Questions
a
S≤rnn−1
b
S=rnn−1
c
S≥rnn−1
d
None of these
detailed solution
Correct option is A
We have r=maxxi−xj and S2=1n−1∑i=1n xi−x¯2 Now, xi−x¯2=xi−x1+x2+⋯+xnn2=1n2xi−x1+xi−x2+⋯+xi−xi−1+xi−xi+1+⋯+xi−xn≤1n2[(n−1)r]2 [∵]xi−xj∣≤r⇒xi−x¯2≤r2⇒∑i=1n xi-x¯2≤nr2⇒1n−1∑i=1n xi−x¯2≤nr2(n−1)⇒S2≤nr2(n−1)⇒S≤rnn−1Talk to our academic expert!
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