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If ∑_(i=1)^9 (x_i-5)=9 & ∑_(i=1)^9 (x_i-5) ^2=45 then standard deviation of the 9 term x_1 x_2 … x_9

Опубликовано: 03 Ноябрь 2024
на канале: Math Master - Impetus Gurukul
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If ∑_(i=1)^9▒〖(x_i-5)=9〗 and ∑_(i=1)^9▒(x_i-5) ^2=45, then the standard deviation of the 9 termx_1,x_2,…,x_9s is
(a) 3 (b) 9 (c) 4 (d) 2
Ans: d
Sol.
The standard deviation is independent of change of origin. So, put x_i-5=y_i
∴∑_(i=1)^9▒〖y_i=9〗 and ∑_(i=1)^9▒〖y_i^2=45〗
S.D. =√(1/n ∑▒〖y_i^2-((∑▒y_i )/n)^2 〗)
=√(45/9-(9/9)^2 )=√(5-1)=√4=2
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If ∑_(i=1)^9 (x_i-5)=9 & ∑_(i=1)^9 (x_i-5) ^2=45 then standard deviation of the 9 term x_1 x_2 … x_9
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