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 temperature and the number of hot drinks sold, (b) the shoe size and the age of children. [2 marks]

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    Model answer

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

    Mark scheme

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

    The scatter graph shows the temperature and the number of ice creams sold by a shop. A line of best fit is drawn. (a) Describe the relationship between the temperature and the number of ice creams sold. [1 mark] (b) Use the line of best fit to estimate the number of ice creams sold when the temperature is 20 degrees. [2 marks] (c) Use the line of best fit to estimate the temperature when 88 ice creams were sold. [2 marks]

    A scatter graph of temperature and ice creams sold with positive correlation and a line of best fit through 60 at 20 degrees and 88 at 27 degrees.
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    Model answer

    (a) As the temperature increases, the number of ice creams sold increases. (b) Going up from 20 degrees to the line and across gives 60. (c) Going across from 88 on the vertical axis to the line and down gives 27 degrees.

    Mark scheme

    • (a) As the temperature increases, the sales increase — B1
    • (b) A line drawn up from 20 to the line of best fit and across — M1
    • (b) 60 (accept 58 to 62) — A1
    • (c) A line drawn across from 88 to the line of best fit and down — M1
    • (c) 27 (accept 26 to 28) — A1
  3. 3 Calculate [3 marks]

    A line of best fit for the hours of revision, \(x\), and the test score, \(y\), has the equation \(y = 2x + 8\). (a) Use the equation to estimate the score for 20 hours of revision. [1 mark] (b) Mia uses the equation to estimate the score for 60 hours of revision. Calculate her estimate. [1 mark] (c) Explain why her estimate is not reliable. [1 mark]

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    Model answer

    (a) \(2 \times 20 + 8 = 48\). (b) \(2 \times 60 + 8 = 128\). (c) The estimate is outside the range of the data, and it is above the maximum possible score of 100.

    Mark scheme

    • (a) 48 — B1
    • (b) 128 — B1
    • (c) Outside the range of the data, or higher than the maximum score — B1
  4. 4 Explain [2 marks]

    There is a strong positive correlation between the number of fire engines at a fire and the amount of damage. Does this show that the fire engines cause the damage? Explain your answer. [2 marks]

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    Model answer

    No. Correlation does not show causation. A bigger fire needs more fire engines and also causes more damage.

    Mark scheme

    • No, correlation does not show causation — B1
    • A third factor, such as the size of the fire — B1
  5. 5 Calculate [3 marks]

    A line of best fit goes through the points \((0, 6)\) and \((20, 16)\). (a) Calculate the gradient of the line. [1 mark] (b) Write down the equation of the line. [1 mark] (c) Use your equation to estimate \(y\) when \(x = 14\). [1 mark]

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    Model answer

    (a) \(\dfrac{16 - 6}{20 - 0} = 0.5\). (b) \(y = 0.5x + 6\). (c) \(0.5 \times 14 + 6 = 13\).

    Mark scheme

    • (a) 0.5 — B1
    • (b) \(y = 0.5x + 6\) — B1
    • (c) 13 — B1 (follow through from (b))
  6. 6 Calculate [3 marks]

    Ben draws a line of best fit through the points \((10, 8)\) and \((30, 48)\). (a) Calculate the gradient. [1 mark] (b) Find the equation of the line in the form \(y = mx + c\). [2 marks]

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    Model answer

    (a) \(\dfrac{48 - 8}{30 - 10} = 2\). (b) \(8 = 2 \times 10 + c\), so \(c = -12\) and \(y = 2x - 12\).

    Mark scheme

    • (a) 2 — B1
    • (b) Substitutes a point to find \(c\) — M1
    • (b) \(y = 2x - 12\) — A1

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 \(x = 0\).