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Section1.2posted - STOR 155, Section 3 Thursday, January...

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STOR 155, Section 3 Thursday, January 14, 2010 IPS6e Section 1.2
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Section 1.2: Describing distributions with numbers Measures of center mean median Measures of spread Quartiles and IQR (Inter-Quartile Range) Standard deviation Five-number summary and boxplots 1.5 x IQR rule and modified boxplots
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Mean of a set of values Mean of a set of values = their sum divided by the number of values in the set. (Same as the familiar average .) Example: the heights in inches of 25 women are shown. These numbers add to 1598.3 . 1598.3 / 25 = 63.9. 58.2 64.0 59.5 64.5 60.7 64.1 60.9 64.8 61.9 65.2 61.9 65.7 62.2 66.2 62.2 66.7 62.4 67.1 62.9 67.8 63.9 68.9 63.1 69.6 63.9 Mean is denoted x (“x-bar”) . _
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Mathematical notation for the mean We refer to the mean of a set of numbers generically as x (“ x - bar”). This is because we refer to a generic set of values as x 1 , x 2 ,x 3 , … , x n . n is the number of values in the set. For this set, n = 25, and . 58 2 . 64 0 . 59 5 . 64 5 . 60 7 . 64 1 . 60 9 . 64 8 . 61 9 . 65 2 . 61 9 . 65 7 . 62 2 . 66 2 . 62 2 . 66 7 . 62 4 . 67 1 . 62 9 . 67 8 . 63 9 . 68 9 . 63 1 . 69 6 . 63 9 _
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Median of a set of values Median of a set of values = middle value. Denoted M . Half the values are lower than the median, half higher. To find it, sort the values from low to high, then find the middle. Example : values are 6 9 1 2 6 4 1 Sorted: 1 1 2 4 6 6 9 M = 4. This set has an odd number of values. If the set has an even number of values, the median is the mean of the middle two . Example : 13 17 11 12 11 14 16 26 Sorted: 11 11 12 13 14 16 17 26 M = (13+14)/2
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Which value is the middle value? If there are n values, then M is the k th smallest value , where k = ( n +1)/2. If
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Section1.2posted - STOR 155, Section 3 Thursday, January...

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