Question

If the mean of observations x, 2x+1,2x+5 and 2x+9 is 30. What is the mean of first threeobservation?

Answer 1

$$\begin{gathered} \mathrm{Given},\mathrm{mean}\mathrm{of}\mathrm{observation}\mathrm{x},2\mathrm{x}+1,2\mathrm{x}+5\mathrm{and}2\mathrm{x}+9=30 \\ \Rightarrow \frac{\mathrm{x}+\left(2\mathrm{x}+1\right)+\left(2\mathrm{x}+5\right)+\left(2\mathrm{x}+9\right)}{4}=30 \\ \Rightarrow \frac{7\mathrm{x}+15}{4}=30 \\ \Rightarrow 7\mathrm{x}+15=120 \\ \Rightarrow 7\mathrm{x}=105 \\ \Rightarrow \mathrm{x}=15 \\ \mathrm{Now}, \\ \mathrm{Mean}\mathrm{of}\mathrm{first}\mathrm{three}\mathrm{observation}=\frac{\mathrm{x}+\left(2\mathrm{x}+1\right)+\left(2\mathrm{x}+5\right)}{3}=\frac{5\mathrm{x}+6}{3}=\frac{5\times 15+6}{3}=\frac{81}{3}=27 \end{gathered}$$