[discia] GCSE Maths › Statistics › Scatter Graphs

Scatter Graphs

discia.org 10 questions · 27 marks
Name Date
  1. Either paper 2 marks

    A shop recorded the highest temperature and the number of bottles of cold water sold on each of nine days.

    481216202428202530354045505560Highest temperature (C)Number sold
    (a)

    Describe the correlation shown by the scatter graph.

    (b)

    Write down what this tells you about the number of bottles of cold water the shop sold.

    Show answer
    (a) Positive correlation
    (b) The warmer the day, the more bottles of cold water the shop sold
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  2. Either paper 4 marks
    A school records the time each of eight students spends gaming each week and their mark in a test, out of 50. The table shows the results.
    Gaming time (hours)1.52.53.545.56.57.58
    Test mark2139262831142413
    The scatter graph shows six of the eight results. 1234567891051015202530354045500Gaming time (hours)
    (a)

    Complete the graph by adding the missing label on the vertical axis and plotting the two missing points.

    (b)

    Describe the correlation shown by the completed graph.

    Write down the type of correlation, positive or negative.

    (c)

    Write down the strength of the correlation, strong or weak.

    Show answer
    (a) Vertical axis labelled Test mark; crosses plotted at (3.5, 26) and (5.5, 31)
    (b) Negative
    (c) Weak
    (a)1234567891051015202530354045500Gaming time (hours)Test mark
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  3. Either paper 2 marks

    The scatter graph shows the height and the mass of each of the nine students in Zainab's tutor group.

    A line of best fit has been drawn.

    145150155160165170175180185190404550556065707580Height (cm)Mass (kg)
    (a)

    Use the line of best fit to estimate the mass of a student of height 170 cm.

    (b)

    Use the line of best fit to estimate the height of a student of mass 57 kg.

    Show answer
    (a) \(63\ \text{kg}\)
    (b) \(158\ \text{cm}\)
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  4. Either paper 3 marks

    Nine students each sat two maths papers. Each paper was marked out of \(60\).

    The scatter graph shows their marks.

    1020304050601020304050600Paper 1 markPaper 2 mark
    (a)

    One of the points is an outlier.

    Write down the coordinates of that point.

    (b)

    Write down what the outlier tells you about that student's marks.

    (c)

    Ignore the outlier.

    Describe the correlation shown by the other eight points.

    Show answer
    (a) \((42, 20)\)
    (b) This student did far worse on Paper 2 than their Paper 1 mark suggests.
    (c) Positive correlation
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  5. Either paper 2 marks

    Here are four scatter graphs.

    Graph A

    xy

    Graph B

    xy

    Graph C

    xy

    Graph D

    xy
    (a)

    For which graph is a straight line of best fit appropriate? Circle your answer.

    A B C D

    (b)

    Which graph has one outlier? Circle your answer.

    A B C D

    Show answer
    (a) A
    (b) D
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  6. Either paper 4 marks

    A cafe records its sales of cups of tea and its sales of cups of coffee each month.

    The scatter graph shows the sales for 10 months.

    300350400450500550600650700200250300350400450500550600650700750Sales of cups of tea (£)Sales of cups of coffee (£)
    (a)

    Write down the type of correlation shown by the graph.

    (b)

    Draw a line of best fit on the graph. Plot two or more points of your line, then rule it.

    (c)

    The manager expects sales of cups of tea next month to be £600.

    Use your line of best fit to estimate the sales of cups of coffee next month.

    Show answer
    (a) Negative correlation
    (b) a straight line close to the mean point \((500, 473)\), for example from \((370, 538)\) to \((630, 408)\)
    (c) \(\text{£}423\)
    (b)300350400450500550600650700200250300350400450500550600650700750Sales of cups of tea (£)Sales of cups of coffee (£)
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  7. Either paper 2 marks
    Isla records the age and the value of seven cars of the same make and model. The table shows the data.
    Age (years)1235678
    Value (£000)2020201614128
    Isla draws this scatter diagram and line of best fit for the data. 123456789102468101214161820222426280Age (years)Value (£000) Write down two mistakes she has made. Mistake 1 Mistake 2
    Show answer
    The point \((2, 20)\) from the table has not been plotted: there is no cross for it. The line of best fit is drawn too low, so it is not close to the crosses.
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  8. Either paper 2 marks

    The scatter graph shows information about ten students. It shows the number of hours of television each student watched in a week and the mark each student got in a test. The line of best fit has been drawn.

