distributionssummarystatistics(英文版)(編輯修改稿)
2025-01-24 07:56 本頁面
【文章內(nèi)容簡介】 the median is a better measure of center: ? Skewed to the left, the mean will be less than the median. ? Skewed to the right, the mean will be more than the median. 20406050 100 150 200 250 300 350102030405010 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44Median Median Mean Mean Measures of Spread ? Standard Deviation: – Typical distance of a value from the mean of a distribution. – Preferred measure of spread. ? Variance: – Square of the std dev. – Used when bining sources of variation. ? Range: – Calculated by subtracting the minimum value from the maximum value. – Examples: ? 2,4,5,5,6,9 ? Range = (92) = 7 ? 2,4,5,5,6,22 ? Range = (222) = 20 ? ? ? ?12??? ?nxxs i Comparison of Range Std Dev Range: – Easy to pute. – Easy to interpret. – More sensitive to outliers. – Ranges are expected to be larger as the sample size increases. Standard Deviation: – Uses information from the entire sample. – More precise estimate as the sample size increases. The ‘Sigma’ Rule ? Most distributions are approximately 6 standard deviations wide. ? The ‘Sigma’ rule allows us to estimate the standard deviation from the range: – s ~ R/6 – Example: ? 2,4,5,6,6,22 ? S ~ (222)/6 = 6 0 7 5 %9 0 9 8 %9 9 1 0 0 %mm sm 2 sm + sm + 2 sm + 3 sm 3 s6s Measures of Spread ? Quartiles: – Four divisions of a distribution – Median = 2nd quartile ? Inter Quartile Range (IQR): – Range of the middle half of the data. – IQR = Q3 Q1. – Used to identify potential outliers: ? Values * IQR beyond Q1 or Q3 102030405010 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 441 / 41 / 4Q1 Q3Q21 / 4 1 / 4Example: – 2,4,5,5,6,7,8,9,10 – Median = 6 – Q1 = Middle of 2,4,5,5,6 = 5 – Q3 = Middle of 6,7,8,9,10 = 8 – IQR = 85 = 3 – Potential ou
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