Stem and Leaf Plots
MA66101
Activity Introduction
Today’s top story: Stem-and-leaf plot. Makes ya think about potted plants, doesn’t it?
Well, gardening has nothing to do with today’s lesson.
For the details, let’s go to the green thumb of this newsroom, Sally Neeeeewsworth!
Direct Instruction
That’s right, Geronimo! Today, we’re not planting begonias. We’re talkin’ graphs with
our favorite Englishman of yesteryear…
Lord Rottington’s stoppin’ by to show ya everything he knows about stem-and-leaf plots
for sets of data. So, as he would say… (in a British accent) Off you go!
Model 1
Stems on a leafy plant? You mean like shrubbery?
Plot sir. Stem-and-leaf plots. Like graphs.
Oh, right… yes, yes. Stem-and-leaf plots! They represent data that’s shown by its place
value.
When you want to see data and how it’s organized, you use the stem-and-leaf plot.
There are five main parts to a stem-and-leaf plot.
There’s the title, which tells what the information is about. The stem tells what the
leading place value is according to the key. In this case, the stems are counting by tens.
There’s the leaf, which represents the ones, or what is combined with the stem to make
the number.
Finally, there are the values. They represent the set of numbers inside the plot. And
then there’s the key, which tells us what the stem and leaf represent.
So far so good. Are you getting this? Or would you like me to throw this truck into
reverse so you can see that again?
Model 2
So now that you know what a stem-and-leaf plot is, let’s look at how you would create
one. Sound like fun? Good. Take it away, Lord Rottington!
First you’ll need a shovel and fertile soil.
Sir, you’ve forgotten that we’re talking graphs. Not gardens.
Oh, of course. Silly me. Graphs? Right. Graphs! So, the first thing to do is take the
data and group it by common leading digits.
For example, in this set of data we’ll group the data by the tens digits and list them in
order from least (pause) to greatest.
The next thing to do is to create a title for the stem-and-leaf plot, and create a plotting
area.
The stem will always go on the left and the leaves will always go on the right. The stem
and leaves are separated by a vertical bar.
For the tens digits, start with the smallest value and list it at the top, under the stem
List the other tens beneath the first value until you get to the tens digit that has the
highest value.
Then, take the leaves values, or the ones digits, that go with the stem values. List these
in order from least to greatest.
The last step is to create a key at the bottom of the stem-and-leaf plot. In order to do
this, take the first stem.
Draw a vertical line to the right of it, and the first value of the ones digits to the right of
the vertical line.
Make an equal sign to the right of the first leaf. Then write the standard number that it is
equal to on the right side of the equal sign.
Still cruisin’ along? If not, I can rewind this for you, lickity-split!
Model 3
We’re done looking at the bike. Let’s get on it and ride!!! Eh-hem… With training
wheels of course. Let’s put on our helmets and cruise the sidewalks of Stem-and-leaf
plotting! Lord Rottington?
Alrighty. Now we’re going to make a stem-and-leaf plot, not plant, that’ll go with this
data. The first thing we need to do is create the title and the plotting area.
Next, you group the data in order from least to greatest by place value, listing the stems
in order from smallest to largest. Notice this time that the smallest stem will be six and
the largest will be ten.
Now list the leaves that go with the stems in order from least to greatest.
The last thing to do is to add the key to the plotting area to tell what sixty-nine is
equivalent to. There! Bob’s your uncle! And off you go!
All of this stem-and-leaf talk makes me wanna prune my petunias! Anyway, what about
you? Wanna keep going or do you want to back things up a bit?
Direct Instruction
Stem-and-leaf plots aren’t just pretty. They’re functional too. They can be used to find
the range of a given set of data. To learn more, let’s go back to the duke of decay…
Lord Rottington!
Model 1
Is it time to talk about Range, sir?
The open range? Ah yes, home on the open range… where the deer and the antelopeFocus, sir.
Just tickling your funny bone today, Antonio. Of course you’re talking about range for
stem-and-leaf plots.
To find the range from a stem-and-leaf plot, you have to find the difference between the
smallest value on the plot and the largest value.
In this stem-and-leaf plot the smallest value is forty-five and the largest value is sixtyeight.
The range in the stem-and-leaf plot is twenty-three because sixty-eight minus forty-five
equals twenty-three.
And… pause. How do you feel about what you just heard? Good enough to move on?
Or do you need to hear it again?
Model 2
Stem-and-leaf plots can be used to find the three M’s as well: The mean, median, and
mode of a given set of data. Let’s start with mode and median…
Mode and median can be quite simple, so we won’t dally. Let me explain…
The mode in a stem-and-leaf plot is the number, when translated into standard form,
which occurs most often in the set of data. The mode in this set of data is thirty-five
because it appears three times.
Now, the median of the stem-and-leaf plot actually requires you to use the information
and list the numbers back into standard form, in order from least to greatest.
Once that’s done, you need to find the number in the middle. In this case, the median
will be eighteen. Good show!
Are ya getting’ it? Feel free to cruise ahead if you are. But if you think one more go at
it’ll help, lemme know.
Model 3
Enough being nice! Now, Lord Rottington’s gonna get mean! Just kidding. He’s the
nicest zombie I know! He’s actually going to show you how to find the mean from a
stem-and-leaf plot. Here we go!
) I hate to be a meanie (chuckles) but-I think you’re quite nice, sir.
Thank you, Antonio. I fancy you as a rather nice guy myself. But I was actually talking
about finding a mean.
Oh, of course, sir.
So, finding the mean is much like finding the median. The first step is to translate the
numbers into standard form. Now list them in order from least to greatest.
Now, if you place an addition sign between each value and add the numbers together,
you‘ll get two-hundred-fifty-nine.
Then, you divide two-hundred-fifty-nine by the number of items in the stem-and-leaf
plot. You will get the quotient, or the mean, for the data. The mean for this set of data
is twenty-five and nine-tenths because you divided two-hundred-fifty-nine by ten.
Did all of that translate for you? If any of it was unclear, lemme know and I can take it
back so you can see it again.
End of Activity Review
Okay, so let’s look at what we’ve covered.
In this activity, you learned that a stem-and-leaf plot can be used to describe the range,
median, mode, and mean for a set of data.
You also learned that stem-and-leaf plots are arranged by place value, from the
smallest value to the largest value; and, that all stem-and-leaf plots contain a title, the
values, and a key to signify what the numbers mean.
Shall we do our finito victory dance? Or should we hold off, until after we review it one
more time?