Lecture3_print - Section 1.3: Normal Distribution Readings:...

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Unformatted text preview: Section 1.3: Normal Distribution Readings: Section 1.3 September 10, 2009 1 Density Curves So far our strategy for exploring data is Graph the data to get an idea of the overall pattern Calculate an appropriate numerical summary to describe the center and spread of the distribution Sometimes the overall pattern of a large number of observations is so regular, that we can describe it by a smooth curve, called a density curve Idea of density curves A density curve is curve that Is always on or above the horizontal axis Has area equal to exactly 1 underneath it A density curve is an idealized description of a distribution of data The mean of the density curve is denoted as and the standard deviation is denoted as When we take actual observations (a sample), we distinguish the mean of the distri- bution of these observations as x and the standard deviation as s 1 A density curve has the following properties: The area under the density curve and above any range of values is the proportion of all observations that fall in that range The mode is the peak point of the curve The median of a density curve is the equal-areas point The mean of a density curve is the balance point The median and the mean are always equal on a symmetric density curve 2 Normal Distribution Normal Curves Normal curves, denoted by N ( , ), are a particularly important class of density curves. Normal curves have the following properties: 2 Symmetric, unimodal, bell-shaped Mean, , always is the center of the curve (the peak) Standard deviation, , controls the spread of the graph (wide or narrow) Probabilities are just the area under the curve (integral) between the points of interest Total area under the normal curve = 1 (or 100%) Curve stretches from...
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This note was uploaded on 04/23/2011 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Lecture3_print - Section 1.3: Normal Distribution Readings:...

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