Q UOTE OF THE D AY As for everything else, so for a mathematical theory: beauty can be perceived but not explained -Arthur Cayley

I NTERPRET S TEM - AND -L EAF P LOTS AND H ISTOGRAMS Section 13.7

O BJECTIVES : Make and interpret stem-and-leaf plots and histograms

K EY V OCABULARY : Stem-and-leaf plot Frequency Frequency table Histogram

S TEM - AND -L EAF P LOTS A stem-and-leaf plot is a data display that organizes data based on their digits Each value is separated into a stem (the leading digit(s)) and a leaf (the last digit) A stem-and-leaf plot has a key that tells you how to read the data.

E XAMPLE 1: The number of home run hit by the 20 baseball players with the best single-season batting averages in Major League Baseball since 1900 are listed below. Make a stem and leaf plot of the data. 14, 25, 8, 8, 7, 7, 19, 37, 39, 18, 42, 23, 4, 32, 14, 21, 3, 12, 19, 41

#1: C OMPLETE. The years in which each of the first 20 states were admitted to the Union are listed below. Make a stem-and-leaf plot of the years. 1788, 1787, 1788, 1816, 1792, 1812, 1788, 1788, 1817, 1788, 1787, 1788, 1789, 1803, 1787, 1790, 1788, 1791, 1788

#2: C OMPLETE. In Example 1, describe the distribution of the data on the intervals represented by the stems. Are the data clustered together in a noticeable way?

E XAMPLE 2: The back-to-back stem-and-leaf plot shows the ages of members of the U.S. men’s and women’s 2004 Olympic gymnastics teams. Compare the ages of the gymnasts on the two teams.

F REQUENCIES, F REQUENCY T ABLES, AND H ISTOGRAMS The frequency of an interval is the number of data values in that interval. A frequency table is used to group data values into equal intervals, with no gaps between intervals and no overlapping intervals. A histogram is a bar graph that displays data from a frequency table. Each bar represents an interval.

E XAMPLE 3: The prices (in dollars) of sandwiches at a restaurant are listed below. Make a histogram of the data. 4.00, 4.00, 4.25, 4.50, 4.75, 4.25, 5.95, 5.50, 5.50, 5.75

#3: C OMPLETE. The back-to-back stem-and-leaf plot shows the percents of students in 24 countries who report watching television for 4 or more hours each data. Compare the data for female and male students.

#4: C OMPLETE. The average number of days each month with precipitation of 0.01 inch or more in Buffalo, New York, are 20, 17, 16, 14, 13, 11, 10, 10, 11, 12, 16, and 19. Make a histogram of the data.

P ARTNER W ORK Page 883 #3, 7, 10, 13, 17

H OMEWORK A SSIGNMENT Page 883 #4, 6, 8, 12, 14, 18, 20, 24, 26