Back to Back Stem-and-Leaf Plots

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  • 0:04 Exploring Data
  • 0:35 Construction
  • 1:37 Example
  • 2:10 Finding the Mode
  • 2:41 Finding the Median
  • 3:06 Lesson Summary
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Lesson Transcript
Instructor: Nick Rogers
When you have a lot of data that is not organized, it can be very difficult to get any usable information from the data. This lesson shows you a graphical technique that allows you to easily organize and compare two sets of numbers.

Exploring Data

Data is only useful if it can be displayed in an easy to read and understand manner. Stem-and-leaf plots are an effective way to present data, allowing us to see at a glance the distribution of numbers. They allow us to quickly tell if there are a lot of high or low numbers, and make it easier to find measures like the mode, which is the most common number in a data set, and the median, which is the middle number in a data set. A back to back stem-and-leaf plot goes one step further and allows for easy comparison of two sets of numbers.


As you recall, in a 2-digit stem-and-leaf plot, the digits in the tens place are the stems and the digits in the ones place are the leaves. If a number is only 1 digit, a 0 is the stem. Now, let's construct a back to back stem-and-leaf plot from this set of data:

Set 1: (1, 2, 5, 12, 18, 15, 17, 22)

Set 2: (3, 4, 16, 21, 25)

We'll start by using the data from Set 2 and create a normal stem-and-leaf plot. The stems for Set 2 are 0 (for the 3 and 4), 1 (for the 16) and 2 (for the 21 and 25). It's most important to note that, coming out from the stem, the leaf numbers go in order from smallest to largest. To create a back to back stem-and-leaf plot, we do the same thing on the left side of the plot using Set 1 data. Again, and this can be a little tricky at first, the leaf numbers go in order with the smallest being closest to the stem and getting larger as you move out further to the left.


Let's apply our techniques to a famous basketball game - the final game in the 1996 NBA championships at the height of Michael Jordan's career between the Seattle SuperSonics and the Chicago Bulls. You can see the number of points that each player scored in the table below:

Team Player Points
Seattle Payton 19
Seattle Hawkins 4
Seattle Schrempf 23
Seattle Kemp 18
Seattle McMillan 7
Seattle Askew 4
Chicago Jordan 22
Chicago Pippen 17
Chicago Rodman 10
Chicago Harper 9
Chicago Longley 12
Chicago Kukoc 10
Chicago Kerr 7

Let's plot each team's points.

NBA Championship Finals 1996

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