Review - Student Lecture Notes 1 Review Measures of central...

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Student Lecture Notes 1 Review 1 Review 1 Review ± Measures of central tendency ± Measures of variation ± Data Distribution, Shape, PDF ± Properties of Normal distribution (PDF) ± Student’s t-Distribution ± Population Parameter estimated by Sample Statistic ± CI (Confidence Interval) ± Confidence Level ± Level of Significance Review 2 Describing Distributions with Numbers ± Measures of central tendency ± Mean (average, balance point of values) ± Median (50%, 50% smaller, 50% larger) ± Measures of variation ± Range = Max – Min ± IQR = Interquartile range = Q3-Q1 ± Variance and Standard Deviation ± Measures of Data Distribution ± 5-number Summary (Min, Q1, Median, Q3, Max) ± Box Plot - graphic 5 number summary: evaluate distribution
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Student Lecture Notes 2 Review 2 Review 3 Numerical Methods for Quantitative Data Numerical Data Properties Mean Mean Median Median Mode Mode Central Tendency Range Range Interquartile Range Interquartile Range Variance Variance Standard Deviation Standard Deviation Variation Shape Skew Skew Review 4 Quantitative Data Properties Central Tendency Central Tendency (Location) (Location) Variation (Dispersion) Shape Shape
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Student Lecture Notes 3 Review 3 Review 5 Standard Notation Measure Measure Sample Sample Population Population Mean Mean X μ Stand. Dev. Stand. Dev. S σ Variance Variance S 2 σ 2 Size Size n N Review 6 Sample Mean ± Affected by outliers ± Balance point
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Student Lecture Notes 4 Review 4 Review 7 Variation – Sample Variance and Standard Deviation Review 8 Median and Quartiles ± Not affected by outliers ± Data placed in ascending order ± Location (observation number for ordered data) of quartile is (n+1)(P/100) ± Value of quartile value at observation number or linear interpolation between adjacent values ± Q1: P=25; Q2: P=50; Q3: P=75 ± 25%, 50%, 75% respectively ± Q1 at (n+1)/4 – median of left half ± Q2 at (n+1)/2 – median of all data ± Q3 at 3(n+1)/4 – median of right half
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Student Lecture Notes 5 Review 5 Review 9 Quartiles - 25% of Observations in each Quartile ± Measure of noncentral tendency ± Split ordered data into 4 quarters ± Position of i-th quartile 25% 25% 25% 25% 25% 25% 25% 25% Q 1 Q 2 Q 3 Positionin Positionin g point of g point of Q i n i = + 1 4 a a f f Review 10 Properties of Distributions ± Shape, Central Tendency, variation and outliers – use Box-Plot and Histogram to evaluate
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Student Lecture Notes 6 Review 6 Review 11 Describing Distributions Five-Number Summary: Shape Review 12 Thinking Challenge ... employees cite low pay -- -- most workers earn only $20,000. $20,000. ... President claims average pay is $70,000! $400,000 $400,000 $70,000 $50,000 $50,000 $30,000 $20,000 $20,000
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Student Lecture Notes 7 Review 7 Review 13 Thinking Challenge Example Problem ± Assume population data ± N= ± SUM(Xi)= ± Mean = SUM(Xi)/N= ± Observation number (ordered data) for ± Min: ± Q1: (n+1)/4 ± Q2=median: (n+1)/2 ± Q3: 3(n+1)/4 ± Max: ± 5-number summary: ± SUM(Xi-Mean)^2= ± Population Variance=[SUM(Xi-Mean)^2]/N = ± Standard Deviation = SQRT(Variance) Review 14 Excel Tools -> Data Analysis -> Descriptive Statistics iX X_ordered (Xi-Mean) i-Mean)^2
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This note was uploaded on 09/25/2009 for the course IDS 371 taught by Professor Staff during the Spring '08 term at Ill. Chicago.

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Review - Student Lecture Notes 1 Review Measures of central...

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