### Video Transcript

A class of students were asked to
count and record the number of bugs that they could find in their yards in 30
minutes. The results were as follows: 21,
35, 42, 11, 13, 77, 14, 17, 31, 27, 15, 53, 12, 25, 31, 18, 22, 16, 72, 14, 91, 34,
19, 23. Write the stems, in ascending
order, of a stem-and-leaf plot for the data. Display the data in a stem-and-leaf
plot. Use your stem-and-leaf plot to find
out how many students counted bugs in their yards.

We can see the list of values here,
which begins with the value of 21 that would indicate that one student had found 21
different bugs in their yard. What we’re asked to do is to take
this list of numerical values and put it into a stem-and-leaf plot. A stem-and-leaf plot is a special
type of table where the leaves of each number will represent the final digit of each
number. As all of the values here are
two-digit numbers, then the leaves will all be the values in the ones column and the
stem will be the value in the tens column.

For example, the stem of the first
number would be two, the second stem would be three, the third stem would be four,
and so on. Notice that a number of these stems
will have duplicates. For example, there’s a number 11
and a number 13, which indicates that there’ll be two values that have a stem of
one. The best way perhaps to write the
stems in ascending order is to start by creating our stem-and-leaf plot. The smallest value that we have is
11, and the largest value is 91. Therefore, our stems will need to
go from one to nine.

So here we have the stems
written. We can include the stem of zero if
we wish, although it’s not essential. As we go through to creating the
stem-and-leaf plot, we’ll also need to include a key. We can choose any value to
represent the key. Here, I’ve chosen a value with a
stem of one and a leaf of two to indicate that that means 12 bugs. So that would be the first part of
the question answered. The stems are written in ascending
order.

We’ll now begin to answer the
second question, which is where we fill in the data values into the stem-and-leaf
plot. Because we have a large data set
here, we can begin by filling in the values so that the leaves are given in an
unordered way. Once we have all of the values into
the stem-and-leaf plot, then we’ll rewrite it so that the leaves are in order. So let’s take the first value of
21. This will have a stem of two and a
leaf of one. The second value of 35 has a stem
of three and a leaf of five.

We can input the next two values of
42 and 11. But notice that when it comes to
the value of 13, we need to put a comma and then the leaf of three. We can continue until all the
values are in the stem-and-leaf plot. We can notice, for example, that
the value of 31 occurred twice, but we must still write it into our stem-and-leaf
plot twice. We’ll now put the leaves in each
stem into ascending order. Having the leaves in order also
allows us to interpret the data and draw any conclusions we may want to. And so that’s our answer for the
second part of the question. Here’s a fully complete and ordered
stem-and-leaf diagram along with the key.

The third part of this question
asks us to find out how many students counted bugs in their yards from the
stem-and-leaf plot. In order to do this, we need to
count the total number of leaves. In the first row, we have 10
different leaves, then five leaves, four, one, one, two, and one. Adding these all together would
give us the value of 24. So our answer would be that 24
students counted bugs in their yards. It’s also a very good check as
we’re completing the stem-and-leaf diagram to make sure that we’ve got all of the
values in. If we’d counted each individual
data value that we were originally given, we would also find that there were 24
different data values.