Welcome to the Wonderful World of AP Stats.…NOT! Chapter 2 Kayla and Kelly

DeNsItY cUrVeS

 Density Curves describe the overall pattern of a distribution.  Density Curves always remain on or above the horizontal axis and have a total area of 1 underneath.  The area under a density curve gives the proportion of observations that fall within a range of values.

 Density Curves are idealized descriptions of the overall pattern of a distribution that smoothes out irregularities in actual data.  Write the mean of a density curve as .  Write the standard deviation of a density curve as .

 The mean, median, and quartiles can be located using your very own eyes!  The Mean  is the balance point of the curve.  The Median divides the area under the curve in half.  The Quartiles with the median divide the area under the curve into quarters.

Special Notes:  The mean and median are equal for a symmetrical density curve.  The mean of a skewed curve is located farther toward the long tail than the median is.  The standard deviation * can’t be located by eye on most density curves.

NoRmAl DiStRiBuTiOnS

 Normal Distributions are described by bell-shaped symmetric density curves, call normal curves.  The mean  and the standard deviation  completely specify a normal distribution N( ,  ).  The mean is the center of the curve.  The standard deviation is the distance from  to the inflection points on either side.

 Normal Distributions satisfy the rule.  The rule describes what percentage of observations fall within 1, 2, and 3 standard deviations of the mean.  An observation’s percentile is the percent of the distribution that is or to the left of the observation.

 All Normal Distributions are the same when measurements are made in units of * about the mean.  These are called….standardized observations.  The standardized value z of an observation x is: z = x -  

 If x has the N(*,*) distribution, then the standardized value z= x -    has the standard normal distribution N (0,1) with the mean 0 and the standard deviation 1.  Table A (in back of book) tells you proportions of standard normal observations that are less than z for many values of z.  If we standardize, we can use Table A for any normal distribution.

NoRmAl PrObAbIlItY pLoTs

 Normal probability plots provide good assessments of the adequacy of normal models for data sets.  Statistic utilities like Minitab and Data Desk can construct theses plots from entered data.  A TI-83 Calculator can also do them.

Calculator Steps for Normal Probability Plots  Using data in a list, a histogram can be generated.  Using 1-Variable Stats  (STAT/CALC/1:1 Var Stats/L 1 )  This will show you the data.  By comparing the mean and medians, one can see if the distribution is fairly symmetric.  A boxplot can be used to confirm the symmetric shape and show outliers.

Well, that’s all Folks. There’s only one more thing to say…

Party on, Wayne Party on, Garth

This presentation was brought to you by: Kayla and Kelly