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Question Number 38059 by suryavi last updated on 21/Jun/18
Prove that Σ(x_i −x^− )=0
ProvethatΣ(xi−x−)=0
Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jun/18
Σ(x_i −x^− ) x^− =((Σx_i )/n) Σ(x_i −x^− ) =(x_1 −x^− )+(x_2 −x^− )+(x_3 −x^− )+...+(x_n −x^− ) =(x_1 +x_2 +x_3 +....)−(x^− +x^− +...+x^− ) =((Σx_i )/n)×n−nx^− =nx^− −nx^− =0
Σ(xi−x−)x−=ΣxinΣ(xi−x−)=(x1−x−)+(x2−x−)+(x3−x−)+…+(xn−x−)=(x1+x2+x3+….)−(x−+x−+…+x−)=Σxin×n−nx−=nx−−nx−=0

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