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Stem-and-Leaf Plots

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Timetable Travel

Credit: Anonymous
Source: http://commons.wikimedia.org/wiki/File:Special_tram_line_timetable_during_Euro_2012_in_Pozna%C5%84.jpg
License: CC BY-NC 3.0

Do you know where you can find stem-and-leaf plots in public? Take a look above. This is a trolley timetable posted in Pozna?, Poland.

Why It Matters

In many parts of the world, public transportation is ingrained in the routine of people’s lives. Every day, people use trains and buses to travel from home to work or from home to school—and back again. In Europe, sometimes stem-and-leaf plots, like those pictured above, are used to display public transportation timetables, with the hours along the “stem” and the minutes as the “leaves.” Check out this bus schedule in Sochi, Russia. You might have to turn your head to recognize the stem-and-leaf plot. In this case, the “stem” is the top row of numbers, and the “leaves” are to be read vertically instead of horizontally.

Credit: Yufereff
Source: http://commons.wikimedia.org/wiki/File:Bus_timetable_in_Sochi,_Russia.jpg
License: CC BY-NC 3.0

You may be thinking, “Why?” Why not just list out all of the departure and arrival times? Well, organizing the data in a stem-and-leaf plot takes up less space, organizes the data neatly, and clearly shows the frequency of arrivals and departures. Below is an example data display without the stem-and-leaf plot:

5.03 7.32 9.02 11.07 13.32 15.07 16.50 18.32 20.07 22.38
6.02 7.37 9.07 11.32 13.37 15.20 17.02 18.37 20.20
6.18 7.50 9.24 11.37 13.50 15.32 17.07 18.50 20.32
6.37 8.02 9.32 12.02 14.02 15.37 17.20 19.02 20.37
6.48 8.05 9.37 12.07 14.07 15.50 17.32 19.07 20.50
6.55 8.20 10.02 12.32 14.20 16.02 17.37 19.20 21.02
7.02 8.24 10.07 12.37 14.32 16.07 17.50 19.32 21.07
7.07 8.32

10.32

13.02 14.37 16.20 18.02 19.37 21.20
7.20 8.37

10.37

13.07 14.50 16.32 18.07 19.50 21.32
7.25 8.51 11.02 13.20 15.02 16.37 18.20 20.02 21.37

Now here is the display after the data has been organized into in a stem-and-leaf plot:

5 3
6 2 18 37 48 55
7 2 7 20 25 32 37 50
8 2 5 20 24 32 37 51
9 2 7 24 32 37
10 2 7 32 37
11 2 7 32 37
12 2 7 32 37
13 2 7 20 32 37 50
14 2 7 20 32 37 50
15 2 7 20 32 37 50
16 2 7 20 32 37 50
17 2 7 20 32 37 50
18 2 7 20 32 37 50
19 2 7 20 32 37 50
20 2 7 20 32 37 50

21

2 7 20 32 37

22

38

See for yourself: http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell10.swf

Explore More

Check out the first link below for an interactive way to learn more about working with stem-and-leaf plots. Then use the second link to build your own plots!

http://www.shmoop.com/basic-statistics-probability/stem-leaf-plots-examples.html

http://illuminations.nctm.org/ActivityDetail.aspx?ID=220

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