Question Video: A Stem-and-Leaf Plot for a Small Data Set Mathematics

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.