Question

if x1, x2, xn.... are n values in a variable x such that summation i=1(xi-2) = 110 and summation i=1(xi-5)= 20. find the value of n and its mean

Answer 1

$<b>Answer</b>$ : n = 30 and Mean = 17/3

$<b>Step-by-step explanation</b>$ :

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

$<b>∑ - 2n = 110</b>$ _(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

$<b>∑ - 5n = 20</b>$ _(ii)

$<b>Subtracting (i) from (ii) we get,</b>$

∑ - 5n - ( ∑ - 2n ) = 20 - 110

- 3n = - 90

n = 30

$<b>Substituting value of n kn eq(ii)</b>$

∑ - 5(30) = 20

∑ = 20 + 150 = 170

So, $<b>Mean = 170/30 or 17/3</b>$

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