Stem and Leaf Plots
A stem and leaf diagram is a graph that show the shape of data using it shape
values. The leaf part is normally the very right-hand digit, which is the digit
in the ones place. The stem part is the rest of the digits to the left. We will use the
dataset on the screen to demonstrate how a stem and leaf diagram is created.
The diagram is simply a T-chart with “stem” written as the heading on the left and
“leaf” written as the heading on the right. To make the diagram, we first group the
numbers according to their stems, from least to greatest. Doing this, the order
changes.
Next, we list the stems in the stem column, only listing each stem once, even if it
occurs more than once. In this case, our stems are one, two, three, four, and five.
The third step is to list the leaves in the leaf column next to the correct stem. So
starting with fourteen, the four is placed in the leaf column next to the one. Then
the five from fifteen is placed next to the four. We will do the same with the
twenties. We have twenty-two, twenty-four and twenty-five, so we will place two,
four, five in the leaf column next to the stem two. There are three numbers in the
thirties: thirty-two, thirty-three, and thirty-five. We place the two, three and five
from the ones place on the leaf side next to the stem three. There is only one
number in the forties, forty-seven, so we place the seven in the leaf column next
to the four. There is also one number in the fifties. You can see by the shape of
the diagram, that in this dataset, the most numbers are in the twenties and
thirties, and the fewest numbers are in the forties and fifties.
Let’s try another example using the data on the screen. Sixteen people were
surveyed to see how many days they spent on vacations during the year.
The results of the survey are in the chart. To make a stem and leaf diagram, we
must order the numbers from least to greatest. First, we make the T-chart and
label the stem and leaf parts.
Next, we list the stems in the stem column. In this case, several of the numbers
in the data only have a ones place. Since they have no tens, the stem for these
numbers will be zero. The other stems will be one, two and three, because there
are numbers with one, two and three in the tens place.
The third step is to list the leaves in the leaf column next to the correct stem. So,
starting with three, the three is placed in the leaf column, next to the zero. Then,
the five is placed to the right of the three, because its stem is zero also. There
are two fives in the dataset and they must both be listed. Also, on this stem, we
should list six, seven, eight, and nine. We will continue with the numbers that
have a one as the stem. The leaves for this stem will be zero, zero, two, four,
four and eight. Notice again that if we have two of the same number, it must be
listed twice to be displayed as part of the dataset. Also in the dataset are the
© K12 Inc. numbers twenty and twenty-two, so we will place zero and two in the leaf column
next to the stem two. There is one number in the thirties, which is thirty-one, so
we will place the one from the ones place on the leaf side next to the stem three .
Now that the stem and leaf diagram is complete, and we can see the shape of
the data, it is easy to tell that most of the people surveyed spent fewer than
twenty days vacationing.
In this last example, we will create a stem and leaf diagram using a dataset
that has a few numbers with digits in the hundreds place. In this case, we
have the weights of several students. The stem and leaf diagram will be created
in the same way that the others were. First, place the numbers in the correct
number order. Then, we need to make the T-chart and list the stems. Notice that
some of these stems have two digits. When you have numbers that are greater
than one hundred, the ones place will still be the leaves and the rest of the digits
to the left will become the stem. Next, we place the leaves next to the appropriate
stems. Soon you will be making your own stem and leaf diagram. Come back to
the tutorial and play through it again if you need help in making your diagram.
© K12 Inc.