Video Transcript
Write the stems, in ascending
order, of a stem-and-leaf plot for the following data set: 67, 81, 74, 10, and
36. Then, complete the stem-and-leaf
plot.
In order to complete a
stem-and-leaf plot, we first need to remember that it’s a special table where the
data values are split into stems and leaves. As all of our data values here are
two-digit numbers, then our leaf, which is usually the digit at the end, will be the
value that’s in the units or ones column and the stem will be the digit in the tens
column. We’re asked to write the stems in
ascending order. That’s from smallest to
greatest. So let’s start by identifying that
our stems will be six, eight, seven, one, and three. In ascending order then, we could
say that the stems are one, three, six, seven, and eight. And that’s the answer for the first
part of this question.
Next, we need to create the
stem-and-leaf plot. We can set up our stem-and-leaf
plot in the following way. Even though we have a very small
data set with just five values, we don’t just want to write the stems that we have,
but we should include the stems in between these values. For example, we could start with a
stem of zero and go up to stem of nine. This would allow us, if in the case
of further data values, that we could continue to fill them in to the stem-and-leaf
plot.
We can now fill in the values. So let’s look at the first value of
67. This will have a stem of six and a
leaf of seven. The next value of 81 has a stem of
eight and a leaf of one. 74 is next. But then, when we come to the value
of 10, we need to be careful. We still need to record a leaf of
zero as, don’t forget, it doesn’t mean a value of zero; it means a value of 10. Finally, we have the value of 36
with a stem of three and a leaf of six. In a stem-and-leaf plot, we must
always make sure that the leaves are also given in ascending order. For example, if we also have the
value of 35, then when we wrote the leaves of six and five, we’d have to order these
so that the leaf of five came before the leaf of six.
But in this case, these five stems
only have one single leaf. But there’s still one thing that
we’re missing in our stem-and-leaf plot. We need to include a key. We can choose any value to
represent how to interpret our stem-and-leaf diagram, but it’s common just to select
the first value. Here, we can write that one and the
bar zero equals 10 to indicate that a stem of one and a leaf of zero would mean
10. And we can give our answer. Here is the fully complete stem and
leaf plot, complete with key.
