CBSE Class 11-science Answered

$C o n s i d e r space a space d a t a space s e t space o f space 10 space w i t h space C o e f f i c i e n t space o f space v a r i a t i o n space C space a n d space s tan d a r d space d e v i a t i o n sigma. I f space f i r s t space 5 space space space d a t a space v a l u e s space a r e space i n c r e a s e d space b y space 2 sigma space t h e space s u m space o f space t h e space s a m e space 5 space d a t a v a l u e s space i s space 10 sigma space t h e n space f i n d space t h e space n e w space c o e f f i c i e n t space o f space v a r i a t i o n.$ Please provide solution to this question

Asked by Topperlearning User | 19 Nov, 2016, 05:08: AM

Expert Answer

$L e t space x with bar on top space b e space t h e space m e a n. W h e n space 5 space o f space t h e space d a t a space v a l u e s space a r e space i n c r e a s e d space b y space space 2 sigma space t h e n space t h e space m e a n space c h a n g e s space t o space space x with bar on top plus 5. fraction numerator 2 sigma over denominator 10 end fraction equals space x with bar on top plus sigma S u p p o s e space t h e space d a t a space v a l u e s space a r e space x subscript 1 comma x subscript 2 comma.... x subscript 10 L e t space x subscript 1 comma x subscript 2 comma x subscript 3 comma x subscript 4 comma x subscript 5 space a r e space i n c r e a s e d space b y space 2 sigma space a n d space x subscript 1 plus x subscript 2 plus x subscript 3 plus x subscript 4 plus x subscript 5 equals 10 sigma T h e space n e w space s tan d a r d space d e v i a t i o n space w i l l space b e square root of fraction numerator left parenthesis x subscript 1 plus 2 sigma right parenthesis squared plus left parenthesis x subscript 2 plus 2 sigma right parenthesis squared plus... plus left parenthesis x subscript 5 plus 2 sigma right parenthesis squared plus x squared subscript 6 plus... plus x squared subscript 10 over denominator 10 end fraction minus open parentheses x with bar on top plus sigma close parentheses squared end root equals square root of fraction numerator x squared subscript 1 plus x squared subscript 2 plus... plus x squared subscript 10 plus 5.4 sigma squared plus 4 sigma left parenthesis x subscript 1 plus x subscript 2 plus x subscript 3 plus x subscript 4 plus x subscript 5 right parenthesis over denominator 10 end fraction minus open parentheses x with bar on top plus sigma close parentheses squared end root equals square root of fraction numerator x squared subscript 1 plus x squared subscript 2 plus... plus x squared subscript 10 over denominator 10 end fraction plus 2 sigma squared plus 4 sigma squared minus x with bar on top squared minus sigma squared minus 2 x with bar on top sigma end root equals square root of x with bar on top squared plus sigma squared plus 2 sigma squared plus 4 sigma squared minus x with bar on top squared minus sigma squared minus 2 x with bar on top sigma end root equals square root of 6 sigma squared minus 2 x with bar on top sigma end root N e w space C. V equals fraction numerator square root of 6 sigma squared minus 2 x with bar on top sigma end root over denominator space x with bar on top plus sigma end fraction equals fraction numerator square root of begin display style fraction numerator 6 sigma squared over denominator space x with bar on top squared end fraction minus 2 fraction numerator sigma over denominator x with bar on top end fraction end style end root over denominator 1 plus fraction numerator sigma over denominator x with bar on top end fraction end fraction G i v e n space fraction numerator sigma over denominator x with bar on top end fraction equals C N e w space C. V equals fraction numerator square root of 6 C squared minus 2 C end root over denominator 1 plus C end fraction$