Question

if the mean of data 5 7 10 14 X 25 32 19 is X what is the value of x​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{The mean of 5,7,10,14,x,25,32,19 is x}$

$\underline{\textsf{To find:}}$

$\textsf{The value of x}$

$\underline{\textsf{Solution:}}$

$\textsf{Usng the formula}$

$\boxed{\begin{minipage}{6cm} \\\textsf{Mean}\mathsf{=\dfrac{\textsf{Sum of observations}}{Total number of observations}}\\\\\textsf{Mean}\mathsf{=\dfrac{\displaystyle{\sum}^{i=n}_{i=1}\,x_i}{n}}\\ \end{minipage}}$

$\implies\textsf{Mean}\mathsf{=\dfrac{5+7+10+14+x+25+32+19}{8}}$

$\implies\mathsf{x=\dfrac{112+x}{8}}$

$\implies\mathsf{8x=112+x}$

$\implies\mathsf{8x-x=112}$

$\implies\mathsf{7x=112}$

$\implies\mathsf{x=\dfrac{112}{7}}$

$\implies\boxed{\mathsf{x=16}}$

$\underline{\textsf{Answer:}}$

$\textsf{The value of x is 16}$

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Answer 2

SOLUTION :

TO DETERMINE

The value of x when the mean of data

5, 7, 10, 14, x , 25, 32, 19 is x

FORMULA TO BE IMPLEMENTED

$\sf{}The \: mean \: of \: n \: given \: numbers \: \: x_1,x_2,..,x_n$

$\displaystyle \sf{} = \frac{ \sum x_i }{n}$

EVALUATION

Here the given numbers are 5, 7, 10 14, x , 25, 32, 19

Sum of the given numbers

$= \sf{}5 + 7 + 10 + 14 + x + 25 + 32 + 19$

$= \sf{}112 + x$

Here the number of observations = 8

So by the given condition

$\displaystyle \sf{} x= \frac{ 112 + x}{8}$

$\implies \sf{}8x = 112 + x$

$\implies \sf{}7x = 112$

$\implies \sf{}x = 16$

FINAL RESULT

Hence the required value of x = 16

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