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Question

Find the standard deviation of 10 observations 111, 211, 311,...,1011

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Solution

The given numbers are,
111,211,311,.....,1011
¯¯¯x=111+211+311+411+511+611+711+811+911+101110=561010=561

Standard deviation =(xi¯¯¯x)210
=(111561)2+(211561)2+(311561)2+......+(911561)+(1011561)210
=(450)2+(350)2+(250)2+(150)2+(50)2+(50)2+(150)2+(250)2+(350)2+(450)210
=202500+122500+62500+22500+2500+2500+22500+62500+122500+20250010
=82500010
=82500
=5033

Hence, this is the answer.

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