# Back to Back Stem and Leaf Plots

Image Source: Modified from http://ex-interim.blogspot.com.au

In this lesson we look at Back to Back Stem and Leaf Plots.

These types of graphs are used for comparing two sets of statistics where the same thing has been measured.

Using a Back to Back Plot we can directly compare the statistics of the two items: eg. Males versus Females, Brand A versus Brand B, Natural versus Synthetic, Team X Performance versus Team Y performance, X-Box versus Playstation, Apple versus Samsung, and so on.

A Back to Back Plot is simply two Stem and Leaf Plots combined together, like the two person seat designed by Eleanor Hutchinson in the opening image for this lesson.

Basic Stem and Leaf Plots

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A Stem and Leaf Plot is basically the same as a Horizontal Bar Chart.

Instead of Grouping the Data and drawing Bars, we Group the Data, but we then write the actual number values of the data to create the bars.

It is necessary to understand Basic Stem and Leaf Plots before attempting Back to Back Stem and Leaf Plots.

If you have never made a Stem and leaf Plot before, then do our previous lesson on this at the link below:

http://passyworldofmathematics.com/stem-and-leaf-plots/

Example Back to Back S & L Plot

Two Mobile Phones have been tested for Battery Life in between charges.

We need to create a Back to Back Stem and Leaf Plot to show the
comparison of the battery life results.

The data for the Battery Life of the two phones is as follows:

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The first step to creating any Stem and Leaf Plot is to write our values out from lowest to highest, and group them into Tens; eg. ones, tens, twenties, thirties, etc

When we do this “Tens” grouping for our Mobile Phone Data, we obtain the following:

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The following diagram shows how we draw the Stem and Leaf Plot for the “Brand A” Phone.

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Notice that in the Stem and Leaf Plot we do not show the full values of battery life on the rows.

Eg. In a Stem and Leaf Plot, the data values are put in order from the Lowest to Highest.

We then group them into :

Ones = 0 to 9
Tens = 10 to 19
and so on.

These groups are called the “Stems”.

The “Leaf” is the last digit on each of the original data values.

So we only show the last digit of each battery life measurement.

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Here is how we make the Stem and Leaf Plot for the “Brand B” phone, following the exact same method we used for our “Brand A” plot.

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Let’s now take a look at our two Stem and Leaf Plots and the final steps we need to take to combine them into a single plot.

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We keep the right hand side blue plot as it is, but we flip around the red left hand side plot so it is reversed like in a mirror.

The situation is like taking two people and turning one of them around, so that they are now “back to back” facing in opposite directions.

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Here is how we reverse the left hand side “Brand B” Stem and Leaf Plot.

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We now have our two Stem and Leaf Plots and we are ready to join them together “Back to Back”.

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We move the two plots towards each other until their stems overlap, and thereby create the combined single back to back plot.

The resulting single diagram looks like this:

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Usually our Stem and Leaf Plots we do in Math Class are not as brightly colored as this, and a typical maths workbook version of the above diagram would look like this:

Image Copyright 2013 by Passy’s World of Mathematics

Videos About Back to Back Stem and Leaf Plots

This first video covers Back to Back Stem and Leaf Plots in reasonable detail.

This short video shows how to draw a back to back stem and leaf plot from two related sets of data.

Here is a quick one minute video showing the structure of back to back plots.

Stem and Leaf Worksheets

This worksheet has Questions 4, 5, and 6 on Stem and Leaf Plots, and contains answers to these questions.

This second worksheet covers back to Back Stem and Leaf Plots, but does not have any answers supplied.

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