Q. 314.8( 6 Votes )

A survey regardin

Answer :

To find mean, we will solve by direct method:

We have got


Σfi = 50 & Σfixi = 7490


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 42, so the corresponding median class is 150 - 160 and accordingly we get Cf = 22(cumulative frequency before the median class).


Now, since median class is 150 - 160.


l = 150, h = 10, f = 20, N/2 = 25 and Cf = 22


Median is given by,




= 150 + 1.5


= 151.5


And we know that,


Mode = 3(Median) – 2(Mean)


= 3(151.5) – 2(149.8)


= 454.5 – 299.6


= 154.9


Hence, mean is 149.8, median is 151.5 and mode is 154.9.

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