AP Statistics Section 2.1 B Data Analysis Toolbox When describing distributions, always use the following strategies: 1. Plot your data: make a graph, usually a __________ histogram or a __________. stemplot 2. Look for the overall pattern: shape _______, _______, center _________ spread ) and for striking deviations such as ________ outliers . Remember: CUSS 3. Calculate a numerical summary to describe the _______ center and spread ________. Note: If the distribution is roughly symmetrical use mean and standard deviation _________________________. If the distribution is skewed use median and IQR _________________. Sometimes, the overall pattern of a large number of observations is so regular that we can describe it using a smooth curve. 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. The curve is a mathematical model for the distribution. A mathematical model is an _________description. This idealized smooth curve is called a ________ density curve. A density curve has the following properties: *the curve is always ____ on or _______ above the horizontal axis, and *the area under curve represents all observations and equals ___. 1 The median of a density curve is the point that divides the area under the curve in half. The mean of a density curve is the point at which the curve would balance if it was made out of some solid material. Example 1: Approximate the mean and median of the density curves below. M M M Example 2: Here is an unusual ‘broken line” density curve. a) Verify that the graph is a valid density curve. (.4)(1) .4 1 (.4)(1 2) .6 2 .4 .6 1 Example 2: Here is an unusual ‘broken line” density curve. 1 (.2)(1 1.5) .25 2 Example 2: Here is an unusual ‘broken line” density curve. .4 .25 .65 Example 2: Here is an unusual ‘broken line” density curve. .49