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

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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