285%2Bchap02-va-3

285%2Bchap02-va-3 - Statistics: Chapter 2 Methods for...

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Chap 3-1 Statistics: Chapter 2 Methods for Describing Sets of Data Part 2
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Chap 3-2 Shape of a Distribution Describes how data is distributed Symmetric or skewed Mean = Median Mean < Median Median < Mean Right-Skewed Left-Skewed Symmetric (Longer tail extends to left) (Longer tail extends to right)
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Chap 3-3 Distribution Shapes
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Chap 3-4 Mean is generally used, unless extreme values (outliers) exist Then Median is often used, since the median is not sensitive to extreme values. Example: Median home prices may be reported for a region – less sensitive to outliers Which measure of location is the “best”?
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Chap 3-5 Other Location Measures Other Measures of Location Percentiles Quartiles 1 st quartile = 25 th percentile 2 nd quartile = 50 th percentile = median 3 rd quartile = 75 th percentile The p th percentile in a data array: p% are less than or equal to this value (100 – p)% are greater than or equal to this value (where 0 ≤ p ≤ 100)
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Chap 3-6 Percentiles The p th percentile in an ordered array of n values is the value in i th position, where Example: Find the 60 th percentile in an ordered array of 19 values. (n) 100 p i = 11.4 (19) 100 60 (n) 100 p i = = = If i is not an integer, round up to the next higher integer value So use value in the i = 12 th position
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Chap 3-7 Quartiles Quartiles split the ranked data into 4 equal groups: Note that the second quartile (the 50 th percentile) is the median 25% 25% 25% 25% Q 1 Q 2 Q 3
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Chap 3-8 Quartiles Sample Data in Ordered Array: 11 12 13 16 16 17 18 21 22 Example: Find the first quartile (n = 9) Q 1 = 25 th percentile, so find i : i = (9) = 2.25 so round up and use the value in the 3 rd position: Q 1 = 13 25 100
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Chap 3-9 Box and Whisker Plot A graphical display of data using a central “box” and extended “whiskers”: Example : 25% 25% 25% 25% Outliers Lower 1st Median 3rd Upper Limit Quartile Quartile Limit * *
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Chap 3-10 Shape of Box and Whisker Plots The Box and central line are centered between the endpoints if data is symmetric around the median (A Box and Whisker plot can be shown in either vertical or horizontal format)
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Chap 3-11 Constructing the Box and Whisker Plot Outliers Lower 1st Median 3rd Upper Limit Quartile Quartile Limit * * The lower limit is Q 1 – 1.5 (Q 3 – Q 1 ) The upper limit is Q 3 + 1.5 (Q 3 – Q 1 ) The center box extends from Q 1 to Q 3 The line within the box is the median The whiskers extend to the smallest and largest values within the calculated limits Outliers are plotted outside the calculated limits
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Chap 3-12 Distribution Shape and Box and Whisker Plot Right-Skewed Left-Skewed Symmetric Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3
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Chap 3-13
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Chap 3-14 Box and Whisker Plot (Cont)
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Chap 3-15 Box and Whisker Plot (Cont)
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Chap 3-16 Box and Whisker Plot (Cont)
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Chap 3-17 Measures of Variation Variation Variance Standard Deviation Coefficient of Variation Population Variance Sample Variance Population Standard Deviation Sample Standard Deviation Range Interquartile Range
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285%2Bchap02-va-3 - Statistics: Chapter 2 Methods for...

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