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# lecture4_2slides - Statistics 528 Lecture 4 Professor Kate...

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Statistics 528 - Lecture 4 1 Statistics 528 - Lecture 4 Professor Kate Calder 1 Section 1.3 Density Curves Mathematical model for the distribution of a variable Alternative to graphical and numerical summaries Idealized description - histogram of the data is not exactly the same as the curve Compact representation of a distribution Statistics 528 - Lecture 4 Professor Kate Calder 2 Relative Frequency of Scores Less Than or Equal to 6.0 0.303 (using the histogram) 0.293 (using the density curve)

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Statistics 528 - Lecture 4 2 Statistics 528 - Lecture 4 Professor Kate Calder 3 Properties of Density Curves A density curve is always on or above the horizontal axis. The area underneath a density curve is exactly 1. The area under a density curve and above any range of values is the relative frequency of all observations that fall in that range. Density curves, like data distributions, can come in many shapes - symmetric, right-skewed, left-skewed. Observations that are outliers are not described by the density curve.
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Unformatted text preview: Statistics 528 - Lecture 4 Professor Kate Calder 4 • The mode of a density curve is a peak point of the curve or a location where the curve is highest. • The median of a density curve is the point that divides the area under the curve in half. • The mean of a density curve is the point at which the curve would balance if made out of solid material. Statistics 528 - Lecture 4 3 Statistics 528 - Lecture 4 Professor Kate Calder 5 • For a symmetric density curve, the median = mean. • For a right-skewed density curve, the mean > median. • For a left-skewed density curve, the mean < median. Statistics 528 - Lecture 4 Professor Kate Calder 6 We need to distinguish the mean and standard deviation of a density curve (characteristics of the mathematical model) from the mean and standard deviation of the data. Notation: Data distribution: mean = sample average ( ), standard deviation (s) Density curve: mean ( μ ), standard deviation ( σ ) x...
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lecture4_2slides - Statistics 528 Lecture 4 Professor Kate...

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