Unit 2: Two-Variable Relationships

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(adapted by Dan Teague from the COMAP curricular project ARISE.)

Two varieties of a tiny biting insect called a midge were discovered in the jungles of Brazil by biologists W.L. Grogan and W.W. Wirth. One kind is the deadly Apf midge that is the carrier of a debilitating disease which causes swelling in the brain if a human is bitten by the infected midge. The other form is the Af midge that is quite harmless and a valuable pollinator. In an efort to distinguish the two types, the biologist took many measurements of the midges that they caught. Two measurements for some of the randomly selected insects are recorded in the table.

Apf Midges (deadly)

Wing span (cm) 1.78 1.86 1.96 2.00 2.00 1.96
Antenna Length (cm) 1.14 1.20 1.30 1.26 1.28 1.18


Af Midges (harmless)

Wing span (cm) 1.72 1.64 1.74 1.70 1.82 1.82 1.90 1.82 2.08
Antella Length(cm) 1.24 1.38 1.36 1.40 1.38 1.48 1.38 1.53 1.56


Please answer the following questions.


1) Is it possible to distinguish between Apf and Af midges on the basis of wing and antenna length? Determine a method of distinguishing the two varieties of midges. Plot the data and then use the data to determine an appropriate model to describe the relationship between Wing Span and Antenna Length.

2) If you make an error in your classification, would you rather call an Af midge Apf or an Apf midge Af? Which error is worse? Why? How does this affect your classification scheme?

3) There seem to be more Af midges than Apf midges, so if a midge is captured, it is more likely to be an Af midge. How could this be taken into account?

4) It is important to know if a midge is dangerous or not. Suppose that biologists capture five more midges. Their measures were:


  A B C D E
Wing Span (cm) 1.70 2.02 1.88 1.96


Antenna Length (cm) 1.36 1.32 1.30 1.54 1.22

How would you classify them? Which midges do you have the most confidence that you have classified correctly?

Please present your answers in a report named ms2yourlastname and drop in the Digital Drop Box.


HINTS: Perhaps by now youv'e tried to compare two variables side-by-side with Fathom. And you've noticed that you can't. Here's how. (And it ain't pretty.)
For example, what you probably want to do is compare wingspans of the AF and APF midges side by side. To do this you need to enter the data in a slightly counter intuitive way.
1) Select "Insert Collection" from the Insert menu.
2) Click once on the collection, and then choose "Insert Case Table"
3) Create three attributes: Wingspan, Antenna, Type
4) Under Wingspan, enter ALL of the wingspans. Under Antenna enter all of the antenna lengths. Under Type, identify whether these numbers belong to the APF or AF midge.