Question

the mean of observations : x, x+2, x+4, x+6 and x+8 is 11, find:

(i) The value of x

(ii) The mean of first three observations​

Answer 1

Given:

• The mean of observations :

•x,x+2,x+4 ,x+6 and x+8 is 11

To find :

i) The value of x :

ii) The mean 0f first Three observations :

Solution :

• As we know that ,

$\star \bold{mean = \frac{sum \: of \: observations}{ \: total \: number \: of \: observations} }$

i)

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

The value of x is 7 .

ii) First three observations are :

x , x+2 and x+4

=> 7 , 9 and 11

$\implies \: \bold{ mean} \: = \frac{7 + 9 + 11}{3} \\ \\ \implies \bold{mean} = \frac{27}{3} = 9$

The mean of first three observations is 9 .

Answer 2

Given:

• The mean of observations :

•x,x+2,x+4 ,x+6 and x+8 is 11

To find :

i) The value of x :

ii) The mean 0f first Three observations :

Solution :

• As we know that ,

\star \bold{mean = \frac{sum \: of \: observations}{ \: total \: number \: of \: observations} }⋆mean=

totalnumberofobservations

sumofobservations

i)

\begin{gathered}\implies \: 11 = \frac{x + x + 2 + x + 4 + x + 6 + x + 8}{5} \\ \\ \implies \: 11 = \frac{5x + 20}{5} \\ \\ \implies \: 55 = 5x + 20 \\ \\ \implies \: x = \frac{35}{5} = 7\end{gathered}

⟹11=

5

x+x+2+x+4+x+6+x+8

⟹11=

5

5x+20

⟹55=5x+20

⟹x=

5

35

=7

The value of x is 7 .

ii) First three observations are :

x , x+2 and x+4

=> 7 , 9 and 11

\begin{gathered}\implies \: \bold{ mean} \: = \frac{7 + 9 + 11}{3} \\ \\ \implies \bold{mean} = \frac{27}{3} = 9\end{gathered}

⟹mean=

3

7+9+11

⟹mean=

3

27

=9

The mean of first three observations is 9 .