Question

The numbers 4, 6 and 8 have the frequencies (x + 2), x and (x – 1) and if their arithmetic mean is 8, find the value of x.

Answer 1

Dear Student,

$$\begin{gathered} if{x}_1,x_2,x_3....x_{n}arethenumbersand{f}_{1,}{f}_2,f_3,f_4...f_{n}arefrequencies,thenarithmaticmeanisgivenbyformula \\ ArithmaticMean=\frac{{\displaystyle \sum _{i=1}^n}{f}_i{x}_i}{{\displaystyle \sum _{i=1}^n}{f}_i} \\ ArithmaticMean=\frac{f_1{x}_1+f_2{x}_2+...+f_n{x}_n}{f_1+f_2+f_3+..+f_n} \\ puttingvaluesweget \\ 8=\frac{4\times \left(x+2\right)+6\times x+8\times \left(x-1\right)}{x+2+x+x-1} \\ 8=\frac{4x+8+6x+8x-8}{3x+1} \\ 24x+8=18x \\ 6x+8=0 \\ x=\frac{-8}{6} \\ x=\frac{-4}{3} \end{gathered}$$
Regards,