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

More on Describing Distributions AP Statistics

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.

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

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.

Frequency, Relative Frequency, Cumulative Frequency & Ogives

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

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

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.

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.

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.

Radioactive Beagles!

# 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 0.150-0.199 4 4/55 = 0.072 = 7% 4 4/55 = 0.072 = 7% 0.200-0.249 2 2/55 = 0.036 = 4% 6 11% 0.250-0.299 5 5/55 = 0.091 = 9% 11 20% 0.300-0.349 21 21/55 = 0.382 = 38% 32 58% 0.350-0.399 9 9/55 = 0.164 = 16% 41 75% 0.400-0.449 9 9/55 = 0.164 = 16% 50 91% 0.450-0.499 4 4/55 = 0.072 = 7% 54 98% 0.500-0.549 0/55 = 0 = 0% 54 98% 0.550-0.599 1 1/55 = 0.018 = 2% 55 100%

Completed Ogive: