# find the mean marks of a student from the following cumulative frequency distribution marks number of students 0 and above 80 10 and above 77 20 and above 72 30 and above 65 40 and above 55 50 and above 43 60 and above 28 70 and above 16 80 and above 10 90 and above 8 100 and above 0

 Greater than type Class interval x cumulative frequency frequency(f) fx 0 and above 0-10 5 80 3 15 10 and above 10-20 15 77 5 75 20 and above 20-30 25 72 7 175 30 and above 30-40 35 65 10 350 40 and above 40-50 45 55 12 540 50 and above 50-60 55 43 15 825 60 and above 60-70 65 28 12 780 70 and above 70-80 75 16 6 450 80 and above 80-90 85 10 2 170 90 and above 90-100 95 8 8 760 100 and above 100-110 105 0 0 0 80 4140

$\mathrm{Mean}=\frac{\sum _{}^{}fx}{\sum _{}^{}f}\phantom{\rule{0ex}{0ex}}=\frac{4140}{80}\phantom{\rule{0ex}{0ex}}=51.75$

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0 and above, 20 and above........... are marks and 80,77,72,.......... are number of students
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