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Direct Method of Finding Mean

Class 0-2020-...

Question

Class 0-20 20-40 40-60 60-80 80-100
Frequency 19 $f_{1}$ 32 $f_{2}$ 19 Total 120
Mean of the above frequency table is given as $50$ . Find $f_{1}$ and $f_{2}$ .

A

28

and

22

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B

25

and

25

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C

24

and

26

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D

20

and

30

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Solution

The correct option is B $25$ and $25$
Class Marks will be $10, 30, 50, 70, 90$ ( $x_{i}$ ).
Mean, $u = \frac{\sum x \times f}{\sum f}$
$u = 50 = \frac{3500 + 30 \times f_{1} + 70 \times f_{2}}{120}$
$30 \times f_{1} + 70 \times f_{2} = 2500$
Also, $f_{1} + f_{2} = 120$
Solving the above equation we get,
$f_{1} = 25$ and $f_{2} = 25$ .
Ans- Option B

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