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Video: Finding the Stems of a Stem-and-Leaf Plot for a Data Set

Tim Burnham

Write the stems, in acsending order, of a stem-and-leaf plot for the following data set: 2, 29, 65, 31, and 93.

03:12

Video Transcript

Write the stems, in ascending order, of a stem-and-leaf plot for the following data set: two, twenty-nine, sixty-five, thirty-one, and ninety-three. Now the important information that we’ve got in this question is that here’s the data; we’re producing a stem-and-leaf plot; and specifically, we need to write the stems from that stem-and-leaf plot. And we need to write them in ascending order when we do that.

Now this is a very small data set and it’s gonna be a very strange stem-and-leaf plot, mainly because there’s only one leaf for every stem in this particular set of data. But let’s draw the stem-and-leaf plot first and then we’ll go on and answer the question. Now if we’d look at our data, they are all one- or two-digit numbers, so we’re gonna use the digit in the tens column as the stem and the digit in the units column as the leaf.

So for example, the number two has zero in the tens column and one in the units column. Twenty-nine has two in the tens column and nine in the units column. Sixty-five has six in the tens column and five in the units column, and so on. So, we’re going to list out our stems; that’s these digits here. And against each then we can plot all of the leaves that go with that particular stem.

Now the strange thing here is there’s only gonna be one leaf for each particular stem, so from a stem-and-leaf plot point of view, as I say, it’s a slightly weird diagram. So what you’d normally do in drawing a stem-and-leaf plot is write out all the stems like this and against each one write down the corresponding stem. So for two, that has a stem of zero and a leaf of two; for twenty-nine, it has a stem of two and a leaf of nine; the sixty-five, it’s got a stem of six and a leaf of five; for thirty-one, it’s got a stem of three and a leaf of one; and for ninety-three, it’s got a stem of nine and a leaf of three.

Now with a bigger data set, you’d end up with more leaves, making a nice big pattern like a big sideways bar chart here. But in this case, that’s the only data we have. Now remember, the other important thing that you need with your stem-and-leaf diagram is a key, so we need to indicate that two line nine means twenty-nine or six line five equals sixty-five. It doesn’t matter which one you choose on your key so long as it’s clear from the key how to interpret your diagram. So the key aspects of a stem-and-leaf diagram are a set of stems, a set of leaves, and a key.

Now the only stems that we’ve used in this case are zero, two, three, six, and nine. And writing those out in ascending order, that means smallest first biggest last, we get our answer is the stems are zero, two, three, six, and nine.