Q. 84.1( 14 Votes )

Find the missing frequencies in the following frequency distribution, whose mean is 50.

Answer :

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



We have,


∑fi = 120 (given)


∑fi = 68 + f1 + f2 = 120


f1 + f2 = 120 - 68


f1 + f2 = 52…. Equation (i)


Now we have,


Mean = 50 (given)


Mean = = 50


50 =


50×68 + f1 + f2 = 3480 + 30f1 + 70f2


3400 + 50 f1 + 50f2 = 3480 + 30f1 + 70f2


50f1 - 30f1 + 50 f2 -70f2 = 3480 – 3400


20f1-20f2 = 80


20(f1-f2) = 80


f1-f2 = ……. Equation (ii)


by adding equation (i) and (ii) we get,


∑f1 = 56



From equation (ii)


f1-f2 = 4


28 – f2 = 4


f2 = 28-4 = 24


Hence missing frequencies are f1 = 28 and f2 = 24.


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