A) 2.5
B) 2.8
C) 2.6
D) 2.4
Correct Answer: D
Solution :
(Bonus) This question is wrong \[\overline{x}=\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}+{{x}_{5}}}{5}=5\] \[\sum\limits_{i=1}^{5}{{{x}_{i}}=25}\] ????.. (i) Also \[{{\sigma }^{2}}=124\] \[\Rightarrow \,\,\,\frac{\sum{x_{1}^{2}}}{5}-{{\left( \overline{x} \right)}^{2}}=124\] \[\Rightarrow \,\,\frac{\sum{x_{1}^{2}}}{5}=124+25=149\] \[\Rightarrow \,\,(x_{1}^{2}+x_{2}^{2}+\,......\,+x_{5}^{2})=745\] \[\Rightarrow \,\,x_{1}^{2}+x_{2}^{2}=704\] ???.....(ii) by (i) \[{{x}_{1}}+{{x}_{2}}=16\] ............. (iii) \[2{{x}_{1}}{{x}_{2}}+704=256\] \[{{x}_{1}}\,{{x}_{2}}=\frac{256-704}{2}\] \[{{x}_{1}}\,{{x}_{2}}=128-352=-224\] ???.....(iv) Now \[\frac{\sum{\left| {{x}_{1}}-5 \right|}}{5}=\frac{\left| {{x}_{1}}-5 \right|+\left| {{x}_{2}}-5 \right|+4+3+1}{5}\] \[=\frac{8+\left| {{x}_{1}}-5 \right|+\left| 11-{{x}_{1}} \right|}{5}\] \[=\frac{8+6}{5}=2.8\]Ans.
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