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    Median, mean, standard deviation, interquartile range

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    Two hundred candidates took each of two examination papers. The diagram shows the cumulative frequency graphs for their marks.

    i) Estimate the median marks for each of the papers.
    ii) State, with a reason, which of the two papers was the easier one.
    iii) It is suggested that the marks on Paper 2 were less varies than those on Paper 1. Use interquartile ranges to comment on this suggestion.

    An additional two questions are attached.

    © BrainMass Inc. brainmass.com June 4, 2020, 12:58 am ad1c9bdddf


    Solution Preview

    See the attached file.

    (i) N=200
    Median = (N+1)/2 th term i.e. 100.5 th term
    So we take the average of marks obtained by 100th and 101st student
    From Graph
    Median (Paper 1) = 38 (approx. from graph)
    Median (Paper 2) = 61 (approx. from graph)

    (ii) In the easier paper, more students will score higher marks. Hence, the median for the easier paper should be higher. Since, ...

    Solution Summary

    This post show how to calculate median, interquartile range and other descriptive statistics using the cumulative frequency chart.