Marks



10



11



12



13



14



16



19



20



Number of students



3



5



4



5



2



3



2



1


We can draw the table in the given format


Marks (x)



Number of students (f)



Cumulative frequency



Fx



10



3



3



30



11



5



8



55



12



4



12



48



13



5



17



65



14



2



19



38



16



3



22



48



19



2



24



38



20



1



25



20




N = 25




∑fx = 332



We have;


N = 25 (odd number)


Median =


= value of 13th term


= 13


Now,


∑fx = 332 and ∑f = N = 25


Mean =


Hence,


Mode = 3(median) – 2 (mean)


= 3×13 - 2×13.28


= 39 – 26.56


= 12.44


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