# Median, mean, standard deviation, interquartile range

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.

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#### 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.