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    PracticeAQA GCSEAQA GCSE Statistics Higher Tier Paper 1Question 08.3
    Medium2 marksStructured
    Data Visualization and RepresentationCorrelationScatter DiagramData InterpretationGCSE

    AQA GCSE · Question 08.3 · Data Visualization and Representation

    0 1 2 3 4 5 Waiting time (minutes) 0 30 60 90 120 150 180 210 240 270 300 Minutes after 9am

    Here is some information about the results sampled for later in the day.

    • After 12.30pm but before 1.30pm all five customers sampled waited between 4 and 5 minutes.
    • From 1.30pm, the six results showed a strong negative correlation.

    Describe the correlation shown by each of these two new sets of data.

    How to approach this question

    1. **Analyse the first piece of information**: "After 12.30pm but before 1.30pm all five customers sampled waited between 4 and 5 minutes." * 12.30pm is 3.5 hours after 9am = 210 minutes. 1.30pm is 4.5 hours after 9am = 270 minutes. So, x-values are between 210 and 270. * The y-values (waiting time) are all between 4 and 5. * If you plotted these points, they would form a horizontal cluster. A horizontal line has no slope, which means there is **no correlation**. 2. **Analyse the second piece of information**: "From 1.30pm, the six results showed a strong negative correlation." * The question explicitly states the correlation type. * Describe what this means: as one variable (time) increases, the other variable (waiting time) decreases. 3. Write down the description for each part.

    Full Answer

    **After 12.30pm but before 1.30pm:** This set of data would show **no correlation** or **very weak correlation**. The points would be clustered in a horizontal band, as the waiting time (y-value) is consistently high (between 4 and 5) while the time of day (x-value) changes. **From 1.30pm:** This set of data shows a **strong negative correlation**, as stated in the question. This means as the time after 1.30pm increases, the waiting time decreases.
    This question tests the understanding of what different patterns on a scatter diagram mean in terms of correlation. * **First period (12.30pm - 1.30pm)**: The information states that all customers waited between 4 and 5 minutes. This means the y-values of the data points would be clustered in a narrow horizontal band at the top of the graph. As the x-value (time) increases, the y-value (waiting time) does not systematically increase or decrease; it stays roughly constant. This pattern represents **no correlation** (or very weak correlation). * **Second period (From 1.30pm)**: The question explicitly states that these results showed a **strong negative correlation**. This means that as the time of day got later, the waiting time for customers got shorter. On a graph, the points would trend downwards from left to right.

    Common mistakes

    ✗ For the first part, guessing positive or negative correlation instead of realising the horizontal pattern means no correlation. ✗ Simply writing "negative correlation" for the second part without the word "strong", which was given in the question.
    Question 08.2All questionsQuestion 08.4

    Practice the full AQA GCSE Statistics Higher Tier Paper 1

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