The marks obtained by 100 students of a class in an examination are given below:


Marks



Number of students



0 - 5



2



5 - 10



5



10 - 15



6



15 - 20



8



20 - 25



10



25 - 30



25



30 - 35



20



35 - 40



18



40 - 45



4



45 - 50



2



Draw cumulative frequency curves by using (i) 'less than' series and (ii) 'more than' series.


Hence, find the median.

(i) The frequency distribution table for ‘less than’ type is:


MARKS



CUMULATIVE FREQUENCY (Cf)



Less than 5



2



Less than 10



2 + 5 = 7



Less than 15



7 + 6 = 13



Less than 20



13 + 8 = 21



Less than 25



21 + 10 = 31



Less than 30



31 + 25 = 56



Less than 35



56 + 20 = 76



Less than 40



76 + 18 = 94



Less than 45



94 + 4 = 98



Less than 50



98 + 2 = 100



(ii) The frequency distribution table for ‘more than’ type is:


MARKS



CUMULATIVE FREQUENCY (Cf)



More than 0



98 + 2 = 100



More than 5



93 + 5 = 98



More than 10



87 + 6 = 93



More than 15



79 + 8 = 87



More than 20



69 + 10 = 79



More than 25



44 + 25 = 69



More than 30



24 + 20 = 44



More than 35



6 + 18 = 24



More than 40



2 + 4 = 6



More than 45



2



Plotting points for ‘less - than ogive’ and ‘more - than ogive’ on the graph,



In this type of graph where ‘less than ogive’ and more than ogive’ are plotted in the same graph, median is found on x - axis by the intersection of these two ogives.


Here, median = 29.5


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