Question

If the mean of $\mathrm{x}+2,2\mathrm{x}+3,3\mathrm{x}+4\mathrm{and}4\mathrm{x}+5\mathrm{is}\mathrm{x}+2$ then find the value of $\mathrm{x}$.

Answer 1

Find the required value:

$\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observations}}$

Given mean of $\mathrm{x}+2,2\mathrm{x}+3,3\mathrm{x}+4\mathrm{and}4\mathrm{x}+5\mathrm{is}\mathrm{x}+2$

$$\begin{gathered} \Rightarrow x+2=\frac{(x+2)+(2x+3)+(3x+4)+(4x+5)}{4} \\ \Rightarrow x+2=\frac{10x+14}{4} \\ \Rightarrow 4(x+2)=10x+14 \\ \Rightarrow 4x+8=10x+14 \\ \Rightarrow 4x-10x=14-8 \\ \Rightarrow -6x=6 \\ \Rightarrow x=\frac{6}{-6} \\ \Rightarrow x=-1 \end{gathered}$$

Hence the value of x is $-1$.