Transcript Powerpoint 2.1 B

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