Question

please help me out whit it​

Answer 1

GIVEN :-

• The observation :- x , x + 2 , x + 4 , x + 6 and x + 8
• The mean of x , x + 2 , x + 4 , x + 6 and x + 8 is 11.

TO FIND :-

• The value of x.

SOLUTION :-

$\\ : \implies \displaystyle \sf \:mean = \frac{sum \: of \: observations}{no. \: of \: observations}$

$: \implies \displaystyle \sf \:11 = \frac{x + x + 2 + x + 4 + x + 6 + x + 8}{5}$

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

$: \implies \displaystyle \sf \:11 \times 5 = 5x + 20$

$: \implies \displaystyle \sf \:55 = 5x + 20$

$: \implies \displaystyle \sf \:5x = 55- 20$

$: \implies \displaystyle \sf \:5x = 35$

$: \implies \displaystyle \sf \:x = \frac{35}{5}$

$: \implies \underline{ \boxed{ \displaystyle \sf \:x = 7}}$

$\therefore\underline{ \textsf{Required value of x for \: given observation is 7.}}$

Answer 2

Given :

• x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 11

• Mean = 11

To find :

• The value of ' x '

We know that,

Mean = Sum / Total no. of. Observations

Sum of the observations :

⟹ x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 )

⟹ ( x + x + x + x + x ) + ( 2 + 4 + 6 + 8 )

⟹ 5x + 20

Total no. of. Observations :

There are two ways to find this :

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➳ Total no. of. Observation = 5

➳ Mean = ( 5x + 20 ) / 5

➳ Mean = 11 { Given }

⟹ 11 = ( 5x + 20 ) / 5

⟹ 11 × 5 = ( 5x + 20 )

⟹ 55 = ( 5x + 20 )

⟹ 5x = 55 - 20

⟹ 5x = 35

⟹ x = 35 / 5

⟹ x = 7

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⟹ ( 5x + 20 / 5 ) { simplify }

⟹ x + 4

➳ Mean = 11 { Given }

➳ x + 4 = Mean

⟹ x + 4 = 11

⟹ x = 11 - 4

⟹ x = 7

∴ The value of ' x ' = 7

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So, It's Done !!