Scatter graphs and correlation Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Scatter graphs and correlation questions. See exactly how to solve problems on reading a scatter graph, describing correlation, positive and negative correlation, strong and weak correlation.

reading a scatter graphdescribing correlationpositive and negative correlationstrong and weak correlationidentifying an outlierline of best fit
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
The scatter graph shows the test score (yy, in marks) against the revision time (xx, in hours) for 88 students. Describe the correlation shown by the scatter graph.

Worked solution

  1. Decide which way the points slope

    x↑⇒y↑x \uparrow \Rightarrow y \uparrow

    As the revision time increases, the test score increases too: the points climb from bottom left to top right. That is positive correlation.

  2. Decide how strong the trend is

    points lie close to a straight line\text{points lie close to a straight line}

    The points lie in a narrow band about a straight line, so the correlation is strong. Strong does not mean steep: it means the points hug the line.

  3. State the correlation

    Strong positive correlation\text{Strong positive correlation}

    The scatter graph shows strong positive correlation.

Answer
Strong positive correlation\text{Strong positive correlation}
Question 2
1 markeasy
The scatter graph shows the value of the car (yy, in thousand pounds) against the age of the car (xx, in years) for 88 cars. Describe the correlation shown by the scatter graph.

Worked solution

  1. Decide which way the points slope

    x↑⇒y↓x \uparrow \Rightarrow y \downarrow

    As the age increases, the value decreases: the points fall from top left to bottom right. That is negative correlation.

  2. Decide how strong the trend is

    points lie close to a straight line\text{points lie close to a straight line}

    The points lie in a narrow band about a straight line, so the correlation is strong. Strong does not mean steep: it means the points hug the line.

  3. State the correlation

    Strong negative correlation\text{Strong negative correlation}

    The scatter graph shows strong negative correlation.

Answer
Strong negative correlation\text{Strong negative correlation}
Question 3
1 markeasy
The scatter graph shows the weekly pocket money (yy, in pounds) against the age (xx, in years) for 88 children. Describe the correlation shown by the scatter graph.

Worked solution

  1. Decide which way the points slope

    x↑⇒y no patternx \uparrow \Rightarrow y \text{ no pattern}

    As you look from left to right the points do not drift up or down — high xx-values come with high and low yy-values alike. There is no trend in either direction.

  2. Decide how strong the trend is

    points spread all over the graph\text{points spread all over the graph}

    The points do not sit near any straight line at all, so there is no correlation to describe as strong or weak — there is simply no correlation.

  3. State the correlation

    No correlation\text{No correlation}

    The scatter graph shows no correlation.

Answer
No correlation\text{No correlation}
Question 4
1 markeasy
The scatter graph shows the arm span above 140140 cm (yy, in cm) against the height above 140140 cm (xx, in cm) for 88 pupils. Describe the correlation shown by the scatter graph.

Worked solution

  1. Decide which way the points slope

    x↑⇒y↑x \uparrow \Rightarrow y \uparrow

    As the height increases, the arm span increases too: the points climb from bottom left to top right. That is positive correlation.

  2. Decide how strong the trend is

    points are spread out about the line\text{points are spread out about the line}

    A trend is there, but the points are scattered quite widely either side of the line rather than hugging it, so the correlation is weak.

  3. State the correlation

    Weak positive correlation\text{Weak positive correlation}

    The scatter graph shows weak positive correlation.

Answer
Weak positive correlation\text{Weak positive correlation}
Question 5
1 markeasy
The scatter graph shows the exam mark (yy, in marks) against the number of hours of TV watched each week (xx, in hours) for 88 students. Describe the correlation shown by the scatter graph.

Worked solution

  1. Decide which way the points slope

    x↑⇒y↓x \uparrow \Rightarrow y \downarrow

    As the TV time increases, the exam mark decreases: the points fall from top left to bottom right. That is negative correlation.

  2. Decide how strong the trend is

    points are spread out about the line\text{points are spread out about the line}

    A trend is there, but the points are scattered quite widely either side of the line rather than hugging it, so the correlation is weak.

  3. State the correlation

    Weak negative correlation\text{Weak negative correlation}

    The scatter graph shows weak negative correlation.

Answer
Weak negative correlation\text{Weak negative correlation}

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