mont4e_sm_ch06_mind

mont4e_sm_ch06_mind - 6-94 a Descriptive Statistics...

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Mind Expanding Exercises 6-95 9 559504 62572 2 9 1 9 1 2 = = = = = n x x i i i i 11 . 7 61 . 50 61 . 50 1 9 9 559504 2572 6 1 2 9 1 9 1 2 2 = = = = = = = s n n x x s i i i i Subtract 30 and multiply by 10 9 22848400 2579200 2 9 1 9 1 2 = = = = = n x x i i i i 6-58
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14 . 71 1 . 5061 1 . 5061 1 9 9 22848400 579200 2 1 2 9 1 9 1 2 2 = = = = = = = s n n x x s i i i i Yes, the rescaling is by a factor of 10. Therefore, s 2 and s would be rescaled by multiplying s 2 by 10 2 (resulting in 5061.1) and s by 10 (71.14). Subtracting 30 from each value has no affect on the variance or standard deviation. This is because . ) ( ) ( 2 X V a b aX V = + 6-96 2 1 2 1 2 ) ( ) ( ) ( a x n x x a x n i i n i i + = = = ; The sum written in this form shows that the quantity is minimized when a = x . 6-97 Of the two quantities () = n i i x x 1 2 and , the quantity ( = n i i x 1 2 μ ) ( = n i i x x 1 2 ) will be smaller given that x . This is because x is based on the values of the ’s. The value of μ
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mont4e_sm_ch06_mind - 6-94 a Descriptive Statistics...

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