A scatter graph of ten points shows one clear outlier. What should you do with that outlier when you draw the line of best fit?

Ignore it, and draw the line through the trend of the other nine points.

Make sure the line passes through it.

Move it onto the line so that all ten points fit the trend.

Draw a curve through all ten points instead of a straight line.

Six students recorded the number of hours they revised and their mark out of 60: (1, 22), (2, 29), (3, 34), (4, 40), (5, 45), (6, 52). Work out the mean number of hours and the mean mark. The line of best fit passes through this mean point.

mean hours = 3.5, mean mark = 37

Are scatter graphs on the Foundation paper as well as Higher?

Yes. Spec ref S6 is crossover content on Edexcel 1MA1, so a scatter graph question can appear near the end of a Foundation paper and in the first two questions of a Higher one. The Higher version tends to add a part asking you to judge an estimate or comment on a claim about cause, rather than only reading a value off the line.

How many marks is a scatter graph question worth on Edexcel Higher?

Usually 3-5 marks in one question of three or four parts. One mark for the type of correlation or the outlier, two for drawing the line and taking a reading from it, and one for the written comment at the end. It sits early in the paper and is among the cheapest marks available.

Does the line of best fit have to go through the origin?

No. Draw it through the trend of the points, with roughly as many points above it as below, and let it meet the vertical axis wherever the data sends it. Forcing it through (0, 0) tilts the whole line, and every estimate you then read off falls outside the range the mark scheme allows.

What is the difference between interpolation and extrapolation?

Interpolation means taking a reading from inside the range of values that were actually collected, and it is treated as reliable. Extrapolation means extending the line beyond that range, which assumes the pattern continues where nothing was measured. Edexcel tests this by handing you a value clearly outside the data and asking you to comment, and the mark needs the reason as well as the word.

Scatter Graphs and Correlation - Edexcel GCSE Higher Maths

Typically 3-5 marks, usually in one question near the start of the paper · Spec 1MA1

A scatter graph plots two measurements taken from the same thing: the age and the value of one car, the height and the arm span of one student, the rainfall and the number of visitors on one day. Every cross is a single member of the sample, and the whole point of the diagram is to show whether the two measurements move together. On Edexcel 1MA1 this is spec ref S6, and it is crossover content, so the same diagram can carry a question at the end of a Foundation paper and at the start of a Higher one. What makes the Higher version harder is everything that comes after the reading: whether the estimate can be trusted, what one stray point does to the line, and whether a correlation licenses any claim about cause.

Edexcel usually sets this as question 1 or question 2, three or four parts hanging off one printed diagram. The opening part is a single mark for the type of correlation, or for the coordinates of an outlier. The middle carries 2 marks: draw a line of best fit, then read an estimate from it, with one mark for the line and one for a value inside the range the mark scheme allows. The last part is where candidates separate, and it is always a written comment, because someone in the question has pushed the trend past the data or has claimed that one quantity causes the other. The topic can come up on any of the three papers and the calculator changes almost nothing, since the numbers are read off the graph rather than worked out.

Two habits protect the marks. Draw the reading lines onto the diagram, across from the value you are given to the line of best fit and then down to the other axis, because the mark scheme accepts a range and those lines show the examiner where your number came from. The second is wording. 'Describe the relationship' wants a sentence naming both quantities and saying which way each one moves, so 'as the age of the car increases, its value falls' earns the mark and the single word 'negative' does not. Keep that separate from 'what type of correlation does the graph show', which is answered with 'negative correlation' and needs nothing else.

Worked example

Ten students recorded the number of hours they spent revising for a test and their mark out of 60. The pairs (hours, mark) were

(1, 19)

(2, 23)

(3, 27)

(4, 31)

(5, 35)

(6, 40)

(7, 43)

(8, 47)

(9, 52)

and

(4, 55)

. (a) One of the points is an outlier. Write down its coordinates. (b) Ignoring the outlier, describe the relationship between the number of hours of revision and the mark. (c) A line of best fit is drawn through

(2, 23)

and

(8, 47)

. Use it to estimate the mark of a student who revised for 6.5 hours. (d) Explain why the line should not be used to estimate the mark of a student who revised for 15 hours.

[5 marks]

(a) The other students who revised for 4 hours sit near a mark of 31, so $(4, 55)$ lies far above the pattern the rest of the data makes. The outlier is $(4, 55)$ .
B1: both coordinates, in the plotted order; giving only one value, or writing them the wrong way round, is the usual loss here
(b) With that point left out, the marks climb steadily as the hours climb: the more hours a student revised, the higher the mark. The points lie close to a straight line, so the correlation is strong and positive.
B1: a sentence naming both quantities and the direction of each; 'positive' on its own does not answer 'describe the relationship'
(c) Gradient of the line $= \frac{47 - 23}{8 - 2} = \frac{24}{6} = 4$ . Going from $x = 2$ to $x = 6.5$ is 4.5 along, so the mark rises by $4.5 \times 4 = 18$ , giving $23 + 18 = 41$ marks.
M1: reading up from 6.5 hours to the line and across, or a correct gradient used. A1: 41, with the mark scheme accepting a range either side
(d) 15 hours is outside the data, which stops at 9 hours, so extending the line assumes a trend that nothing here has tested. The line gives $4 \times 15 + 15 = 75$ , and the test is only out of 60.
C1: extrapolation named with a reason; 'the graph does not go that far' on its own is not enough for the mark

Practice questions

These are original questions in Edexcel 1MA1 Higher style. There are no diagrams here, so each scatter graph is given as its list of $(x, y)$ pairs and every line of best fit is described by two points it passes through, which is exactly what a ruler laid on graph paper would give you. Anything read off a line carries a tolerance, so a sensible estimate near the stated value is marked correct, and the reasoning parts are set as multiple choice because that is how they are marked on the paper: on the reason, not the phrasing.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [1 mark]

A dealer records the age, in years, and the value, in £, of six cars of the same model: $(1, 9500)$ , $(2, 8200)$ , $(3, 7000)$ , $(4, 6100)$ , $(5, 4900)$ , $(6, 3800)$ . What type of correlation does the scatter graph of this data show?

