Question

If the mean of first five observations x, x+2, x+4, x+6, + 8 is 11., find mean of first three observations.​

Answer 1

$\LARGE\sf {\underline{\underline\green{Required \:  Answer:-}}}$

$\sf{11 = \dfrac{x + (x + 2)(x + 4)(x + 6)(x + 8)}{5} }$

$\sf{\implies{11 = \dfrac{5x + 20}{5} }}$

$\sf{\implies{55 = 5x + 20}}$

$\sf{\implies{5x = 35}}$

$\sf{\implies{ \sf{x = 7}}}$

$\sf \large{\therefore{Mean \: of \: first \: three \: observations:} }$

$\sf{ = \dfrac{x(x + 2) + (x + 4)}{3} } = \dfrac{3x + 6}{3}$

$\large\sf { \underline{\boxed{ = x + 2 = 7 + 2 = 9}}}$

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Answer 2

$\LARGE\sf {\underline{\underline\green{Required \:  Answer:-}}}$

$\sf{11 = \dfrac{x + (x + 2)(x + 4)(x + 6)(x + 8)}{5} }$

$\sf{\implies{11 = \dfrac{5x + 20}{5} }}$

$\sf{\implies{55 = 5x + 20}}$

$\sf{\implies{5x = 35}}$

$\sf{\implies{ \sf{x = 7}}}$

$\sf \large{\therefore{Mean \: of \: first \: three \: observations:} }$

$\sf{ = \dfrac{x(x + 2) + (x + 4)}{3} } = \dfrac{3x + 6}{3}$

$\large\sf { \underline{\boxed{ = x + 2 = 7 + 2 = 9}}}$

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