Q. 64.8( 19 Votes )

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Answer :


For median:


We have, total frequency, N = 100


N/2 = 100/2 = 50


Observe, cf = 76 is just greater than 50.


Thus, median class = 7-10


Median is given by



Where,


L = Lower class limit of median class = 7


N/2 = 50


cf = cumulative frequency of the class preceding median class = 36


f = frequency of the median class = 40


h = class interval of the median class = 3


Substituting these values in the formula of median, we get




Median = 7 + 1.05


Median = 8.05


For mean:


Mean is given by



[Refer the values from the table given above]


Mean = 8.32


For mode:


Here, highest frequency is 40.


So, the modal class = 7-10


Mode is given by



Where,


L = Lower class limit of the modal class = 7


h = class interval of the modal class = 3


f1 = frequency of the modal class = 40


f0 = frequency of the class preceding the modal class = 30


f2 = frequency of the class succeeding the modal class = 16


Substituting values in the formula of mode,




Mode = 7 + 0.88


Mode = 7.88


Thus, median is 8.05, mean is 8.32 and mode is 7.88.


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