Transcript Welcome to the Wonderful World of AP Stats.…not!

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
68-95-99.7 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/L1)
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