question_answer

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

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

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