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# 1.3 - Assignment#2 1.120 1.122 1.126 1.132 1.136 1.142...

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Assignment #2 1.120, 1.122, 1.126, 1.132, 1.136, 1.142, 1.146, 2.22, due September 16

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2 Density Curves and Normal Distributions
What we have learned Plot the data Look for overall pattern and deviations from the pattern Compute numerical summaries

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Mathematical model If the pattern is sufficiently regular, approximate it with a smooth curve A curve that is always on or above the horizontal axis and has total area underneath equal to 1 is called a density curve .

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Density curves Area under the curve in a range of values indicates the proportion of values in that range Keep in mind that density is only an approximation (an idealized mathematical model), but it simplifies analysis and is generally accurate enough for practical use.

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Median and mean of a density curve Median: the point with 50% of the area on either side Mean: the balancing point of the curve, if it were a solid mass; can be calculated by using calculus

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Mean Variance

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Mean and standard deviation of an idealized model Mean and standard deviation of observed data

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Density curves come in a variety of shapes, but the family of “ normal ” distributions with familiar bell-shaped density curves is commonly used
Normal distributions All the normal distributions can be generated from the standard normal distribution by changing locations and scales ( linear transformations ) The standard normal distribution has density function defined by It has mean equal to 0 and variance equal to 1.

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Symmetric (about 0), single peak, bell-shaped
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1.3 - Assignment#2 1.120 1.122 1.126 1.132 1.136 1.142...

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