question_answer

If the mean of \[{{X}_{1}}\] and \[{{X}_{2}}\] is \[{{M}_{1}}\], and that of \[{{\text{X}}_{1}},{{\text{X}}_{2}},{{\text{X}}_{\text{3}}},{{\text{X}}_{\text{4}}}\]is \[{{M}_{2}}\], the mean of \[{{\text{X}}_{1}}\],\[\frac{{{\text{X}}_{2}}}{a}\],\[{{\text{X}}_{\text{3}}}+a\]\[{{\text{X}}_{\text{4}}}\text{- a}\] is

A)  \[{{M}_{2}}+\frac{(a-1)({{x}_{1}}-2{{M}_{1}})}{4a}\]  

B)  \[{{M}_{1}}+\frac{(a-1){{x}_{1}}+2{{M}_{2}}}{4a}\]

C)  \[\frac{{{M}_{2}}}{4a}+(a-1){{x}_{1}}+2{{M}_{1}}\]

D)  \[\frac{{{M}_{1}}}{4a}+(a-1){{x}_{2}}+2{{M}_{2}}\]