Q. 14.3( 9 Votes )

Find the mean, mode and median of the following frequency distribution:

Answer :

To find mean, we will solve by direct method:

We have got


Σfi = 50 & Σfixi = 1910


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 = 50


N/2 = 50/2 = 25


The cumulative frequency just greater than (N/2 = ) 25 is 37, so the corresponding median class is 40 - 50 and accordingly we get Cf = 25(cumulative frequency before the median class).


Now, since median class is 40 - 50.


l = 40, h = 10, f = 16, N/2 = 25 and Cf = 25


Median is given by,



⇒ 


= 40 + 0


= 40


And we know that,


Mode = 3(Median) – 2(Mean)


= 3(40) – 2(38.2)


= 120 – 76.4


= 43.6


Hence, mean is 38.2, median is 40 and mode is 43.6.

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