CBSE Class 11-science Answered

$T h e space c o e f f i c i e n t space o f space v a r i a t i o n space o f space 2 space d a t a space s e t s space a r e space C subscript 1 space a n d space C subscript 2 space r e s p e c t i v e l y. I f space i n space t h e space f i r s t space d a t a space s e t space e a c h space v a l u e space i s space i n c r e a s e d space b y space 2 sigma subscript 1 space a n d space i n space t h e space s e c o n d d a t a space s e t space e a c h space v a l u e space i s space d e c r e a s e d space b y space 2 sigma subscript 2 space t h e n space f i n d space t h e space n e w space c o e f f i c i e n t space o f space v a r i a t i o n s f o r space t h e space d a t a space s e t s. left parenthesis sigma subscript 1 space a n d space sigma subscript 2 space a r e space t h e space s tan d a r d space d e v i a t i o n s space o f space t h e space d a t a space s e t s right parenthesis$ Please provide solution to this question

Asked by Topperlearning User | 19 Nov, 2016, 03:10: AM

Expert Answer

$C o n s i d e r space f i r s t space d a t a space s e t colon C subscript 1 equals fraction numerator sigma subscript 1 over denominator space stack x subscript 1 with bar on top end fraction space w h e r e space stack x subscript 1 with bar on top equals m e a n W h e n space e a c h space d a t a space i s space i n c r e a s e d space b y space 2 sigma subscript 1 space t h e n space t h e space m e a n space b e c o m e s space space stack x subscript 1 with bar on top plus 2 sigma subscript 1 T h e r e space w i l l space b e space n o space c h a n g e space i n space t h e space s tan d a r d space d e v i a t i o n. N e w space C. V space C to the power of apostrophe subscript 1 equals fraction numerator sigma subscript 1 over denominator space stack x subscript 1 with bar on top plus 2 sigma subscript 1 end fraction equals fraction numerator fraction numerator sigma subscript 1 over denominator space stack x subscript 1 with bar on top end fraction over denominator 1 plus 2 fraction numerator sigma subscript 1 over denominator space stack x subscript 1 with bar on top end fraction end fraction equals fraction numerator C subscript 1 over denominator 1 plus 2 C subscript 1 end fraction C o n s i d e r space S e c o n d space d a t a space s e t colon C subscript 2 equals fraction numerator sigma subscript 2 over denominator space stack x subscript 2 with bar on top end fraction space w h e r e space stack x subscript 2 with bar on top equals m e a n W h e n space e a c h space d a t a space i s space d e c r e a s e d space b y space 2 sigma subscript 2 space t h e n space t h e space m e a n space b e c o m e s space space stack x subscript 2 with bar on top plus 2 sigma subscript 2 T h e r e space w i l l space b e space n o space c h a n g e space i n space t h e space s tan d a r d space d e v i a t i o n. N e w space C. V space C to the power of apostrophe subscript 2 equals fraction numerator sigma subscript 2 over denominator space stack x subscript 1 with bar on top minus 2 sigma subscript 2 end fraction equals fraction numerator fraction numerator sigma subscript 2 over denominator space stack x subscript 2 with bar on top end fraction over denominator 1 minus 2 fraction numerator sigma subscript 2 over denominator space stack x subscript 2 with bar on top end fraction end fraction equals fraction numerator C subscript 2 over denominator 1 minus 2 C subscript 2 end fraction$