Question

The mean of the following distribution is 35. Find the values of x₁ and x₂, if the sum of the frequencies is 25.

Answer 1

It is given that ,

Sum of the frequencies = 25

From the table ,

=> Sigma ( fixi ) = 17 + x1 + x2 = 25 ---( 1 )

=> x1 + x2 = 25 - 17

=> x1 + x2 = 8 -----( 2 )

Mean = 35 [ given ]

=> [ Sigma fixi ]/( sigma fi ) = 35

=> ( 605 + 15x1 + 45x2 )/25 = 35

=> 605 + 15x1 + 45x2 = 875

=> 15x1 + 45x2 = 875 - 605

=> 15x1 + 45x2 = 270

Divide each term by 15 , we get

=> x1 + 3x2 = 18 ----( 3 )

Subtracting equation ( 2 ) from ( 3 ),

we get,

2x2 = 10

=> x2 = 5

put x2 = 5 in equation ( 2 ) , we get

x1 = 8 - 5 = 3

Therefore ,

x1 = 3 , x2 = 5

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