8 - September 25 The Normal Curve

8 - September 25 The Normal Curve - "There are two ways to...

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    "There are two ways to slide easily through  life:   to BELIEVE  everything  or  to DOUBT  everything;   both ways save us from thinking." –  Theodore Rubin  
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    The Empirical Rule The Empirical Rule 68%  fall be twe e n  -1 and +1 s tandard de viatio ns 95% fall between  -2 and +2 standard deviations 99.7% fall between  -3 and +3 standard deviations
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    The Empirical Rule The Empirical Rule
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    The Empirical Rule The Empirical Rule
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    The Empirical Rule The Empirical Rule S=Standard Deviation
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    The Normal Curve The Normal Curve Mirro ro rriM Im ag e  o f Its e lf .5000 is AREA .5000 + .5000 = 1.00 = AREA
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    Standard Deviation Standard Deviation S  = s tandard de viatio n        Σ  =  s um X = ite m /o bs e rvatio n     X = m e an       N – 1 = de g re e  o f fre e do m 2
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    Standard Deviation Standard Deviation De n A Cowboy   8 Black   6 Athlete   6 Swimmer   2 Polar   5 Fireman   3 Σ  = 30 Mean = 30/6 = 5 2 3 5 6 6 8 Median = 5.5 Mode = 6
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    Standard Deviation Standard Deviation Den B  Tradition 7 Ma Kettle 6 Shy 8 Aussie 4 Aggie 3 Baby 2     Σ  = 30 Mean = 30/6 = 5 2 3 4 6 7 8 Median = 5 Mode = N/A
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    Standard Deviation Standard Deviation Den A Cowboy 8 Black 6 Athlete 6 Swimmer 2 Polar 5 Fireman 3 Σ = 30 Den B Tradition 7 Ma Kettle 6 Shy 8 Aussie 4 Aggie 3 Baby 2 Σ = 30
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    Standard Deviation Standard Deviation The standard deviation of a set of scores is  the square root of the variance of those  scores.  That is, the standard deviation, s,  is found by: 2 2
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    Standard Deviation Standard Deviation S = standard deviation Σ = sum X = item/observation  X = mean N – 1 = degree of freedom 2 2
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    Standard Deviation Standard Deviation Den A Den A X X - X (X - X) 2 8 6 6 2 5 3 Totals 3 1 1 -3 0 -2 0 (Mean Deviation) 9 1 1 9 0 4 24
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    Variance – Variance – Den A Den A
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    Standard Deviation Standard Deviation Den A Den A 2
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