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AP Statistics Section 2.1 B
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Data Analysis Toolbox When describing distributions, always use the following strategies: 1. Plot your data: make a graph, usually a __________ or a __________. histogram stemplot
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2. Look for the overall pattern: _______, _______, _________ ) and for striking deviations such as ________ . Remember: CUSS shape center spread outliers
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3. Calculate a numerical summary to describe the _______ and ________
3. Calculate a numerical summary to describe the _______ and ________. Note: If the distribution is roughly symmetrical use _________________________. If the distribution is skewed use _________________. center spread mean and standard deviation median and IQR
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Sometimes, the overall pattern of a large number of observations is so regular that we can describe it using a smooth curve.
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Density Curves Consider the histogram below
Density Curves Consider the histogram below. We can sketch a smooth curve through the tops of the histogram for a good description of the overall pattern of the data.
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The curve is a mathematical model for the distribution
The curve is a mathematical model for the distribution. A mathematical model is an _________description. This smooth curve is called a ________ curve. idealized density
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A density curve has the following properties:
A density curve has the following properties: *the curve is always ____ or _______ the horizontal axis, and *the area under curve represents all observations and equals ___. on above 1
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The median of a density curve is the point that
divides the area under the curve in half.
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The mean of a density curve is the point at which
the curve would balance if it was made out of some solid material.
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Example 1: Approximate the mean and median of the density curves below.
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Example 2: Here is an unusual ‘broken line” density curve
Example 2: Here is an unusual ‘broken line” density curve a) Verify that the graph is a valid density curve.
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Example 2: Here is an unusual ‘broken line” density curve.
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Example 2: Here is an unusual ‘broken line” density curve.
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Example 2: Here is an unusual ‘broken line” density curve.
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