Answer :

To find mean, we will solve by direct method:

We have got


Σfi = 100 & Σfixi = 4970


mean is given by





To find median,


Assume Σfi = N = Sum of frequencies,


h = length of median class,


l = lower boundary of the median class,


f = frequency of median class


and Cf = cumulative frequency


Lets form a table.



So, N = 100


N/2 = 100/2 = 50


The cumulative frequency just greater than (N/2 = ) 50 is 71, so the corresponding median class is 45 - 55 and accordingly we get Cf = 38(cumulative frequency before the median class).


Now, since median class is 45 - 55.


l = 45, h = 10, f = 33, N/2 = 50 and Cf = 38


Median is given by,




= 45 + 3.64


= 48.64


And we know that,


Mode = 3(Median) – 2(Mean)


= 3(48.64) – 2(49.7)


= 145.92 – 99.4


= 46.52


Hence, mean is 49.7, median is 48.64 and mode is 46.52.


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