What is the meaning of the question that "Standard Deviation is independent with the choice of the origin"? please answer and explain with the help of an example.

Asked by akjain31 | 24th Mar, 2015, 01:05: AM

Expert Answer:

L e t space t h e space d a t a space b e space 1 comma 2 comma 3 comma 4 comma 5 T h u s comma space m e a n equals fraction numerator 1 plus 2 plus 3 plus 4 plus 5 over denominator 5 end fraction equals 15 over 5 equals 3 s tan d a r d space d e v i a t i o n squared equals 1 fifth open square brackets open parentheses 1 minus 3 close parentheses squared plus open parentheses 2 minus 3 close parentheses squared plus open parentheses 3 minus 3 close parentheses squared plus open parentheses 4 minus 3 close parentheses squared plus open parentheses 5 minus 3 close parentheses squared close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 fifth open square brackets 4 plus 1 plus 0 plus 1 plus 4 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 fifth open square brackets 10 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sigma equals s tan d a r d space d e v i a t i o n equals square root of 2 S u p p o s e space y o u space a r e space a d d i n g space 2 space t o space e a c h space o f space t h e space d a t a colon T h e n space n e w space s e t space o f space d a t a colon space 3 comma space 4 comma space 5 comma space 6 comma space 7 T h e n space n e w space m e a n equals fraction numerator 3 plus 4 plus 5 plus 6 plus 7 over denominator 5 end fraction equals 25 over 5 equals 5 space n e w space s tan d a r d space d e v i a t i o n squared equals 1 fifth open square brackets open parentheses 3 minus 5 close parentheses squared plus open parentheses 4 minus 5 close parentheses squared plus open parentheses 5 minus 5 close parentheses squared plus open parentheses 6 minus 5 close parentheses squared plus open parentheses 7 minus 5 close parentheses squared close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 fifth open square brackets 4 plus 1 plus 0 plus 1 plus 4 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 fifth open square brackets 10 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 space n e w space sigma equals n e w space s tan d a r d space d e v i a t i o n equals square root of 2 rightwards double arrow s tan d a r d space d e v i a t i o n equals n e w space s tan d a r d space d e v i a t i o n equals square root of 2 T h u s comma space sigma space i s space i n d e p e n d e n t space o f space c h o i c e space o f space t h e space o r i g i n

Answered by Vimala Ramamurthy | 24th Mar, 2015, 10:29: AM

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