If the sum of 10 observations is 12 and the sum of their squares is 18, then the standard deviation is: 

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SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)
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  1. 4/5
  2. 2/5
  3. 3/5
  4. 1/5

Answer (Detailed Solution Below)

Option 3 : 3/5
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The correct answer is 3/5
Key Points

Standard deviation = (xix¯)2n=Variance 
Therefore, Variance V(X) = 1n(xix¯)2
or, v(x)=1n[Σ(xi22×xi×x¯+x¯2)]

=Σxi2n2x¯(Σxin)+Σx¯2n

=Σxi2n2x¯2+n.x¯2n

=Σxi2n2x¯2+x¯2

V(x)=Σxi2nx¯2
Given, the sum of 10 observations is 12 and the sum of their squares is 18. 
Thus, n = 10, xi=12xi2=18 
Therefore, mean x¯=1.2
Plugging this information into the equation of variance V(X), we have

V(x)=Σxi2nx¯2

=110×18(1.2)2

= 1.8 - 1.44

=0.36
Hence, the required standard deviation Variance=(0.36)=0.6=35

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