Question

A student was asked to find the mean of 3,11,7,915,13,8,1917,21,14 and x. he found the mean
be 12, find x ​

Answer 1

Answer :

$\large{\star\:\:\boxed{\bf{x\:=\:7}}\:\:\star}$

Correct Question :–

A student was asked to find the mean of 3 , 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x. He found the mean  be 12, find x .

Explanation :

Given :–

• The Observations are 3, 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x .
• The mean of the above observations is 12 .

To Find :–

The value of x .

Formula Applied :–

• $\boxed{\star\:\:\bf{Mean\:(\overline{x})\:=\:\dfrac{Sum\:of\:all\:the\:Observations}{Total\:Number\:of\:Observations} }\:\:\star}$

Solution :–

We have ,

• The number of observations = 12
• Mean of all the observations = 12

Putting these values in the Formula :

$\rightarrow\sf{Mean\:=\:\dfrac{Sum\:of\:all\:the\:Observations}{Total\:Number\:of\:Observations}}$

$\rightarrow\sf{12\:=\:\dfrac{3\:+\:11\:+\:7\:+\:9\:+\:15\:+\:13\:+\:8\:+\:19\:+\:17\:+\:21\:+\:14\:+\:x}{12}}$

$\rightarrow\sf{12\:\times\:12\:=\:137\:+\:x}$

$\rightarrow\sf{144\:=\:137\:+\:x}$

$\rightarrow\sf{x\:=\:144\:-\:137}$

$\rightarrow\boxed{\bf{x\:=\:7}}$

∴ The value of x will be 7 .

Answer 2

Answer :

\large{\star\:\:\boxed{\bf{x\:=\:7}}\:\:\star}

x=7

Correct Question :–

A student was asked to find the mean of 3 , 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x. He found the mean be 12, find x .

Explanation :

Given :–

The Observations are 3, 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x .

The mean of the above observations is 12 .

To Find :–

The value of x .

Formula Applied :–

\boxed{\star\:\:\bf{Mean\:(\overline{x})\:=\:\dfrac{Sum\:of\:all\:the\:Observations}{Total\:Number\:of\:Observations} }\:\:\star}

⋆Mean(

x

)=

TotalNumberofObservations

SumofalltheObservations

⋆

Solution :–

We have ,

The number of observations = 12

Mean of all the observations = 12

Putting these values in the Formula :

\rightarrow\sf{Mean\:=\:\dfrac{Sum\:of\:all\:the\:Observations}{Total\:Number\:of\:Observations}}→Mean=

TotalNumberofObservations

SumofalltheObservations

\rightarrow\sf{12\:=\:\dfrac{3\:+\:11\:+\:7\:+\:9\:+\:15\:+\:13\:+\:8\:+\:19\:+\:17\:+\:21\:+\:14\:+\:x}{12}}→12=

12

3+11+7+9+15+13+8+19+17+21+14+x

\rightarrow\sf{12\:\times\:12\:=\:137\:+\:x}→12×12=137+x

\rightarrow\sf{144\:=\:137\:+\:x}→144=137+x

\rightarrow\sf{x\:=\:144\:-\:137}→x=144−137

\rightarrow\boxed{\bf{x\:=\:7}}→

x=7

∴ The value of x will be 7 .