Answer options for question 1
Strong negative correlation Weak negative correlation Strong positive correlation No correlation
Question 2 Warm-up [2 marks]

A scatter graph plots the height, in cm, against the arm span, in cm, of ten students. The line of best fit passes through $(150, 148)$ and $(180, 181)$ , with the height plotted first. Use the line to estimate the arm span of a student whose height is 165 cm.

Your answer (fractions like 1/2 are fine)
Question 3 Warm-up [2 marks]

Twelve students sat a maths test and a science test, each marked out of 60. On the scatter graph the maths mark is plotted first, and the line of best fit passes through $(10, 16)$ and $(50, 48)$ . One student scored 40 in the science test but missed the maths test. Use the line to estimate her maths mark.

Your answer (fractions like 1/2 are fine)
Question 4 Exam pace [1 mark]

A scatter graph of ten points shows one clear outlier. What should you do with that outlier when you draw the line of best fit?

Answer options for question 4
Ignore it, and draw the line through the trend of the other nine points. Make sure the line passes through it. Move it onto the line so that all ten points fit the trend. Draw a curve through all ten points instead of a straight line.
Question 5 Exam pace [2 marks]

Six students recorded the number of hours they revised and their mark out of 60: $(1, 22)$ , $(2, 29)$ , $(3, 34)$ , $(4, 40)$ , $(5, 45)$ , $(6, 52)$ . Work out the mean number of hours and the mean mark. The line of best fit passes through this mean point.

mean hours = mean mark =
Question 6 Stretch [3 marks]

A line of best fit on a scatter graph gives an estimate of $y = 38$ when $x = 4$ , and an estimate of $y = 68$ when $x = 14$ . Use the line to estimate the value of $x$ when $y = 50$ .

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Answering 'describe the relationship between the rainfall and the number of visitors' with the single word 'negative', which describes the correlation rather than the relationship and scores nothing.

Write a sentence with both quantities in it: 'as the rainfall increases, the number of visitors falls'. Save 'negative correlation' for the part that asks what type of correlation the graph shows.
Letting a clear outlier drag the ruler towards it, so a line that should run through the middle of the points sits two or three squares high and every reading taken from it lands outside the accepted range.

Find the outlier and ring it lightly before you pick up the ruler, then place the line through the remaining points with roughly as many above it as below. The line follows the trend of the data, not the number of points it happens to touch.
Joining the plotted points dot to dot, or forcing the line down to the origin because 'that is where a graph starts'.

One straight ruled line, drawn right across the width of the plotted data. It only reaches $(0, 0)$ if the data is heading there, and on a graph of car age against value it plainly is not.
Extending the line well past the last point and reporting the reading as though it were as good as one taken inside the data, which is how a 16-year-old car ends up valued at minus £2200.

Check where the reading sits before you write it down. Inside the range of the data it is interpolation and it is reliable; outside that range, say so and give the reason, that there is no evidence the straight-line trend carries on past the values that were measured.
Treating correlation as proof of cause, so a positive correlation between ice cream sales and cases of sunburn becomes 'buying ice cream causes sunburn'.

State what the graph does show, that the two quantities rise and fall together, then look for a third quantity that could drive both. Hot, sunny weather explains the ice creams and the sunburn. When a question asks whether the data proves that one causes the other, the answer is no, with a reason.

Frequently asked questions

Are scatter graphs on the Foundation paper as well as Higher?: Yes. Spec ref S6 is crossover content on Edexcel 1MA1, so a scatter graph question can appear near the end of a Foundation paper and in the first two questions of a Higher one. The Higher version tends to add a part asking you to judge an estimate or comment on a claim about cause, rather than only reading a value off the line.
How many marks is a scatter graph question worth on Edexcel Higher?: Usually 3-5 marks in one question of three or four parts. One mark for the type of correlation or the outlier, two for drawing the line and taking a reading from it, and one for the written comment at the end. It sits early in the paper and is among the cheapest marks available.
Does the line of best fit have to go through the origin?: No. Draw it through the trend of the points, with roughly as many points above it as below, and let it meet the vertical axis wherever the data sends it. Forcing it through $(0, 0)$ tilts the whole line, and every estimate you then read off falls outside the range the mark scheme allows.
What is the difference between interpolation and extrapolation?: Interpolation means taking a reading from inside the range of values that were actually collected, and it is treated as reliable. Extrapolation means extending the line beyond that range, which assumes the pattern continues where nothing was measured. Edexcel tests this by handing you a value clearly outside the data and asking you to comment, and the mark needs the reason as well as the word.

Scatter Graphs and Correlation - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics