Lec3-1 - Section 2.4 How Can We Describe the Spread of...

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Agresti/Franklin Statistics, 1 of 63 Section 2.4 How Can We Describe the Spread of Quantitative Data?
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Agresti/Franklin Statistics, 2 of 63 Measuring Spread: Range Range: difference between the largest and smallest observations
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Agresti/Franklin Statistics, 3 of 63 Measuring Spread: Standard Deviation Creates a measure of variation by summarizing the deviations of each observation from the mean and calculating an adjusted average of these deviations 1 ) ( 2 - - = n x x s
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Agresti/Franklin Statistics, 4 of 63 Empirical Rule For bell-shaped data sets: Approximately 68% of the observations fall within 1 standard deviation of the mean Approximately 95% of the observations fall within 2 standard deviations of the mean Approximately 100% of the observations fall within 3 standard deviations of the mean
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Agresti/Franklin Statistics, 5 of 63 Parameter and Statistic A parameter is a numerical summary of the population A statistic is a numerical summary of a sample taken from a population
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Agresti/Franklin Statistics, 6 of 63 Section 2.5 How Can Measures of Position Describe Spread?
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Agresti/Franklin Statistics, 7 of 63 Quartiles Splits the data into four parts The median is the second quartile, Q 2 The first quartile, Q 1 , is the median of the lower half of the observations The third quartile, Q 3 , is the median of the upper half of the observations
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Agresti/Franklin Statistics, 8 of 63 Example: Find the first and third quartiles Prices per share of 10 most actively traded stocks on NYSE (rounded to nearest $) 2 4 11 12 13 15 31 31 37 47 a. Q 1 = 2 Q 3 = 47 b. Q 1 = 12 Q 3 = 31 c. Q 1 = 11 Q 3 = 31 d. Q 1 =11.5 Q 3 = 32
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Agresti/Franklin Statistics, 9 of 63 Measuring Spread: Interquartile Range The interquartile range is the distance between the third quartile and first quartile: IQR = Q3 – Q1
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Agresti/Franklin Statistics, 10 of 63 Detecting Potential Outliers
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This note was uploaded on 04/22/2008 for the course STAT 280 taught by Professor Thomas during the Spring '08 term at Rice.

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Lec3-1 - Section 2.4 How Can We Describe the Spread of...

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