Math, asked by swaroopnjr, 1 year ago

find the missing frequencies f1 f2 and f3 in the following frequency distribution when it is given that f2:f3 and mean=50

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Answered by Anonymous
237

Answer:

f1 = 28, f2 = 32, f3 = 24

Step-by-step explanation:

Since the ratio f2 : f3 = 4 : 3, we can write f2 = 4t and f3 = 3t for some value t.

The total number of observations is 120, so

17 + f1 + f2 + f3 + 19 = 120

=> f1 + 4t + 3t = 120 - 17 - 19

=> f1 + 7t = 84.      (*)

The mean is 50, so

( 10 x 17 + 30 f1 + 50 f2 + 70 f3 + 90 x 19 ) / 120 = 50

=> 170 + 30 f1 + 200 t + 210 t + 1710 = 50 x 120 = 6000

=> 17 + 3 f1 + 20 t + 21 t + 171 = 600

=> 3 f1 + 41 t = 600 - 171 - 17 = 412.     (**)

Multiplying equation (*) by 3, we have

3 f1 + 21 t = 3 x 84 = 252.

Subtracting this from equation (**), we get

20 t = 412 - 252 = 160   =>   t = 8.

So f2 = 4t = 32, f3 = 3t = 24, and f1 = 84 - 7t = 84 - 56 = 28.


swaroopnjr: thank you very much sir
Anonymous: My pleasure! I hope you find the reasoning helpful for other similar problems.
Answered by ajaykumarfdk2019
16

Answer:

Given frequency =120

⇒17+f

1

+32+f

2

+19=120

⇒f

1

+f

2

=52

Mean =

∑f

i

∑x

i

f

i

⇒mean =

120

(10×17)+(30×f1)+(50×32)+(72×f2)+(90×19)

⇒mean =

120

170+30f

1

+1600+70f

2

+1710

=50

⇒3f

1

+7f

2

=252

⇒3f

1

+7(52−f

1

)=252

⇒f

1

=28

⇒f

2

=24

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