Question

The mean of 5 observations x, x+2,x+4,x+6 and x+8 is 11 then the Value of x is

Answer 1

Given:

Mean= 11 and

observations are x, x+2 , x+4 , x+6

and x+8

As we know that

$\red{\boxed{mean = \frac{sum \: of \: observations}{number \: of \: observtions} }}$

So put the values

$\rightarrow \: 11 = \frac{x + x + 2 + x + 4 + x + 6 + x + 8}{5} \\ \rightarrow \: 11 = \frac{5x + 20}{5} \\ \rightarrow \: 11 \times 5 = 5x + 20 \\ \rightarrow \: 55 = 5x + 20 \\ \rightarrow \: 35 = 5x \\ \rightarrow \: x = \frac{35}{5} = 7$

Hence the value of the x is

$\boxed { \huge \blue{\mathfrak{7}}}$

Answer 2

$\huge{\red{\underline{\underline{\rm{Solution:}}}}}$

$\large{\underline{\bf{Given:}}}$

$\sf{\implies No.\;of\;observation=5}$

$\sf{\implies Observations=x,\;x+2,\;x+4,\;x+6,\;x+8}$

$\sf{\implies Mean=11}$

$\large{\underline{\bf{To\;Find:}}}$

$\sf{\implies Value\;of\;x.}$

$\large{\underline{\bf{Formula\;used:}}}$

$\sf{\implies Mean=\dfrac{Sum\;of\;observations}{No.\;of\;observations}}$

$\textsf{Now, put the values in the formula,}$

$\sf{\implies Mean=\dfrac{Sum\;of\;observations}{No.\;of\;observations}}$

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

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

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

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

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

$\large{\boxed{\boxed{\blue{\sf{\implies x=7}}}}}$

Hence, the value of x is 7.