Find the missing frequency p for the following frequency distribution whose mean is 28.25.


X



15



20



25



30



35



40



F



8



7



P



14



15



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Let’s draw the table and calculate the relative value of variables ∑xi×fi


(xi)



(fi)



(xi×fi)



15



8



120



20



7



140



25



P



25P



30



14



420



35



15



525



40



6



240




∑fi = 50 + P



∑xi×fi = 1445 + 25P



By putting the formula of mean we get;


Mean = = 28.25 (given)



28.25(50 + P) = 1445 + 25P


28.25×50 + 28.25×P = 1445 + 25P


1412.50 + 28.25P = 1445 + 25P =


28.25P – 25P = 1445 – 1412.50


3.25P = 32.5



= 10


Hence the value of P is 10.


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