F i n d space 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 f i r s t space n space n a t u r a l space n u m b e r s.

Please provide solution to this question

Asked by Topperlearning User | 19th Nov, 2016, 03:21: AM

Expert Answer:

S u m space o f space f i r s t space n space n a t u r a l space n u m b e r s space i s space S subscript n equals fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction
because M e a n equals S subscript n over n equals fraction numerator left parenthesis n plus 1 right parenthesis over denominator 2 end fraction
S u m space o f space s q u a r e space o f space f i r s t space n space n a t u r a l space n u m b e r s space i s space S subscript 2 equals fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis over denominator 6 end fraction
sigma equals square root of S subscript 2 over n minus open parentheses fraction numerator left parenthesis n plus 1 right parenthesis over denominator 2 end fraction close parentheses squared end root
equals square root of fraction numerator left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis over denominator 6 end fraction minus fraction numerator left parenthesis n plus 1 right parenthesis squared over denominator 4 end fraction end root
equals square root of fraction numerator 4 n squared plus 6 n plus 2 minus 3 n squared minus 3 minus 6 n over denominator 12 end fraction end root
equals square root of fraction numerator n squared minus 1 over denominator 12 end fraction end root
C. V equals fraction numerator sigma over denominator m e a n end fraction equals fraction numerator 2 square root of n squared minus 1 end root over denominator square root of 12 left parenthesis n plus 1 right parenthesis end fraction equals fraction numerator 1 over denominator square root of 3 end fraction square root of fraction numerator n minus 1 over denominator n plus 1 end fraction end root

Answered by  | 19th Nov, 2016, 05:21: AM

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