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Math for Kids23 chapters | 325 lessons

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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.

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.

By looking at this chart, you should be able to see that a lot of Chicago's success came from their supporting players, who filled in the second row of the stem-and-leaf plot. Now let's use this back to back stem-and-leaf plot to find the mode and the median for both teams.

Finding the mode is a two-step process. First, for each set of points, find the number that occurs the most in the leaf part of the plot. For Seattle, we can immediately see that the number that occurs the most is 4. The second step is to look at the stem that goes with that leaf. For Seattle, the stem is 0, so 4 is the mode.

Now let's find the mode for Chicago. First, the number that occurs the most in the leaf is 0. Looking at the stem for that leaf, we see that it's a 1. So, putting the stem and leaf together, Chicago's mode is 10.

Remember that the median is the number in the middle. To find the median, alternate removing the lowest value number and the highest value until only one remains. For Chicago, there is an odd amount of data values and after all of our removing, we are left with 10 for the median. For Seattle, the number of scoring players was even, so we have both a 7 and 8 remaining. In this case, we take the average, so the median for Seattle is 7.5.

Let's take a few moments to recap what we've learned about back to back stem-and-leaf plots and how they work. **Back to back stem-and-leaf plots** allow for easy comparison of two sets of like data. By breaking your data into 'stems' and 'leaves,' you can easily find the **mode** (i.e. the most frequently occurring number in a data set) and **median** (i.e. the middle number of a data set), as well as other information regarding the distribution of numbers.

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Math for Kids23 chapters | 325 lessons

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