The following table shows the marks scored by 80 students in an examination:


Marks



Less than 5



Less than 10



Less than 15



Less than 20



Less than 25



Less than 30



Less than 35



Less than 40



Number of eggs



3



10



25



49



65



73



78



80



Calculate the mean marks correct to 2 decimal places.


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

Here, let A = 17.5 and h = 5


Since, the class intervals are less - than type, we’ll first convert it into exclusive type.


WEIGHT(G)



MID - POINT(xi)



DEVIATION(di)


di = xi – 17.5



NUMBER OF EGGS(fi)



ui = di/h



fiui



0 - 5



2.5



- 15



3



- 3



- 9



5 - 10



7.5



- 10



7



- 2



- 14



10 - 15



12.5



- 5



15



- 1



- 15



15 - 20



17.5 = A



0



24



0



0



20 - 25



22.5



5



16



1



16



25 - 30



27.5



10



8



2



16



30 - 35



32.5



15



5



3



15



35 - 40



37.5



20



2



4



8



TOTAL





80




17



We have got


A = 17.5, h = 5, Σfi = 80 & Σfiui = 17


∵ mean is given by



⇒


⇒


Thus, mean marks correct to 2 decimal places are 18.56.


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