Chapter-2-10-11 - Chapter 2 The Normal Distributions...

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Chapter 2: The Normal Distributions
Section 2.1: Density curves and the Normal Distributions rom chapter 1 we have a strategy for exploring data on a single quantitative variable: lot your data: make a graph, usually a histogram or a stemplot. ook for the overall pattern (shape, center, spread) and for any striking deviations such as outliers. 2
Here is the next step: If the overall pattern of a large number of observations is very regular we can describe it with a smooth curve. This curve is a mathematical model for the distribution and it gives a compact picture of the overall pattern. This is also known as a density curve. 3
A density curve is a curve that:
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The Median and Mean of a Density curve: The mean of a density curve is the balance point, at which the curve would balance if made of solid material. The median of a density curve is the equal-areas point, the point that divides the area under the curve in half. 5
The median and mean are the same location if the density curve is symmetric, and they both lie at the center of the curve. The mean of a skewed curve is pulled away from the median in the direction of the long tail. 6
Since a density curve is an idealized description of the distribution of data, we need to distinguish between the mean and standard deviation of the density curve and the mean and standard deviation computed from the actual observations. The new notation is the Greek letter mu for the mean and the Greek letter sigma for standard deviation. μ σ 7
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Normal distributions: Normal curves are curves that are symmetric, single-peaked, and bell- shaped.
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