Question

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

Answer 1

Given frequency distribution :

x :

10  30  50  70  90

f:

17  f1  32  f2  19

Total 120

Solution :

From the table :

Σfixi = 3480 + 30f1 + 70f2  , Σfi = 68 + f1 + f2

Given : Σfi = 120 , Mean = 50

Σfi = 68 + f1 + f2

120 = 68 + f1 + f2

f1 + f2 = 120 - 68

f1 + f2 = 52  

f1 = 52 - f2 ………….(1)  

MEAN = Σfixi / Σfi

50 = (3480 + 30f1 + 70f2) /120

50 × 120 = (3480 + 30f1 + 70f2)

6000 = 3480 + 30f1 + 70f2

6000 - 3480 = 30f1 + 70f2

2520 = 30f1 + 70f2

30f1 + 70f2 = 2520

10 ( 3f1 + 7f2) = 2520

3f1 + 7f2 = 2520/10

3f1 + 7f2 = 252 ……………(2)

3(52 - f2) + 7f2 = 252  

[From eq 1]

156 - 3f2 + 7f2 = 252

156 + 4f2 = 252  

4f2 = 252 - 156  

4f2 = 96

f2 = 96/4

f2 = 24

Putting this value of f2 in eq 1  

f1 = 52 - f2

f1 = 52 - 24

f1 = 28  

Hence, the value of f1 is 28 & f2 is 24 .

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Answer 2

Step-by-step explanation:

here is your answer

X=28 and y=24