# lec05 - STATISTICS 13 Lecture 5 Oct 4 2010 Shape of the...

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STATISTICS 13 Lecture 5 Oct 4, 2010

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Review Shape of the data -Bell shaped -Skewed -Bimodal Measures of center – Arithmetic Mean – Median – Mode Effects of outliers and skewness
Measures of Variability A quantitative measure that describes the spread or dispersion of the data along the horizontal axis of the data distribution Data sets may have the same center (e.g., mean), but look different because the way the numbers spread out from the center

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Measures of Variability (Cont.) Example: two data sets -data set one: 1,2,3,3,4,4,4,4,5,5,5,5,5,5,6,6,6,6,7,7,8,9 -data set two: 3,4,4,5,5,5,6,6,7 -
Measures of Variability: (I) Range Range of a sample of n measurements is the difference between the maximum and the minimum : R = Max – Min Example : daily number of phone calls in five days: 5, 2, 14, 3, 6 ; Drawback : depends on only two values among the measurements, very highly affected by outliers

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Measures of Variability: (II) Variance Variance of a sample of n measurements is the sum of squared deviation from the sample mean, divided by (n-1) ; It measures how far away the measurements are from their mean. Example : phone calls -data: 5, 2, 14, 3, 6 ;n=5 -mean = -deviations : -squared deviations : -variance: 1 ) ( 2 2 = n x x s i
Population vs. Sample Variance of a population of N subjects is the averaged squared variation from the population mean μ ; σ 2 usually is not calculable due to the lack of data of the whole population Variance of a sample of n measurements is the sum of squared deviation from the sample mean, divided by (n-1) N x N x i i 2 2 ) ( µ = = 1 ) ( 2 1 2 1 = = = = n x x s n x x i n i i n i

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Why Divided by n-1 ?
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lec05 - STATISTICS 13 Lecture 5 Oct 4 2010 Shape of the...

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