1. AP Statistics Section 2.1 B

2. Data Analysis Toolbox When describing distributions, always use the following strategies: 1. Plot your data: make a graph, usually a __________ or a __________.
histogram
stemplot

3. 2. Look for the overall pattern: _______, _______, _________ ) and for striking deviations such as ________ . Remember: CUSS
shape
center
spread
outliers

4. 3. Calculate a numerical summary to describe the _______ and ________
3. Calculate a numerical summary to describe the _______ and ________. Note: If the distribution is roughly symmetrical use _________________________. If the distribution is skewed use _________________.
center
spread
mean and standard deviation
median and IQR

5. Sometimes, the overall pattern of a large number of observations is so regular that we can describe it using a smooth curve.

6. Density Curves Consider the histogram below
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.

7. The curve is a mathematical model for the distribution
The curve is a mathematical model for the distribution. A mathematical model is an _________description. This smooth curve is called a ________ curve.
idealized
density

8. A density curve has the following properties:
A density curve has the following properties: *the curve is always ____ or _______ the horizontal axis, and *the area under curve represents all observations and equals ___. on
above 1

9. The median of a density curve is the point that
divides the area under the curve in half.

10. The mean of a density curve is the point at which
the curve would balance if it was made out of some solid material.

11. Example 1: Approximate the mean and median of the density curves below.

15. Example 2: Here is an unusual ‘broken line” density curve
Example 2: Here is an unusual ‘broken line” density curve a) Verify that the graph is a valid density curve.

16. Example 2: Here is an unusual ‘broken line” density curve.

17. Example 2: Here is an unusual ‘broken line” density curve.

18. Example 2: Here is an unusual ‘broken line” density curve.