Question Number 93691 by Aniruddha Ghosh last updated on 10/Jun/20
$$\boldsymbol{\mathrm{If}}\:\underset{\boldsymbol{{i}}\:=\:\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\boldsymbol{\mathrm{x}}_{\mathrm{i}} +\mathrm{4}\right)\:=\:\mathrm{60}\:\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\bar {\boldsymbol{{x}}}. \\ $$
Commented by hknkrc46 last updated on 15/May/20
$$\underset{{i}={k}} {\overset{{m}} {\sum}}{c}=\left({m}−{k}+\mathrm{1}\right){c} \\ $$$${c}={x}+\mathrm{4}\:;\:{m}=\mathrm{10}\:;\:{k}=\mathrm{1} \\ $$$$\Rightarrow\underset{{i}=\mathrm{1}} {\overset{\mathrm{10}} {\Sigma}}\left({x}+\mathrm{4}\right)=\left(\mathrm{10}−\mathrm{1}+\mathrm{1}\right)\left({x}+\mathrm{4}\right)=\mathrm{60} \\ $$$$\Rightarrow\mathrm{10}\left({x}+\mathrm{4}\right)=\mathrm{60}\Rightarrow{x}+\mathrm{4}=\mathrm{6}\Rightarrow{x}=\mathrm{2} \\ $$
Commented by i jagooll last updated on 14/May/20
$$\underset{\mathrm{i}\:=\:\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\:\left(\mathrm{x}_{\mathrm{i}} +\mathrm{4}\right)\:=\:\mathrm{60}\:.\: \\ $$
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
$$\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\boldsymbol{{x}}+\mathrm{4}\right)\:=\:\boldsymbol{{x}}_{\mathrm{1}} +\boldsymbol{{x}}_{\mathrm{2}} +\boldsymbol{{x}}_{\mathrm{3}} +….+\boldsymbol{{x}}_{\mathrm{10}} +\left(\mathrm{4}×\mathrm{10}\right)\:=\:\mathrm{60} \\ $$$$\Rightarrow\:\boldsymbol{{x}}_{\mathrm{1}} +\boldsymbol{{x}}_{\mathrm{2}} +………..+\boldsymbol{{x}}_{\mathrm{10}\:} =\:\mathrm{60}−\mathrm{40} \\ $$$$\Rightarrow\:\boldsymbol{{x}}_{\mathrm{1}} +\boldsymbol{{x}}_{\mathrm{2}} +………..+\boldsymbol{{x}}_{\mathrm{10}} \:=\:\mathrm{20} \\ $$$$\therefore\:\bar {\boldsymbol{{x}}}\:=\:\frac{\boldsymbol{{x}}_{\mathrm{1}} +\boldsymbol{{x}}_{\mathrm{2}} +\boldsymbol{{x}}_{\mathrm{3}} +…..+\boldsymbol{{x}}_{\mathrm{10}} }{\mathrm{10}\left(\mathrm{frequency}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{20}}{\mathrm{10}} \\ $$$$\:\:\:\:\:\:\:\:\:=\:\mathrm{2} \\ $$$$ \\ $$