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How to Find Stem Unit

## How to Find Stem Unit

Just in case you aren’t sure, the stem unit is the 20% of flowers or leaves you put in the vase to fill it up and make it look fuller.

### Look

via GIPHY

The stemplot is a quick way to graph data and gives an exact picture of the data. You want to look for an overall pattern and any outliers. An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down [latex]50[/latex] instead of [latex]500[/latex]) while others may indicate that something unusual is happening. It takes some background information to explain outliers, so we will cover them in more detail later.This plot looks a little odd because many of the stems have no leaves and those that do have only one leaf. But it is necessary to list all the possible stems within the range of the data to get a complete picture of how the data looks. In this case, since our smallest value is 10 and our largest is 81, we have chosen stems to cover all possible values from 0 up to 99. At times we might want to use nonuniform class-intervals when describing frequencies. For example, we may want to look at age distribution of children with ages grouped as preschool (2-4 years), elementary school (5-11-years), middle-school (12-13-years), and highschool (14-19-years). The data from Table 1 can now be displayed as follows: That's all well and good, but we could do better. First and foremost, no one in their right mind is going to want to create too many of these stem-and-leaf plots by hand. Instead, you'd probably want to let some statistical software, such as Minitab or SAS, do the work for you. Here's what Minitab's stem-and-leaf plot of the 64 IQs looks like:

But the leaves are fairly long this way, because the values are so close together. To spread the values out a bit, I can break each leaf into two. For instance, the leaf for the two-hundreds class can be split into two classes, being the numbers between 200 and 240 and the numbers between 250 and 290. I can also reverse the order, so the smaller values are at the bottom of the "stem". The new plot looks like this:These values have one decimal place, but the stem-and-leaf plot makes no accomodation for this. The stem-and-leaf plot only looks at the last digit (for the leaves) and all the digits before (for the stem). So I'll have to put a "key" or "legend" on this plot to show what I mean by the numbers in this plot. The ones digits will be the stem values, and the tenths will be the leaves. Analyse Elliot's stem and leaf plot. What is his most common score on the geography quizzes? What is his highest score? His lowest score? Rotate the stem and leaf plot onto its side so that it looks like a bar graph. Are most of Elliot's scores in the 10s, 20s or under 10? It is difficult to know from the plot whether Elliot has improved or not because we do not know the order of those scores. Each morning, a teacher quizzed his class with 20 geography questions. The class marked them together and everyone kept a record of their personal scores. As the year passed, each student tried to improve his or her quiz marks. Every day, Elliot recorded his quiz marks on a stem and leaf plot. This is what his marks looked like plotted out: (Source: www150.statcan.gc.ca)

### Use

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Hmmm.... how does the plot differ from ours? First, Minitab tells us that there are n = 64 numbers and that the leaf unit is 1.0. Then, ignoring the first column of numbers for now, the second column contains the stems from 6 to 14. Note, though, that Minitab uses two rows for each of the stems 7, 8, 9, 10, 11, 12, and 13. Minitab takes an alternative here that we could have taken as well. When you opt to use two rows for each stem, the first row is reserved for the leaves 0, 1, 2, 3, and 4, while the second row is reserved for the leaves 5, 6, 7, 8, and 9. For example, note that the first 9 row contains the 0 to 4 leaves, while the second 9 row contains the 5 to 9 leaves. The decision to use one or two rows for the stems depends on the data. Sometimes the one row per stem option produces the better plot, and sometimes the two rows per stem plot option produces the better plot.

A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley's work in the early 1900s, and are useful tools in exploratory data analysis. Stemplots became more commonly used in the 1980s after the publication of John Tukey's book on exploratory data analysis in 1977. Stem-and-leaf displays are useful for displaying the relative density and shape of the data, giving the reader a quick overview of the distribution. They retain (most of) the raw numerical data, often with perfect integrity. They are also useful for highlighting outliers and finding the mode. However, stem-and-leaf displays are only useful for moderately sized data sets (around 15–150 data points). With very small data sets a stem-and-leaf displays can be of little use, as a reasonable number of data points are required to establish definitive distribution properties. A dot plot may be better suited for such data. With very large data sets, a stem-and-leaf display will become very cluttered, since each data point must be represented numerically. A box plot or histogram may become more appropriate as the data size increases. (Source: en.wikipedia.org)

### Follow

via GIPHY

Since the data values are to two significant figures and range from 0.8 to 4.3, it makes sense to choose our stems as 0, 1, 2, 3, and 4. These cover the units for each number and every possibility for data with values between 0.0 and 4.9. So, for example, 1.2 will have stem “1.” And if the leaves are the “tenths,” that is, the numbers after the decimal points, 1.2 will have leaf “2.” We can fill in our stem-and-leaf plot using the ordered data as follows. To write the stems, we first put the data itself in ascending order, starting with the lowest value 10 so that we have 10, 36, 67, 74, and 81. The data are all two-digit numbers, so we will use the “tens” as the stems. Therefore, we can list the stems in order as 1, 3, 6, 7, and 8. To create a stem-and-leaf plot, we list all the possible stems, as follows.

A stem-and-leaf plot is a way of organizing data into a form to easily look at the frequency of different types of values. The process will be easiest to follow with sample data, so let's pretend that a sports statistician wants to make a stem-and-leaf plot for a recent game played by the Blues basketball team. The total minutes played by each team member has been recorded.If I try to use the last digit, the hundredths digit, for these numbers, the stem-and-leaf plot will be enormously long, because these values are so spread out. (With the numbers' first three digits ranging from 232 to 270, I'd have thirty-nine leaves, most of which would be empty.) So instead of working with the given numbers, I'll round each of the numbers to the nearest tenth, and then use those new values for my plot. Rounding gives me the following list: (Source: www.purplemath.com)

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