Box Plots

    OCR
    GCSE

    Box plots (box-and-whisker diagrams) provide a standardized graphical summary of a dataset based on the five-number summary: minimum, lower quartile, median, upper quartile, and maximum. They are essential for visualizing the dispersion and skewness of data, facilitating the rapid comparison of multiple distributions through measures of location and spread. Advanced application involves the rigorous calculation of the interquartile range (IQR) to identify and plot outliers, typically defined as values falling beyond specific boundaries relative to the quartiles. Mastery requires interpreting the asymmetry of the box and whiskers to deduce the underlying distribution characteristics.

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    Objectives
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    Exam Tips
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    Pitfalls
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    Key Terms
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    Mark Points

    What You Need to Demonstrate

    Key skills and knowledge for this topic

    • Award 1 mark for accurately plotting the median, lower quartile, and upper quartile at the correct scale positions
    • Award 1 mark for correctly extending whiskers to the minimum and maximum values, ensuring they do not pass through the box
    • Credit responses that compare distributions by explicitly citing the difference in medians to infer a shift in average within context
    • Credit responses that compare the Interquartile Range (IQR) to infer differences in consistency or spread of data
    • Award 1 mark for identifying the direction of skew (positive/negative) based on the position of the median relative to the quartiles

    Example Examiner Feedback

    Real feedback patterns examiners use when marking

    • "You have correctly calculated the IQR, but you need to explain what a smaller IQR implies about the consistency of the data"
    • "Ensure your comparison mentions both the median and a measure of spread like the IQR, linking both back to the scenario"
    • "Check your plotting scale; you placed the Upper Quartile at 14.5 instead of 15"
    • "Excellent use of the term 'skewness' to describe the shape of the distribution — now link this to the data's distribution"

    Marking Points

    Key points examiners look for in your answers

    • Award 1 mark for accurately plotting the median, lower quartile, and upper quartile at the correct scale positions
    • Award 1 mark for correctly extending whiskers to the minimum and maximum values, ensuring they do not pass through the box
    • Credit responses that compare distributions by explicitly citing the difference in medians to infer a shift in average within context
    • Credit responses that compare the Interquartile Range (IQR) to infer differences in consistency or spread of data
    • Award 1 mark for identifying the direction of skew (positive/negative) based on the position of the median relative to the quartiles

    Examiner Tips

    Expert advice for maximising your marks

    • 💡When asked to compare, always write two distinct sentences: one comparing the medians (average) and one comparing IQRs (consistency), both linked to the context
    • 💡Use the term 'consistent' when describing a smaller IQR; this is a key discriminator vocabulary word for high-level interpretation in OCR mark schemes
    • 💡Check the scale carefully before plotting; incorrect plotting of a single value often results in the loss of the accuracy mark for the whole diagram

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Plotting the quartiles or median at incorrect intervals due to misreading the scale (e.g., assuming one small square is 1 unit when it is 2)
    • Stating 'Group A is higher' without specifying which statistic (median) is being compared or failing to relate it to the context
    • Confusing the range with the interquartile range when commenting on the spread or consistency of the data
    • Drawing a line through the entire box plot rather than stopping the whiskers at the box edges

    Study Guide Available

    Comprehensive revision notes & examples

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    Key Terminology

    Essential terms to know

    Construction from five-number summary
    Calculation and representation of outliers
    Interpretation of skewness and distribution shape
    Comparative analysis of location and spread

    Likely Command Words

    How questions on this topic are typically asked

    Construct
    Compare
    Calculate
    Interpret
    State

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