    1234567891011102030405060700Hours of TV per weekMark in test (out of 80)

    Ben says, “There is strong negative correlation.”

    Is Ben correct? Give a reason for your answer.

    Show answer
    Yes. The crosses are close to the line and y goes down as x goes up, so there is strong negative correlation.
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  9. Either paper 3 marks
    The table shows the number of pupils on the roll of a school in each of eight years.
    Year20142015201620172018201920202021
    Number of pupils470475465455450420385350
    A time series graph is drawn to show the data. The first four points have been plotted. YearNumber of pupils201320152017201920212023300310320330340350360370380390400410420430440450460470480
    (a)

    Complete the graph by plotting the other four points.

    (b)

    Use the graph to estimate the number of pupils on the roll in 2022, by continuing the trend of the last three years.

    Show answer
    (a) Points plotted at \((2018, 450)\), \((2019, 420)\), \((2020, 385)\) and \((2021, 350)\)
    (b) \(317\)
    (a)YearNumber of pupils201320152017201920212023300310320330340350360370380390400410420430440450460470480
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  10. Either paper 3 marks

    Nine students recorded how long they spent revising for a test and the mark they scored. The test was marked out of \(100\).

    The scatter graph shows the results, with a line of best fit.

    24681012141618201020304050607080901000Revision time (hours)Test mark
    (a)

    Use the line of best fit to estimate the mark of a student who revised for 13 hours.

    (b)

    Anya says the graph can be used to estimate the mark of a student who revised for 40 hours.

    Explain why she would not be able to rely on that estimate.

    Show answer
    (a) \(56\)
    (b) 40 hours is far outside the range of the data (2 hours to 18 hours), so there is no evidence that the pattern carries on that far; the line would give a mark of 164, which is impossible out of 100.
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discia.org Scatter Graphs · sheet 1
Answers Scatter Graphs · sheet 1
  1. (a) Positive correlation
    (b) The warmer the day, the more bottles of cold water the shop sold
  2. (a) Vertical axis labelled Test mark; crosses plotted at (3.5, 26) and (5.5, 31)
    (b) Negative
    (c) Weak
    (a)1234567891051015202530354045500Gaming time (hours)Test mark
  3. (a) \(63\ \text{kg}\)
    (b) \(158\ \text{cm}\)
  4. (a) \((42, 20)\)
    (b) This student did far worse on Paper 2 than their Paper 1 mark suggests.
    (c) Positive correlation
  5. (a) A
    (b) D
  6. (a) Negative correlation
    (b) a straight line close to the mean point \((500, 473)\), for example from \((370, 538)\) to \((630, 408)\)
    (c) \(\text{£}423\)
    (b)300350400450500550600650700200250300350400450500550600650700750Sales of cups of tea (£)Sales of cups of coffee (£)
  7. The point \((2, 20)\) from the table has not been plotted: there is no cross for it. The line of best fit is drawn too low, so it is not close to the crosses.
  8. Yes. The crosses are close to the line and y goes down as x goes up, so there is strong negative correlation.
  9. (a) Points plotted at \((2018, 450)\), \((2019, 420)\), \((2020, 385)\) and \((2021, 350)\)
    (b) \(317\)
    (a)YearNumber of pupils201320152017201920212023300310320330340350360370380390400410420430440450460470480
  10. (a) \(56\)
    (b) 40 hours is far outside the range of the data (2 hours to 18 hours), so there is no evidence that the pattern carries on that far; the line would give a mark of 164, which is impossible out of 100.
discia.org Scatter Graphs · sheet 1