
Histogram
Sorting
Joan
Garfield Department of Educational Psychology University
of Minnesota 315 Burton Hall 178 Pillsbury Drive S.E.
Minneapolis, MN 55455
Statistics Teaching
and Resource Library, June 24, 2002
© 2002 by Joan Garfield, all rights reserved. This text may be freely
shared among individuals, but it may not be republished in any
medium without express written consent from the authors and
advance notification of the editor.
This activity provides students with
24 histograms representing distributions with differing shapes and
characteristics. By sorting the histograms into piles that seem to
go together, and by describing those piles, students develop
awareness of the different versions of particular shapes (e.g.,
different types of skewed distributions, or different types of
normal distributions), that not all histograms are easy to
classify, that there is a difference between models (normal,
uniform) and characteristics (skewness, symmetry,
etc.).
Key
words: Histogram, shape, normal, uniform, skewed, symmetric,
bimodal
Objectives
The objective of this activity is to
give students experience with a variety of histograms of data and
to help them better recognize different shapes and
characteristics. Too often students only see one or two perfect
examples (e.g., normal, right skewed) and have a difficult time
describing and classifying histograms of real data. This activity
also helps students determine which characteristics can appear
together (e.g., skewed and bimodal) and which cannot be used
together to describe a distribution (e.g., skewed and symmetric).
This activity may be used to help students better understand the
relationship between descriptions of data sets and the graphs that
could be created from these data sets.
Materials
needed
This writeup includes a set
of 24 histograms, generated by data on ActiveStats, and graphed
using Data Desk software. One set of these graphs is needed for
each group of students doing the activity. The pages need to be
cut so that only one graph is on a piece of paper. These graphs
can then be placed in an envelope or clipped together. A
website (http://app.gen.umn.edu/faculty_staff/delmas/gc_1454_course/distribution_file s/distribution.html)
can be used for a followup debriefing
activity.
Time
involved
5 minutes to introduce the
activity 1015 minutes for students to work in groups, sorting
graphs 10 minutes for instructorled discussion of graphs 5
minutes for follow up questions
Teacher notes
Make sure you have enough piles of
graphs for each group of students to use. Groups of three to five
students work well for this activity. It is best to have students
do this activity BEFORE they have formally study different shapes
of graphs. However, they will still recognize familiar shapes and
use terms like normal and skewed.
The groups the students
will sort their graphs into will typically be: uniform, normal,
skewed, and bimodal. There may be some smaller groupings such as
right skewed and left skewed.
After the students have
finished sorting and discussing, the instructor can lead a class
discussion, asking the students questions such as:
 What was the easiest group to
sort? Which graphs are in that group?
 How many different groups did you
find? Which graphs are in each? What did you call them? What
features did they have in common? Etc.
 Which graphs were hardest to sort
or classify? Why?
Students will often find the uniform
graphs easiest to sort, and also the bellshaped. They also find
unimodal graphs easier to classify than bimodal graphs. They have
more difficulty with the graphs that are skewed and bimodal.
The instructor can use the graphs on this website to refer
to as the students suggest their
categories:
http://app.gen.umn.edu/faculty_staff/delmas/gc_1454_course/distribution_file s/distribution.html.
This applet includes most of the
graphs in the activity. There are buttons along the bottom that
represent five different categories of distributions. When you
click one, it brings up the set of graphs with that type of
characteristic. You use the PREV and NEXT buttons on the right to
view the graphs in each set.
The instructor can first ask
the students to tell about one of their sortings and the words
they used to describe them. The teacher can respond: "So, is this
one of the graphs in that group?” and it usually will be one of
them. A discussion can follow about the words they use for
descriptions, then introduce the statistical term for the same
characteristic (e.g. Statisticians use "uniform" to refer to what
you mean by "even", "rectangular", or "steady state”).
The
correct statistical terms for the graphs (uniform, normal, right
and left skewed, bimodal) can be introduced if students have not
yet learned these terms. Models (uniform, normal) can be described
in terms of symmetry and shape (bell shape or rectangular). Other
distributions that don’t fit these models can be described in
terms of their characteristics (skewness, bimodality or
unimodality, etc). A discussion of which descriptors can and
cannot go together may follow.
These points may be included
in the discussion of graphs following the activity:

Ideal
shapes: density curves vs. histograms 

Different versions of ideal
shapes 

Idea
of models, characteristics of distributions 

Statistical words vs. descriptors 

Normal, skewed, uniform, bimodal, symmetric: which
can be used together? How well do they fit the graphs? Which
fit best? Using judgment. 

Other
ways to describe a distribution 

Why
is it important to describe a distribution? Developing
statistical thinking. 
Assessment
To assess students’ ability to
correctly describe graphs and understand the difference between
graphs, these types of assessment can be
used:

Give
students one or more histograms of data to describe in
detail 
For example:
For the
graph below, of heights of singers in a large chorus, please
write a complete description of the histogram. Be sure to
comments on all the important features.

Ask
students to generate graphs for data sets such
as: 
 The salaries of all persons
employed by Northwest Airlines
 The scores on a basic
multiplication test for a group of college math
majors
 The scores on an art history
test for a group of college math majors

