MeasurementofLocation&Variability

MeasurementofLocation&Variability - (3.1 3.2 3.4...

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(3.1, 3.2, 3.4) Measures of Location Mean : average value Sample mean: denoted by i x x n Population mean: denoted i x N Median : value in the middle when the data are arranged in ascending order (smallest to largest). With an odd number of observations, the median is the middle value, however with an even number of observations, having no middle value, the average of the two middle values is the median. Find the median for the set of numbers below 5, 6, 8, 10, 13, 15, 15 Median = _____ Now find the median for this set of numbers 1, 3, 4, 5, 7, 8, 9, 12 Median = _______ Mode : the value that occurs with greatest frequency (may be more than one mode in a set of data). Percentile : the pth percentile is the value such that at least p percent of the observations are less than or equal to this value and at least (100-p) percent of the observations are greater than or equal to this value. For example: If you scored in the 90 th percentile on the verbal part of your SAT’s, this would mean that you scored above 90% of all verbal scores for the SAT’s at that time. To calculate the pth percentile: 1. arrange the data in ascending order 2. compute an index i=(p/100)*n 3. if i is not an integer, round up, the next integer greater than I denotes the position of the pth percentile 4. if i is an integer the pth percentile is the average of the values in positions i and i+1.
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Practice Finding Percentile: 48 57 64 70 74 77 84 88 93 99 49 57 65 70 75 78 84 89 94 99 51 58 66 71 75 79 85 91 95 100 52 59 66 72 76 82 87 91 97 101 54 63 67 73 76 83 87 92 98 106 There are 50 elements in this data set. The median is: To find the 85 th percentile: Quartiles : used to divide the data into 4 parts. Q1 : first quartile, _____ percentile Q2 : second quartile, _____ percentile, median Q3 : third quartile, _____ percentile 5 number summary : 1. Smallest value 2. first quartile (Q1) 3. Median (Q2) 4. third quartile (Q3) 5. Largest value So the 5 number summary for this data set is: Measures of Variability Range : largest value smallest value In this example: Inter-quartile range ( IQR) : Q3 Q1, the range of the middle 50% of the data.
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This note was uploaded on 02/06/2012 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue.

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MeasurementofLocation&Variability - (3.1 3.2 3.4...

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