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June 2019 p61 q4
2458
The Mathematics and English A-level marks of 1400 pupils all taking the same examinations are shown in the cumulative frequency graphs below. Both examinations are marked out of 100.
Use suitable data from these graphs to compare the central tendency and spread of the marks in Mathematics and English.
Solution
To find the median, locate the 700th pupil on the cumulative frequency graph (since there are 1400 pupils in total). For Mathematics, the median is at 40 marks, and for English, it is at 55 marks.
To find the interquartile range (IQR), locate the 350th and 1050th pupils on the cumulative frequency graph. For Mathematics, the IQR is from 12 to 80, giving an IQR of 68. For English, the IQR is from 42 to 62, giving an IQR of 20.
Thus, the median of English is larger than the median of Mathematics, indicating a higher central tendency for English marks. The IQR for Mathematics is larger than for English, indicating a greater spread in Mathematics marks.