# Stem and leaf diagram statistics pdf

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A random sample of 64 people were selected to take the Stanford-Binet Intelligence Test. After each person completed the test, they were assigned an intelligence quotient IQ based on their performance on the test. The resulting 64 IQs are as follows:. Once the data are obtained, it might be nice to summarize the data.

We could, of course, summarize the data using a histogram. One primary disadvantage of using a histogram to summarize data is that the original data aren't preserved in the graph. A stem-and-leaf plot , on the other hand, summarizes the data and preserves the data at the same time. The basic idea behind a stem-and-leaf plot is to divide each data point into a stem and a leaf. We could divide our first data point, , for example, into a stem of 11 and a leaf of 1.

We could divide 85 into a stem of 8 and a leaf of 5. We could divide 83 into a stem of 8 and a leaf of 3. And so on. To create the plot then, we first create a column of numbers containing the ordered stems.

Our IQ data set produces stems 6, 7, 8, 9, 10, 11, 12, 13, and Once the column of stems are written down, we work our way through each number in the data set, and write its leaf in the row headed by its stem.

Here's what the our stem-and-leaf plot would look like after adding the first five numbers , 85, 83, 98, and Now, rather than looking at a list of 64 unordered IQs, we have a nice picture of the data that quite readily tells us that:.

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:. Then, ignoring the first column of numbers for now, the second column contains the stems from 6 to Note, though, that Minitab uses two rows for each of the stems 7, 8, 9, 10, 11, 12, and 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. Do you notice any other differences between Minitab's plot and our plot? Note that the leaves in Minitab's plot are ordered. That's right Minitab orders the data before producing the plot, and thereby creating what is called an ordered stem-and-leaf plot.

Now, back to that first column of numbers appearing in Minitab's plot. That column contains what are called depths. The depths are the frequencies accumulated from the top of the plot and the bottom of the plot until they converge in the middle. For example, the first number in the depths column is a 1.

It comes from the fact that there is just one number in the first 6 stem. The second number in the depths column is also a 1. The third number in the depths column is a 3. Minitab continues accumulating numbers down the column until it reaches 32 in the last 9 stem. Then, Minitab starts accumulating from the bottom of the plot. Let's take the efficient route, as most anyone would likely be taken in practice, by letting Minitab generate the plot for us:.

Minitab tells us that the leaf unit is 0. The depths column contains something a little different here, namely the 7 with parentheses around it. It seems that Minitab's algorithm for calculating the depths differs a bit here. It still accumulates the values from the top and the bottom, but it stops in each direction when it reaches the row containing the middle value median of the sample.

The frequency of that row containing the median is simply placed in parentheses. That is, the median of the 20 numbers is Therefore, because the stem contains 7 leaves, the depths column for that row contains a 7 in parentheses.

In our previous example, the median of the 64 IQs is Because Breadcrumb Home 13 Font size. Font family A A. Content Preview Arcu felis bibendum ut tristique et egestas quis: Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris Duis aute irure dolor in reprehenderit in voluptate Excepteur sint occaecat cupidatat non proident. Lorem ipsum dolor sit amet, consectetur adipisicing elit. Odit molestiae mollitia laudantium assumenda nam eaque, excepturi, soluta, perspiciatis cupiditate sapiente, adipisci quaerat odio voluptates consectetur nulla eveniet iure vitae quibusdam?

Excepturi aliquam in iure, repellat, fugiat illum voluptate repellendus blanditiis veritatis ducimus ad ipsa quisquam, commodi vel necessitatibus, harum quos a dignissimos. Close Save changes. Help F1 or? Here's what the our stem-and-leaf plot would look like after adding the first five numbers , 85, 83, 98, and and here's what the completed stem-and-leaf plot would look like after adding all 64 leaves to the nine stems: Now, rather than looking at a list of 64 unordered IQs, we have a nice picture of the data that quite readily tells us that: the distribution of IQs is bell-shaped most of the IQs are in the 90s and s the smallest IQ in the data set is 68, while the largest is That's all well and good, but we could do better.

Here's what Minitab's stem-and-leaf plot of the 64 IQs looks like: Hmmm Let's take a look at another example.

Example Section. Solution Let's take the efficient route, as most anyone would likely be taken in practice, by letting Minitab generate the plot for us: Minitab tells us that the leaf unit is 0. Save changes Close.

## Stem And Leaf Plot Pdf

Our printable stem-and-leaf plot worksheets contain a set of data that are to be ordered and to be presented in a stem and leaf plot. The data are to be interpreted and questions based on it are to be answered in the make and interpret plot pages. Stem-and-leaf plots also contain back-to-back plots, rounding data, truncating data and more. These pdf worksheets are recommended for students of grade 4 through grade 8. Our free stem and leaf plots can be accessed instantly.

Intro Examples. The following examples provide some practice with stem-and-leaf plots, as well as explaining some details of formatting, and showing how to create a "key" for your plot. Stem-and-Leaf Plots. The first thing I'll do is reorder this list. It isn't required, but it surely makes life easier.

Information identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please contact us to request a format other than those available. A stem and leaf plot, or stem plot, is a technique used to classify either discrete or continuous variables. A stem and leaf plot is used to organize data as they are collected. A stem and leaf plot looks something like a bar graph. Each number in the data is broken down into a stem and a leaf, thus the name.

## Stem-and-leaf display

One simple graph, the stem-and-leaf graph or stemplot , comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example, 23 has stem two and leaf three.

Stem And Leaf Plot Pdf. In the extreme cases, stand production was 3. A stem-and-leaf plot shows how data are distributed. Count how many observations fall in each class in-terval.

The basic idea is to provide information on the frequency distribution and retain the values of the data at the same time. Indeed, the stem corresponds to the class intervals and the leaf to the number of observations in the class represented by the different data. It is then possible to directly read the values of the data. Its concept is based on the histogram , which dates back to the 18th century. Skip to main content Skip to table of contents.

### Stem-and-leaf Plot Worksheets

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 s, and are useful tools in exploratory data analysis. Stemplots became more commonly used in the s after the publication of John Tukey 's book on exploratory data analysis in Modern computers' superior graphic capabilities have meant these techniques are less often used. This plot has been implemented in Octave [2] and R.

A random sample of 64 people were selected to take the Stanford-Binet Intelligence Test. After each person completed the test, they were assigned an intelligence quotient IQ based on their performance on the test. The resulting 64 IQs are as follows:.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Math Statistics and probability Displaying and comparing quantitative data Displaying quantitative data with graphs. Practice: Creating frequency tables. Practice: Creating dot plots. Dot plots and frequency tables review.