Question

Find the missing frequencies f1 and f2 if the mean of 50 observations given below
is 38.2.
Class interval Frequency
0 – 10 4
10 - 20 4
20 – 30 f1
30 - 40 10
40 - 50 f2
50 - 60 8
60 – 70 5

Answer 1

Solution :-

Class interval Fi Xi FiXi

0 – 10 4 5 20

10 - 20 4 15 60

20 – 30 f1 25 25fi

30 - 40 10 35 350

40 - 50 f2 45 45f2

50 - 60 8 55 440

60 – 70 5 65 325

⅀Fi = 31+f1+f2 ⅀FiXi = 1195+25fi+45f2

we know that,

• Mean = ⅀FiXi / ⅀Fi

so,

→ 31 + f1 + f2 = 50

→ f1 + f2 = 50 - 31

→ f1 + f2 = 19 --------------- Eqn.(1)

and,

→ 38.2 = (1195 + 25f1 + 45f2)/50

→ 1910 = 1195 + 25f1 + 45f2

→ 25f1 + 45f2 = 1910 - 1195

→ 25f1 + 45f2 = 715

→ 5(5f1 + 9f2) = 715

→ 5f1 + 9f2 = 143 ----------- Eqn.(2)

Multiply Eqn.(1) by 5 and subtracting the result from Eqn.(2),

→ (5f1 + 9f2) - 5(f1 + f2) = 143 - 5*19

→ 5f1 - 5f2 + 9f2 - 5f2 = 143 - 95

→ 4f2 = 48

→ f2 = 12 .

putting value of f2 in Eqn.(1),

→ f1 + 12 = 19

→ f1 = 19 - 12

→ f1 = 7 .

Hence, missing frequencies f1 and f2 are 7 and 12 respectively .

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