Overview: Students measure their hand spans and those of other students to provide data for a frequency histogram of variation. Students then produce and analyze a frequency histogram for their population. This lab is ideal for helping students to understand the concept of variation and a good class activity to introduce frequency histograms (a type of bar graph) and the concept of a data driven visualization.
Histograms - Data Driven designs
Science: Biology - Evolution
NC Scientific and Technical Visualization Objectives:
If this lesson is done as a class with step by step teacher instructions it is a Level I project. If it is done independently by the student who is given only the initial problem, then it is a Level II project.
4.04 Describe visual methods for representing data driven visualizations.
5.03 Produce computer based data driven visualization projects.
2.01 Describe advanced principles and techniques of scientific visualization.
2.02 Apply advanced principles and techniques of scientific visualization.
NC Biology Goals and Objectives:
Goal 2: Science process skills:
2.1 Demonstrate the ability to observe.
2.3 Demonstrate the ability to use numbers.
2.4 Demonstrate the ability to communicate.
2.5 Demonstrate the ability to measure.
Goal 7: Continuity of Life:
7.3: Demonstrate knowledge that organic variation is important and necessary for species survival:
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Darwin's theory of evolution by natural selection rests on the following four principles:
1. More offspring are produced
than can possible survive.
2. Variation exists among the offspring.
3. Organisms must compete to survive and reproduce.
4. The ones best suited to the environment will survive and pass these traits on to their offspring.
Variation can include differences in size, shape, color, immune function, strength, heartbeat, etc. We now know that genetic information (DNA) controls the variation that is heritable and that mutations are the source of genetic variation.
This lab can be carried out on any population of organisms which can be measured. For example, students can measure 100 acorns or 100 bean seeds (don't use machine sorted dried beans) if that is more convenient. It increases interest in younger students to measure themselves - but hand span is less socially sensitive than height or weight. In biology class it is appropriate to do one animal example (humans) and one plant example (seed length) and include a discussion of how variation will tend to be less if all of the offspring have one or both of the same parents. (All acorns from one oak)
Once the class has collected sufficient data introduce the concept of a frequency histogram. Discuss why this is the best method to present this type of data.
A frequency histogram for hand span data might look like this:
This is also a good opportunity to discuss the concept of a normal distribution (bell shaped curve). The more student data you have the more likely it is that your data will approach a normal distribution. 100 or more students is ideal. One way to manage this is to have several classes do measurements on the first day and then use your total data the next day. Other alternatives include students collecting data from other classes.
Data can be discrete or continuous. Discrete data has no in between points. An example would be rolling a die. The handspan data is continuous. A handspan could be exactly 16 cm or exactly 17 cm or anyplace in between. To do a frequency histogram for continuous data, the data must be separated into categories and it is up to the person producing the visualization to decide how many categories (bins) will be used and how large the bins will be. Too few or too many bins give an unclear picture of the data. With a larger sample size you can have smaller bins. However, the bins should not be
The same data as above in too few bins:
The same data as above in too many bins:
If necessary, give students software specific instructions for producing a frequency histogram.
Links to Step by Step Instructions:
Excel Delta Graph Manual
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With data from several classes each class can produce frequency histograms of their own class and then of the total data. Compare the shapes of these graphs to discuss the concepts of sample size and a normal distribution. Data may be bimodal with two peaks. This is often caused by an underlying discontiuity in the sample. For example in the hand span sample males may have a larger handpan on average than females. Separating the sample into males and females and then graphing side by side might be one way of seeing this. The class should also discuss the misleading visual effect of an unequal number of members of the two groups in the sample.
Sample bimodal data histogram:
Bimodal data is best visualized with stacked or side by side graphs.
This example has fewer females than males.
It is important for students to realize that for natural selection, bigger isn't always better. What's better depends on the particular characteristics of the total environment the organism is in. For example, an animal might need a small hand to reach into crevices and get food out.
With a more mathematical group, this experiment provides a nice springboard for a discussion of the difference between discrete and continuous data and alternative ways of dealing with this type of data.
Advanced Biology Students can research sexual dimorphism and sexual selection. (Good articles on these topics appear in the April and July 1998 issues of Scientific American)
If the measurements are rounded to the nearest tenth, this can be good data to show a stem and leaf plot.
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Braun, S. and Young, J. (1989). Heath Biology Laboratory Investigations: Investigation 14A (pp97-98). Lexington, MA: DC Heath and Company.
Scientific and Technical Visualization Date____ Per ____
Purpose: To observe, measure, and analyze variation in organisms and to use the computer to display a graphical representation of that information.
1. Spread your hand flat on a table stretching out the distance from you thumb to your pinkie as far as possible.
2. Measure the distance from the tip of your thumb to the tip of your pinkie. Round to the nearest centimeter.
4. Collect data from one or more classes of students and record
in the chart below or directly in a class spreadsheet.
| measurement in cm
|number of persons at measurement|
6. Check your visualization to be sure that:
a) it has an explanatory title.
b) the axes are both labeled.
c) label printing is clear and a good size.
d) the bin size produces a clear picture of your data.
e) the axes are a good length and scale for your data.
f) the grid marks chosen help, don't distract the viewer
Biology Questions: 1. Define the term variation in your own words.
2. Describe the pattern of variation in your population.
3. What causes the variation in hand spread that you have observed.
4. Describe a situation in which a larger hand might provide an advantage.
5. Describe a situation in which a smaller hand might provide an advantage.
6. Besides hand size list at least ten other characteristics
that vary in human populations. Try to think of some that are internal
rather than externally visible.
7. Why is variation an advantage to the population overall?
Scientific Visualization Questions:
1. Why is this called a data driven visualization?
2. What is the effect of the width of the bars?
3. What happens in a frequency histogram if the bin size chosen
is too large?
4. What happens in a frequency histogram if the bin size
chosen is too small?
5. What effect does sample size have on the bin size that can
6. What other types of graphs could be used to visualize this type of data?
Teachers may call or e-mail the scivis project to obtain answer keys.
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