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Chapter 13 (1)

# Chapter 13 (1) - Chapter 13 The Normal Distribution Outline...

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Chapter 13 The Normal Distribution

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Outline Density Curves Center and Spread of Density Curves Normal Distributions The 68 – 95 – 99.7 Rule Percentiles of Normal Distributions
Motivation Drawing a curve based on data vs. using the Normal Curve

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Density Curves
Density Curves vs. Histograms Histograms Y axis is counts Total area under the curve depends on the number of observations Area doesn’t have a valuable interpretable meaning Density Curves Y axis is density Total area under curve = 1

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Density: A little deeper Histogram: Describe the distribution of a random variable by describing the values it can take on and the number of times it takes on those values. Density: Describes the distribution of a random variable without worrying about how many observations we took.
Density vs. Frequency 8 6 4 2 0 -2 -4 300 250 200 150 100 50 0 8 6 4 2 0 -2 -4 N=2000 Frequency N=5000 Histogram  8 6 4 2 0 -2 -4 0.20 0.15 0.10 0.05 0.00 8 6 4 2 0 -2 -4 N=2000 Density N=5000 Density Plot

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The Center and Spread of a Density
Center Median – Equal areas point The middle value of the distribution. Since half of the observations are less than this value and half are larger, then half of the area under a density curve is to the right of the median and half is to the left. Mean – Balancing point If the observations had weights, the mean is the center of gravity. Median puts half of the observations on each side of it. Mean puts half of the total value of the observations on each side of it.

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Mean vs. Median A. Symmetric Observations to the left of the median are just as far from the median as the observations to the right of the median. B. Skewed Right Observations to the right of the median are much farther from the median than the observations to the left of the median
Mean as a Balancing point Since observations to the right of the median are “more extreme” they have more leverage. The mean must scoot over to account for the extra leverage.

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Chapter 13 (1) - Chapter 13 The Normal Distribution Outline...

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