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Chapter 3

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STAT 101
Rick Routledge

CHAPTER 3 Exploring a Distribution  Plot your data, usually a histogram or stemplot  Evaluate overall pattern (shape, center, spread)  And for striking deviations (outliers)  Calculate a numerical summery to describe the center and spread Density Curve – a curve that approximately describes the overall pattern of a distribution  Median – the point with half the observations on either side Quartiles divide the area under the curve into quarters ⁄ of the area is left of the first quartile ⁄ of the area is left of the third quartile  Mean ( ) – the point at which the curve would balance if made of solid material  The mean is pulled to the direction of the long tail in a screwed density curve Normal Distributions N( , )  All Normal curves have the same overall shape: symmetric, single-peaked, bell-shaped  Any specific Normal curve isdescribed by its mean, and standard deviation  Mean ( ) – the center of the symmetric Normal curve  Standard deviation ( )– the distance from the center to the change-of-curvature points on either side  Changing the without changing the moves the Normal curve along the horizontal axis without changing its spread  Standard deviation ( ) controls the spread of a Normal curve  Curves with larger standard deviations are more spread out  Importance of the Normaldistribution - Normal distributions are good descriptions for distributions of real data (test scores, repeated careful measurements) - Normal distributions are good approximations to the results of many kinds of chance outcomes
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