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Question Number 93691 by Aniruddha Ghosh last updated on 10/Jun/20

$$\mathbf{If}\underset{\mathit{i}=1}{\sum ^{10}}({\mathbf{x}}_{\mathrm{i}}+4)=60\mathbf{then}\mathbf{find}\mathbf{the}\mathbf{value}\mathbf{of}\overline{\mathit{x}}.$$

Commented by hknkrc46 last updated on 15/May/20

$$\underset{i=k}{\sum ^m}c=(m-k+1)c$$$$c=x+4;m=10;k=1$$$$\Rightarrow \underset{i=1}{\stackrel{10}{\mathrm{\Sigma }}}(x+4)=(10-1+1)(x+4)=60$$$$\Rightarrow 10(x+4)=60\Rightarrow x+4=6\Rightarrow x=2$$

Commented by i jagooll last updated on 14/May/20

$$\underset{\mathrm{i}=1}{\sum ^{10}}({\mathrm{x}}_{\mathrm{i}}+4)=60.$$

Commented by Aniruddha Ghosh last updated on 10/Jun/20

right. it was by mistake

Answered by Aniruddha Ghosh last updated on 14/May/20

$$\underset{\mathit{i}=1}{\sum ^{10}}(\mathit{x}+4)={\mathit{x}}_1+{\mathit{x}}_2+{\mathit{x}}_3+....+{\mathit{x}}_{10}+\left(4\times 10\right)=60$$$$\Rightarrow {\mathit{x}}_1+{\mathit{x}}_2+...........+{\mathit{x}}_{10}=60-40$$$$\Rightarrow {\mathit{x}}_1+{\mathit{x}}_2+...........+{\mathit{x}}_{10}=20$$$$\therefore \overline{\mathit{x}}=\frac{{\mathit{x}}_1+{\mathit{x}}_2+{\mathit{x}}_3+.....+{\mathit{x}}_{10}}{10\left(\mathrm{frequency}\right)}$$$$=\frac{20}{10}$$$$=2$$$$$$

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