Find the arithmetic mean of the following frequency distribution using step - deviation method:


Age (in years)



18 - 24



24 - 30



30 - 36



36 - 42



42 - 48



48 - 54



Number of workers



6



8



12



8



4



2


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 = 33 and h = 6


AGE(years)



MID - POINT(xi)



DEVIATION(di)


di = xi – 33



NUMBER OF WORKERS(fi)



ui = di/h



fiui



18 - 24



21



- 12



6



- 2



- 12



24 - 30



27



- 6



8



- 1



- 8



30 - 36



33 = A



0



12



0



0



36 - 42



39



6



8



1



8



42 - 48



45



12



4



2



8



48 - 54



51



18



2



3



6



TOTAL





40




2



We have got


A = 33, h = 6, Σfi = 40 & Σfiui = 2


mean is given by





Thus, mean age is 33.3 years.


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