Stemplots

On the
Side

Stemplots

Introduction

A web page containing the text on this page.

Activities

Greed

Good fun, and a nice introduction
to stemplots

STEPS
Tutorials

Interactive computer-based tutorials

Worksheets

Advanced Stemplots

featuring real,
live data!

Worked Solutions

Datasets
Visit the Datasets page for more datasets and stories to support this topic.

Or, get some ideas on how students can gather their own data

FYI

The Six Characteristics of a Dataset

A 'starter set' of features of a dataset that should be considered.

The plural of anecdote is not data!

The purpose of displaying data graphically is to give a visual display of the interesting and important features of the dataset. Which particular displays are best is not a question that can necessarily be answered before the data is viewed, hence a statistican will view the data in different ways.

A stemplot shows the shape of the distribution and indicates whether there are potential outliers. Constructing a stemplot is often the first step in analysing a dataset, and helps to determine what analysis is appropriate.

Stemplots are useful for displaying small datasets with only positive values. They are also appropriate if it is important to retain the original data. They are quicker and easier to construct by hand than histograms.

The choices of ‘bin width’ are limited, so for some datasets that otherwise meet the criteria, a stemplot may not be very useful. The bins may be too large or too small to properly display the distribution of the data. For these datasets, a histogram is preferable.

How to displaying a particular dataset with a stemplot often requires judgement. How to split the stems, how to represent outliers and whether to truncate the data are decisions that often have to be made. The main point is that the plot should quickly inform us about the salient features of the dataset.

Once a stemplot is constructed, students should consider these questions:

What is the location of the data?

How much is the data spread out?

What is its overall shape; is it symmetric, skew or bi-modal?

Are there any unusual data values such as outliers?

Is there evidence of clustering?

Students should also note any unusual features of the dataset not highlighted by the above questions. For example one row may have many more elements in it than the other rows. The student might ask, ‘Is this a random occurance or is it a relevant feature of this dataset?’ Often answering such questions isn’t easy.

Constructing a Stemplot

If you have never constructed a stemplot, visit the webpage Greed!. It is a nice activity where amongst other things students will learn how to construct a stemplot.

Advanced Stemplots

Some might say 'advanced stemplots' is an oxymoron. However with some datasets it may be necessary to split the stems, and with others to truncate the data. There is also the decision on what to do with outliers - do we include a large number of empty rows between an outlier and its nearest value? Finally how do we handle very large and very small numbers? The worked solutions to the worksheet Advanced Stemplots illustrates some common practices.

STEPS

The STEPS modules are a collection of hypertext-based tutorials covering a wide range of statistics topics, including the graphical display of data. Visit the STEPS page for further information and a list of the modules available.