A) \[n\bar{X}-nk\]
B) \[n\bar{X}-k\]
C) \[\bar{X}-nk\]
D) \[\bar{X}-k\]
Correct Answer: B
Solution :
Let the numbers be \[{{x}_{1}},{{x}_{2}},{{x}_{3}}.....{{x}_{n}}\].Then \[\overline{\text{X}}=\frac{1}{n}\sum\limits_{i=1}^{n}{{{X}_{1}}}\] \[\Rightarrow \] \[\overline{\text{X}}=\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+.....+{{x}_{n-1}}+{{x}_{n}}}{n}\] \[=\frac{k+{{x}_{n}}}{n}[\because {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+.....+{{x}_{n-1}}=k]\] \[\Rightarrow \] \[{{x}_{n}}=c\overline{\text{X}}-k\]
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