1. Warm-Up (Add to your notes!)
Determine whether the following types of data are categorical or quantitative.
Hair Color
Political Affiliation
Crop Yield
Gender
Zip Code
GPA
Salary
Temperature
College Attended
Rain Fall
categorical
categorical
quantitative
categorical
categorical
quantitative
quantitative
quantitative
categorical
quantitative

2. More on Describing Distributions
AP Statistics

3. Marriage Data
Create back-to-back stem plots for the age of the husband and wife. Write a sentence or two to compare and contrast the two distributions.

4. Back-To-Back Stem Plot
Wife: skewed right
Wife Med: 31
Hus.: skewed right
Wife Range: 57 (16-73)
Hus. Med: 30.5
Hus. Range: 52 (19-71)
No Outliers

5. Both husband ages and wife ages seem to be centered in the late 20s (29 for wives, 30 for husbands). Both range over 50 years (57 for wives, 52 for husbands). Both age groups are skewed right. It appears that the age at which a person gets married is the same for males and females.

6. Frequency, Relative Frequency, Cumulative Frequency & Ogives

7. A Histogram is built on frequencies.
Display the distribution
of values of a
quantitative variable.

8. A Relative Frequency Histogram uses percentages in the vertical scale rather than counts:

9. A Cumulative Frequency Histogram shows the accumulation of counts through the progressive classes. Each class consists of its own frequency plus all the classes that come before it.

10. A Relative Cumulative Frequency Histogram shows the accumulation of percentages through the progressive classes. Each class consists of its own relative frequency plus all the classes that come before it.

11. An Ogive is a line graph based on the relative cumulative frequencies
An Ogive is a line graph based on the relative cumulative frequencies. The Ogive is used to read percentiles. pth percentile—the value such that p percent of the observations fall at or below it.
Construction:
Start the line graph at the lowest level of class one. This point should have 0 height, since there is no percentage of the data lower than the initial value. The next and every subsequent point is graphed at the lower end of each class, reflecting the percentages from the relative cumulative histogram.

12. Radioactive Beagles!

13. # of times a value occurs in the data set.
The fraction or proportion of times the value occurs.
Add counts in freq. that fall at or below current class interval.
Divide Cum. Freq. entries by total # of individuals.
Freq 55
Cum Freq 55 4
4/55 = = 7% 4
4/55 = = 7% 2
2/55 = = 4% 6
11% 5
5/55 = = 9% 11
20% 21
21/55 = = 38% 32
58% 9
9/55 = = 16% 41
75% 9
9/55 = = 16% 50
91% 4
4/55 = = 7% 54
98%
0/55 = 0 = 0% 54
98% 1
1/55 = = 2% 55
100%

15. Completed Ogive: