Cumulative Frequency

    OCR
    GCSE

    Cumulative frequency analysis requires the calculation of running totals from grouped continuous data to visualize the accumulation of values across a range. Candidates must construct cumulative frequency graphs (ogives) by plotting upper class boundaries against cumulative totals to estimate robust measures of location and spread, specifically the median, quartiles, and percentiles. This graphical method underpins the construction of box plots, enabling the rigorous comparison of distributions through the analysis of central tendency and interquartile variation.

    0
    Objectives
    3
    Exam Tips
    3
    Pitfalls
    5
    Key Terms
    4
    Mark Points

    What You Need to Demonstrate

    Key skills and knowledge for this topic

    • Award 1 mark for plotting points strictly at the upper class boundaries of each interval
    • Award 1 mark for joining points with a smooth curve or straight line segments starting from the lowest boundary at frequency 0
    • Credit responses that clearly indicate reading of the median or quartiles by drawing construction lines on the graph
    • Award 1 mark for calculating the Interquartile Range (IQR) as Upper Quartile (UQ) minus Lower Quartile (LQ) using values read from the candidate's graph

    Example Examiner Feedback

    Real feedback patterns examiners use when marking

    • "Check your plotting — you used midpoints, but cumulative frequency represents 'up to' a value, so use upper boundaries"
    • "You found the median correctly. To get full marks, show the construction lines on the graph"
    • "Be careful with 'greater than' questions — the graph shows 'less than or equal to'. You need to subtract your reading from the total"
    • "When comparing, mention both a measure of average (median) and a measure of spread (IQR) with context"

    Marking Points

    Key points examiners look for in your answers

    • Award 1 mark for plotting points strictly at the upper class boundaries of each interval
    • Award 1 mark for joining points with a smooth curve or straight line segments starting from the lowest boundary at frequency 0
    • Credit responses that clearly indicate reading of the median or quartiles by drawing construction lines on the graph
    • Award 1 mark for calculating the Interquartile Range (IQR) as Upper Quartile (UQ) minus Lower Quartile (LQ) using values read from the candidate's graph

    Examiner Tips

    Expert advice for maximising your marks

    • 💡Always draw horizontal and vertical construction lines on your graph to show the examiner exactly where you read your values
    • 💡When asked to estimate the number of values 'greater than' x, read the cumulative frequency for x and subtract it from the total frequency
    • 💡Ensure your curve passes through the plotted points; do not force a 'line of best fit' that misses the specific cumulative data points

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Plotting points at the midpoints of class intervals rather than the upper boundaries, causing a horizontal shift in the distribution
    • Failing to anchor the cumulative frequency curve at the start of the first interval (cumulative frequency = 0), leaving the curve 'floating'
    • Misinterpreting the vertical scale when reading off quartiles, often assuming 1 small square = 1 unit when it may represent 2 or 5 units

    Key Terminology

    Essential terms to know

    Calculation of cumulative totals from grouped frequency tables
    Plotting coordinates using Upper Class Boundaries (UCB)
    Estimation of Median, Quartiles (Q1, Q3), and Interquartile Range (IQR)
    Construction and interpretation of Box Plots (Box-and-Whisker diagrams)
    Comparative analysis of distributions regarding consistency and average

    Likely Command Words

    How questions on this topic are typically asked

    Construct
    Estimate
    Calculate
    Draw
    Compare

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