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The Mean of the Folowing is 62.8 and the Sum of All the Frequencies is 50. Find the Missing Frequency `F_1 and F_2` - Mathematics

The mean of the folowing is 62.8 and the sum of all the frequencies is 50. find the missing frequency `f_1 and f_2` 

Class  0-20 20-40 40-60 60-80 80-100 100-120
Freq 5 `f_1` 10  `f_2` 7 8

 

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Solution

class  Freq (f) Mid value  fx
0-20 5 10 50
20-40 `f_1` 30 30`f_1`
40-60 10 50 500
60-80 `f_2` 70 70`f_2`
80-100 7 90 630
100-120 8 110 880
total      30+`f_1`+`f_2`   2060+30`f_1`+70`f_2`

Now, `∑ f= 30+f_1+f_2 and ∑ fx=2060+30f_1+70f_2` .........(1)    

∑ f=50; mean=62.8 ...........(2)  

From(1) 

`30+f_1+f_2=50`

`f_1+f_2=20`.........(3) 

Using (1) and (2) 

`Mean=(2060+30f_1+70f_2)/50` 

`62.8=(2060+30fi+70f_2)/50`

`2060+30f_1+70f_2=62.8xx50` 

`2060+30f_1+70f_2=3140` 

`30f_1+70f_2=1080` 

`3f_1+7f_2=108`........(4) 

From (3)and (4) 

`f_1=8` 

`f_2=12`

 

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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode)
Exercise 24 (B) | Q 9 | Page 362
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