Video Transcript
Write the stems, in ascending order, for the following data set and, hence, make a stem-and-leaf plot from the data: 14, 42, 21, 33, 36, 27, 29.
We can remember that a
stem-and-leaf plot is a special type of table where each data value is split into a
stem part and a leaf part. When we create a stem-and-leaf
plot, the leaves are usually single-digit values. As all of the data values here are
two-digit numbers, then the stems will be the numbers in the tens column and the
leaf will be the part that’s in the units column. We can set up the structure of our
stem-and-leaf plot, but we must remember to include one important thing. And that’s a key. Here, for example, we could say
that a stem of one and a leaf of four would indicate the value of 14.
We’re asked to begin by writing the
stems in ascending order from smallest to greatest. And that’s actually the way any
stem-and-leaf plot would be. The lowest value here is 14. So the smallest stem we have would
be one, which would be the same as 10. The largest value in the data set
is 42. So our stem must go up to four. And there we have the stems in
ascending order: one, two, three, and four. We can now take each value in turn
and fill it in to the stem-and-leaf plot. The first value of 14, as we’ve
already demonstrated with the key, would be written in the row with the stem of one,
and we fill in the value four for the leaf.
If we have a large data set, then
it’s worthwhile crossing through or taking each value as we go. The next value is 42 so that we’ll
have a stem of four and a leaf of two. We can continue crossing off the
values as we go. When we have two values with the
same stem, for example, 33 and 36, then we must put a comma between the leaves. And there is our completed
stem-and-leaf plot. It’s always worth checking that we
have the same number of data values as we do in the stem-and-leaf plot. For example, we were given seven
data values to start with. And if we count the leaves, we can
see that there are seven different leaves. So there we have our complete
answer for the stem-and-leaf plot and not forgetting the key.
Just one final point, when we
filled in the data, the leaves are actually in ascending order. For example, the leaves with a stem
of two go from one, seven, and nine. If, for example, we had the value
of 29, then 21, then 27, we’d need to reorder these so that they occurred one, then
seven, then nine. This will be true of every
stem. The leaves must be given in
ascending order.
