OpenRevise

Exam questions · Maths · Statistics

Scatter Graphs

  • 6 exam questions
  • 18 marks
  • 9 quick checks
  1. 1 Write down [2 marks]

    Write down the type of correlation between (a) the number of hours of sunshine and the sales of sun cream, (b) the age of a car and its value.

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    Model answer

    (a) Positive correlation. (b) Negative correlation.

    Mark scheme

    • (a) Positive — B1
    • (b) Negative — B1
  2. 2 Estimate [5 marks]

    The scatter graph shows the hours of sunshine in a week and the number of plants sold by a garden centre in that week. A line of best fit is drawn. (a) Describe the correlation. (1 mark) (b) In one week there were 20 hours of sunshine. Use the line of best fit to estimate the number of plants sold. (2 marks) (c) Gavin uses the line to estimate the number of plants sold in a week with 60 hours of sunshine. Comment on the reliability of his estimate. (2 marks)

    A scatter graph of hours of sunshine and plants sold with positive correlation and a line of best fit through 10 at 0 hours and 50 at 20 hours.
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    Model answer

    (a) Positive correlation: as the hours of sunshine increase, the number of plants sold increases. (b) Going up from 20 hours to the line and across gives 50 plants. (c) The estimate is not reliable. 60 hours is outside the range of the data, so this is extrapolation and the pattern may not continue.

    Mark scheme

    • (a) Positive, in context — B1
    • (b) A line drawn up from 20 to the line of best fit and across — M1
    • (b) 50 (accept 48 to 52) — A1
    • (c) States that the estimate is not reliable — B1
    • (c) Explains that 60 is outside the range of the data — B1
  3. 3 Work out [3 marks]

    A line of best fit for the revision time, \(x\) hours, and the test score, \(y\), has the equation \(y = 3x + 5\). (a) Use the equation to estimate the score for 8 hours of revision. (1 mark) (b) What does the number 3 in the equation represent? (1 mark) (c) What does the number 5 in the equation represent? (1 mark)

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    Model answer

    (a) \(3 \times 8 + 5 = 29\). (b) The score goes up by about 3 marks for each extra hour of revision. (c) The estimated score with no revision.

    Mark scheme

    • (a) 29 — B1
    • (b) The score increases by 3 for each extra hour — B1
    • (c) The estimated score with 0 hours of revision — B1
  4. 4 Explain [2 marks]

    There is a positive correlation between ice cream sales and the number of people with sunburn. Hay says, “Eating ice cream causes sunburn.” Comment on what Hay says.

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    Model answer

    Hay is not necessarily correct. Correlation does not mean causation. Hot, sunny weather causes both ice cream sales and sunburn to increase.

    Mark scheme

    • States that correlation does not prove causation — B1
    • Gives a third factor such as hot weather — B1
  5. 5 Write down [2 marks]

    These are points on a scatter graph: \((1, 3)\), \((2, 4)\), \((3, 5)\), \((4, 6)\) and \((5, 15)\). (a) Write down the outlier. (1 mark) (b) Say how this should affect the line of best fit. (1 mark)

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    Model answer

    (a) \((5, 15)\), as it is far from the pattern of the other points. (b) The outlier should be ignored when the line of best fit is drawn.

    Mark scheme

    • (a) \((5, 15)\) — B1
    • (b) It should be ignored — B1
  6. 6 Work out [4 marks]

    A line of best fit goes through the points \((10, 30)\) and \((30, 70)\). (a) Work out the equation of the line. (3 marks) (b) Use your equation to estimate \(y\) when \(x = 25\). (1 mark)

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    Model answer

    (a) The gradient is \(\dfrac{70 - 30}{30 - 10} = 2\). Then \(30 = 2 \times 10 + c\), so \(c = 10\) and \(y = 2x + 10\). (b) \(2 \times 25 + 10 = 60\).

    Mark scheme

    • (a) Gradient \(\dfrac{40}{20}\) — M1
    • (a) Substitutes a point to find \(c\) — M1
    • (a) \(y = 2x + 10\) — A1
    • (b) 60 — B1 (follow through from (a))

Quick check

  1. 1

    What type of correlation has points sloping downwards from left to right?

    1. APositive
    2. BNone
    3. CPerfect
    4. DNegative
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    D: Negative

    One variable falls as the other rises.

  2. 2

    Which statement describes positive correlation?

    1. AAs one variable increases, the other decreases
    2. BThe points are scattered at random
    3. CAs one variable increases, the other increases
    4. DThe points form a curve
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    C: As one variable increases, the other increases

    Positive correlation slopes upwards.

  3. 3

    What is an outlier?

    1. AThe mean of the points
    2. BA point that does not fit the pattern of the others
    3. CA point on the line of best fit
    4. DThe first point plotted
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    B: A point that does not fit the pattern of the others

    Outliers are far from the trend.

  4. 4

    A line of best fit has equation \(y = 4x + 8\). Estimate \(y\) when \(x = 12\).

    1. A\(56\)
    2. B\(20\)
    3. C\(60\)
    4. D\(48\)
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    A: \(56\)

    \(4 \times 12 + 8 = 56\).

  5. 5

    Data runs from 2 to 16 hours of revision. What do we call an estimate for 25 hours?

    1. AInterpolation
    2. BCorrelation
    3. CCausation
    4. DExtrapolation
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    D: Extrapolation

    Outside the range of the data is extrapolation.

  6. 6

    Which estimate is likely to be more reliable?

    1. AOne far outside the range of the data
    2. BOne from a graph with no correlation
    3. COne inside the range of the data
    4. DOne from only two points
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    C: One inside the range of the data

    Interpolation is more reliable than extrapolation.

  7. 7

    Ice cream sales and sunburn are positively correlated. What is the best explanation?

    1. AIce cream causes sunburn
    2. BHot weather increases both
    3. CSunburn causes ice cream sales
    4. DThey are completely unrelated
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    B: Hot weather increases both

    A third factor can cause both.

  8. 8

    The line of best fit is \(y = 4x + 8\), where \(x\) is hours of revision and \(y\) is the test score. What does the gradient mean?

    1. AEach extra hour of revision adds about 4 marks
    2. BThe score with no revision is 4
    3. CThe maximum score is 8
    4. DEach mark takes 4 hours
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    A: Each extra hour of revision adds about 4 marks

    The gradient is the change in score for each extra hour.

  9. 9

    In \(y = 4x + 8\), what does 8 represent?

    1. AThe number of hours needed
    2. BThe gradient
    3. CThe maximum possible score
    4. DThe estimated score with no revision
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    D: The estimated score with no revision

    It is the \(y\)-intercept, the value when \(x = 0\).