Question

the numbers 4,6,8 have a frequencies X+2,X,x-1 if their arthemetic mean is 8 then the value of x​

Answer 1

$\green{\large\underline{\sf{Solution-}}}$

$\begin{gathered}\boxed{\begin{array}{c|c|c} \bf x & \bf f& \bf fx \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{}& \frac{\qquad \qquad}{} \\ \sf 4 & \sf x + 2& \sf 4x + 8 \\ \\ \sf 6 & \sf x& \sf 6x \\ \\ \sf 8 & \sf x - 1& \sf 8x - 8 \end{array}} \\ \end{gathered}$

$\blue{\bf :\longmapsto\: \sum \: f = 3x + 1}$

$\blue{\bf :\longmapsto\: \sum \: fx = 18x }$

$\blue{\bf :\longmapsto\: Mean \: = 8}$

We know,

$\dashrightarrow\bf Mean = \dfrac{ \sum f x}{ \sum f}$

$\rm :\longmapsto\:8 = \dfrac{18x}{3x + 1}$

$\rm :\longmapsto\:24x + 8 = 18x$

$\rm :\longmapsto\:6x = - 8$

$\rm :\longmapsto\:which \: is \: not \: possible.$

$\bf\implies \:There \: is \: no \: possible \: value \: of \: x$

Additional Information :-

$\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i d_i}{ \sum f_i}$

$\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i u_i}{ \sum f_i} \times h$

$\dashrightarrow\sf Median= l + \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} - cf \bigg)}{f} \Bigg \}$