If 10∑i=1(x1−15)=12 and 10∑i=1(xi−15)2=18, then the S.D. of observations x1,x2.............x10 is
A
25
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B
35
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C
45
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D
none of these
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Solution
The correct option is A35 Given 10∑i=1(xi−15)=12 and 10∑i=1(xi−15)2=18 ⇒ 10∑i=1xi−10∑i=115=12 and 10∑i=1x2i−3010∑i=1xi+10∑i=1225=18 ⇒10∑i=1xi=12+150=162 Now 10∑i=1x2i=3010∑i=1xi−10∑i=1225+18=30×162+18−225×10=2628 Hence required S.D =√262810−(16210)2=√925=35