Question

Find the x, if the mean of x-2,9,x+1,7,1,5,3 is 4. also find
step by step explanation
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Answer 1

Answer:

Correct Question:-

Find the x, if the mean of x-2,9,x+1,7,1,5,3 is 4. also find mode if the data.

Given:-

• Mean of x-2, 9,x+1, 7, 1, 5 ,3 is 4

To Find:-

• Value of x? and mode of data?

Solution:-

We know that,

${\boxed{ \boxed{ \rm{Mean= \frac{Sum \: of \: Observations}{Number \: of \: Observations} }}}}$

$: { \implies{ \rm{ {4 = \frac{(x - 2) + 9 + (x + 1) + 7 + 1 + 5 + 3}{7} }}}}$

$: { \implies{ \rm{4 = \frac{x - 2 + 9 + x + 1 + 7 + 1 + 5 + 3}{7} }}}$

$: { \implies{ \rm{4 = \frac{2x +24 }{7} }}}$

$: { \implies{ \rm{7 \times 4 = 2x + 24}}}$

$: { \implies{ \rm{28 = 2x + 24}}}$

$: { \implies{ \rm{2x = 28 - 24}}}$

$: { \implies{ \rm{2x = 4}}}$

$: { \implies{ \rm{ \pmb{x = 2}}}}$

By Substituting:-

→ x - 2 = 2 - 2 = 0

→ x + 1 = 2 + 1 = 3

Mode of the Data:-

The data is 0 , 9 , 3 , 7 , 1 , 5 , 3

Here 3 is the most repeated term.

∴ Mode of the data is 3

Answer 2

$\large\rm\underline\red{Given \: :-}$

Observation : x-2,9,x+1,7,1,5,3

Mean : 4

$\large\rm\underline\red{To \: find \: :- }$

x

$\large\rm\underline\red{Solution \: :-}$

Required Formula :-

${\small{\underline{\boxed{\bf{\red{Mean = \frac{Sum \: of \: all\: observations}{No. \: of \: observations}}}}}}}$

Now,

Put the values

$\sf\longrightarrow{4 = \frac{x - 2 + 9 + x + 1 + 7 + 1 + 5 + 3}{5} } \\ \\ \sf\longrightarrow{4 = \frac{x - 2 + x + 1 + 16}{5} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\longrightarrow{5 \times 4 =2x - 1 + 16} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\longrightarrow{20 - 16 = 2x - 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\longrightarrow{ \frac{4}{2} = x- 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\longrightarrow{x = 2 + 1 = \boxed{ \bf \red{ 3}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

X = 3

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