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STEM AND LEAF PLOTS? IS THIS MATH? GARDENING? OR BOTH?

Hi All,

A very common question among upper elementary and middle school parents, and students, and even many teachers, is "What are stem and leaf plots?" Is it math? Is it botany? Is it gardening? Followed quickly by, "And why do we need to know what they are anyway?"

I can't remember being taught stem and leaf plots in school either, but as I've come to work with them, I wonder why not, because they can be a very useful and revealing tool with certain kinds of data. Plus they're easy to do.

For example, let's say you are growing bean plants. You planted 10 plants and you recorded their heights on a chart:

1. 18"
2. 20"
3. 18"
4. 17"
5. 16"
6. 18"
7. 80''
8. 18"
9. 18"
10. 17"

Your friend hears about the bean plants and says, "I'm thinking of growing bean plants too. About how high do they grow on average?" 

 You know how to find averages. You add up all the heights and divide that sum by the number of plants. So you add up all the heights and get 240". You divide 240" by 10 (because there are 10 plants) and the average height is 24".

 But, when you look at your plants you see that not one of them is higher than 20". How can the average be higher than the tallest plant? Most are like 17" or 18". Oh, wait there was that one crazy tall plant. You're not even sure now if it was actually a bean plant. It was 80" tall! And that threw the average off.

 A stem and leaf plot would reveal the height of a typical bean plant much more clearly than the chart above and the mathematical average. Here's how you make a stem and leaf plot. Let's use the bean plant data:

 1. Write the data in order from least to greatest.
16, 17, 17, 18, 18, 18, 18, 18, 20, 80

 2. Find the greatest and the least values.
16 is the least
80 is the greatest

 3. Choose the stems. Use the 3 different digits in the tens place as the stems and write them in a vertical list from least to greatest. Draw a vertical line alongside.

 1I
2I
8I

 4. Show each piece of data by writing its ones digit next to its tens digit. (The ones digits are the leaves if you will.)

 1I 6 7 7 8 8 8 8 8
2I 0
8I 0

 5. Add a key and a title to your plot.

 Bean Plant Heights
1I 6 7 7 8 8 8 8 8
2I 0
8I 0

Key: 1I8 means a height of 18 inches.

As you can see, the stem and leaf plot organizes the data in such a way that the average or typical height of your bean plants is much more apparent than your list type chart or the mathematical average.

Attached are a few more problems that feature data where a stem and leaf plot might be very useful in analyzing and understanding that data. You can use the bean plant data above for the first problem.

 https://drive.google.com/file/d/1E8Emubq65FD6nHVPew7yAdbfiLOI7n7x/view?usp=sharing

Enjoy!
All the best and blessings to you. Stay safe, y'all.
Bob



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