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Question: Which of the following set of numbers has the highest Standard deviation?
1,0,1,0,1,0
-1,-1,-1,-1, -1,-1
1,1,1,1,1,1
1,1,0,-1,0,- 1
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| June 06, 2007 03:24:26 |
#1 |
| Sam |
Member Since: Visitor Total Comments: N/A |
RE: Which of the following set of numbers has the high...
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Which of the following set of numbers has the highest Standard deviation?
a) 1,0,1,0,1,0
b)-1,-1,-1,-1,-1,-1
c) 1,1,1,1,1,1
d) 1,1,0,-1,0,-1
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Formula
Mean = (x1+x2+...+x6)/6
SD= SrRoot( 1/6 * [ x1- Mean]^2+[x2- Mean]^2+...[x6-Mean]^2 )
Note : The Number : 6 denotes no. of terms in a particular option and ^2 - denotes Square
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Take Option (a)
Mean(M) = (1+0+1+0+1+0)/6 = 3/6 = 1/2
SD = Sqroot( 1/6 * [ (1 - 1/2)^2 + (0-1/2)^2+ (1 -1/2)^2 + (0-1/2)^2 + (1 - 1/2)^2 + (0-1/2)^2 ] )
= Sqroot( 1/6 * [ 1/4 + 1/4 +1/4 + 1/4 + 1/4 +1/4] )
= Sqroot( 1/6 * 6 * 1/4 )
= Sqroot (1/4) = 1/2 = 0.5
For option (b)
Mean = -6/6= -1
SD = Sqroot( 1/6 * [ (-1 - (-1))^2 + (-1 - (-1))^2 + (-1 - (-1))^2 + (-1 - (-1))^2 + (-1 - (-1))^2 + (-1 - (-1))^2 ] )
= Sqroot ( 1/6 * [ 0 + 0 +0 + 0+ 0 + 0 ] )
= 0
For option (c)
Mean = 6/6 = 1
SD = Sqroot (1/6 * [ (1-1)^2 +(1-1)^2 +(1-1)^2 + (1-1)^2 + (1-1)^2 + (1-1)^2 ] )
= Sqroot (1/6 * 0 )
= 0
For option (d)
Mean = 0/6 = 0
SD = Sqroot ( 1/6 * ( [1-0]^2 + [1-0]^2 + [0-0]^2 + [-1-0]^2 + [0-0]^2 + [-1-0]^2 ) )
= Sqroot ( 1/6 * ( 1+1+0+1+0+1) )
= Sqroot(2/3) = 0.816
Hence the Soln = Option (d)
For reference : en.wikipedia . org/wiki/Standard_deviation
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