Back to Back Stem and Leaf Plots

Back to Back Stem and Leaf Plot 1
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

Back to Back Stem and Leaf Plot 2
Image Copyright 2013 by Passy’s World of Mathematics

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:

Back to Back Stem and Leaf Plot 3
Image Copyright 2013 by Passy’s World of Mathematics

 

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:

Back to Back Stem and Leaf Plot 4
Image Copyright 2013 by Passy’s World of Mathematics

 

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

Back to Back Stem and Leaf Plot 5
Image Copyright 2013 by Passy’s World of Mathematics

 

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.

Back to Back Stem and Leaf Plot 6
Image Copyright 2013 by Passy’s World of Mathematics

 

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.

Back to Back Stem and Leaf Plot 7
Image Copyright 2013 by Passy’s World of Mathematics

 

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.

Back to Back Stem and Leaf Plot 8
Image Copyright 2013 by Passy’s World of Mathematics

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.

Back to Back Stem and Leaf Plot 9
Image Copyright 2013 by Passy’s World of Mathematics

 

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

Back to Back Stem and Leaf Plot 10
Image Copyright 2013 by Passy’s World of Mathematics

 

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

Back to Back Stem and Leaf Plot 11
Image Copyright 2013 by Passy’s World of Mathematics

 

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:

Back to Back Stem and Leaf Plot 12
Image Copyright 2013 by Passy’s World of Mathematics

 

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:

Back to Back Stem and Leaf Plot 13
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.

Click here for Stem and Leaf Worksheet 1

 

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

Click here for Stem and Leaf Worksheet 2

 
 

Related Items

Stem and Leaf Plots
Mean Median Mode of Grouped Data
Mean Median Mode of Ungrouped Data
Mean Median Mode and MS Excel
Grouped Data Histogram Graphs
Symmetry and Skew
Basic Histogram Graphs
MS Excel Charts and Graphs
MS Excel Column Graphs and Pie Charts
Funny Graphs from Graph Jam
Misleading Graphs
Real Life Graphs
Free Online Graph Makers

 
 

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