Ch3-0928 - The Normal Distributions Chapter 3 1 How to...

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Chapter 3 The Normal Distributions 1
How to explore a distribution Graphical summary (a plot, a graph, a histogram) Overall pattern (shape, center, spread); outliers Numerical summary to describe center and spread. Another way: Density Curve
Histogram of the test scores of 947 students The smooth curve drawn over the histogram is called a density curve . This curve is a mathematical model for the distribution.
Histograms and areas The total area under a the histogram is equal to 1 (or 100%). The shaded area represents the proportion of scores that are less than or equal to 6.0. (This proportion is equal to 0.303 or 30.3%).
Density curves and areas If the scale is adjusted so the total area under the curve is exactly 1, then this curve is called a density curve . The proportion of the area to the left of 6.0 is now equal to 0.293. A density curve can be a good approximation to the distribution.
Density Curve: Definition A density curve is a curve that: Always on or above the horizontal axis has an area of exactly 1 underneath it Area under the curve and above any range of values is the proportion of all observations that fall in that range.
Density Curves Our measures of center and spread apply to density curves as well as to actual sets of observations . The median of a density curve is the equal-areas point , the