Question

Compute s2 and s for the data set: -2, -1, -3, -2, 1, -3 1.33; 1.15...

Compute s2 and s for the data set: -2, -1, -3, -2, 1, -3

1.33; 1.15

2.27; 1.51

1.6; 1.26

19.07; 4.37

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Answer #1

To calculate the sample standard deviation and sample variance we need to find the sample mean as:

Mean = (-2 + -1 + -3 + -2 + 1 + -3)/6
= -10/6
Mean = -1.6667

and the standard deviation is calculated as:

Standard Deviation s = √(1/6 - 1) x ((-2 - -1.6667)2 + ( -1 - -1.6667)2 + ( -3 - -1.6667)2 + ( -2 - -1.6667)2 + ( 1 - -1.6667)2 + ( -3 - -1.6667)2)
= √(1/5) x ((-0.3333)2 + (0.6667)2 + (-1.3333)2 + (-0.3333)2 + (2.6667)2 + (-1.3333)2)
= √(0.2) x ((0.11108889) + (0.44448889) + (1.77768889) + (0.11108889) + (7.11128889) + (1.77768889))
= √(0.2) x (11.33333334)
= √(2.266666668)
= 1.51

and sample variance s2 = 1.512  = 2.27

So,  s2 and s are

2.27 : 1.51

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