The lengths of 40 leaves of a plant are measured correct to the nearest milli meter, and the data obtained is represented in the following table:


Length (in mm)



Number of leaves



118 - 126


127 - 135


136 - 144


145 - 153


154 - 162


163 - 171


172 - 180



3


5


9


12


5


4


2



Find the median length of the leaves


(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5)

The cumulative frequency of the data can be calculated as:


Class interval



frequency



Cumulative frequency



117.5-126.5



3



3



126.5-135.5



5



8



135.5-144.5



9



17



144.5-153.5



12



29



153.5-162.5



5



34



162.5-171.5



4



38



171.5-180.5



2



40



As per the question,


N= 40



Hence,


Median class =144.5-153.5


Lower limit, l = 144.5


cf = 17


f = 12


h = 9


Now,


Median can be calculated as:




= 144.5 +


= 146.75


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