Question

if x1,x2,...,xn are the values of n in the variable x such that summation(xi-2)=110 and summation(xi-5)=20 then find the value of n and it's mean

Answer 1

Answer : n = 30 and Mean = 17/3

Step-by-step explanation :

Since we know that,

∑ = ( x1 + x2 +.......+ xn )

So, ∑( xi - 2 ) = ( x1 - 2 ) + ( x2 - 2 ) +......+ ( xn - 2 )

Also, ∑( xi - 2 ) = 110

( x1 - 2 ) + ( x2 - 2 ) +......+ ( xn - 2 ) = 110

( x1 + x2 +.....+ xn ) - 2n = 110

∑ - 2n = 110 _(i)

Similarly,

∑( xi - 5 ) = ( x1 - 5 ) + ( x2 - 5 ) +.....+ ( xn - 5 )

Also, ∑( xi - 5 ) = 20

( x1 - 5 ) + ( x2 - 5 ) +.....+ ( xn - 5 ) = 20

( x1 + x2 +..... + xn ) - 5n = 20

∑ - 5n = 20 _(ii)

Subtracting (i) from (ii) we get,

∑ - 5n - ( ∑ - 2n ) = 20 - 110

- 3n = - 90

n = 30

Substituting value of n kn eq(ii)

∑ - 5(30) = 20

∑ = 20 + 150 = 170

So, Mean = 170/30 or 17/3

Answer 2

Please find the value of x also.....