Find the mean of the following frequency distribution using a suitable method:


Class



20 - 30



30 - 40



40 - 50



50 - 60



60 - 70



Frequency



25



40



42



33



10


We will find the mean of the frequency distribution using step - deviation method, where A = Assumed mean and h = length of class interval.

Here, let A = 45 and h = 10


CLASS



MID - POINT(xi)



DEVIATION(di)


di = xi – 45



FREQUENCY(fi)



ui = di/h



fiui



20 - 30



25



- 20



25



- 2



- 50



30 - 40



35



- 10



40



- 1



- 40



40 - 50



45 = A



0



42



0



0



50 - 60



55



10



33



1



33



60 - 70



65



20



10



2



20



TOTAL





150




- 37



We have got


A = 45, h = 10, Σfi = 150 & Σfiui = - 37


∵ mean is given by



⇒


⇒


Thus, mean is 42.53.


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