shows the
scores that 10 students received on their science test compared to the number of
lessons that they missed. Part a) State the coordinates of
the point that is an outlier. Part b) Ignoring the outlier, 1)
first draw the line of best fit for the remaining points then 2) describe the type
of correlation. Another student in the class missed
six lessons. Part c) Estimate the score they
There is also a part d that we will
look at later. The first part of our question
asked us to identify the outlier. Well, an outlier is a point on the
scatter diagram that doesn’t follow the general pattern or trend of the other
In this question, the point circled
doesn’t follow the general trend. The coordinates of this point are
six, 70. We go along the corridor to six and
up to 70. This means that the student missed
six lessons and scored 70 in the science test.
The next part of our question asked
us to draw a line of best fit. A line of best fit needs to have
roughly the same number of points above and below the line. It must also have points above and
below the line at the start and at the end of the line. Our line of best fit will look
something like this.
It’s important to note that
everyone’s line of best fit will be slightly different. Therefore, there is a margin for
error in the exam. This will also impact on our answer
to part c.
The second part of part b asked us
to describe the correlation. Once we have drawn our line of best
fit, the type of correlation, it could be positive or negative. If our line of best fit slopes
upwards from left to right, it is a positive correlation as the slope has a positive
gradient. If our line slopes down from left
to right, it has a negative correlation as the gradient is negative.
In this case, we have a negative
correlation. This means that the more lessons a
student missed, the lower their mark in the science test. As one variable increases, the
other one decreases.
Part c of our question told us
about another student in the class who missed six lessons. We need to use our line of best fit
to estimate the score they received. Remember everyone’s line of best
fit will be slightly different. So your answer here might be
slightly different to ours. This will be taken into account in
the mark scheme in any exam.
In order to estimate the score they
received, we firstly need to go up from six lessons. Once we hit our line of best fit,
we need to go horizontally across to the 𝑦-axis. On our diagram, this gives us an
answer of 42 marks as each little square is worth two marks and we are one square
above 40. We can, therefore, estimate that a
student that missed six lessons would have a science score of 42.
The final part of the question said
Any student who scored less than 40
failed the test. Part d) Do you agree or disagree
with the following statement? “Any student who missed seven
lessons or more failed the test. Justify your answer.”
Well, the key bit of information
here is that we’re interested in any student who missed seven lessons or more. The scatter diagram only shows
students who missed seven lessons or less. This means that we have no data for
students who missed eight or more lessons. It is also important to note that
the line of best fit is just an estimate and therefore it doesn’t show the
This means that the statement is
false. So the correct answer is disagree
because the line of best fit doesn’t show guaranteed scores and we have no data for
students who missed eight lessons or more.
This question has shown us how we
can use a scatter diagram to draw a line of best fit, identify the correlation, and
estimate scores. However, any estimation must be
within the dataset of the particular question and also that our line of best fit
doesn’t guarantee the result, as shown by the outlier in part a of the question.