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Student Page 3.3.3 Gulliver Graphs
A4US

In Gulliver’s Travels, the Lilliputians made a coat for Gulliver that fit him perfectly. They did this after taking only one measurement, the circumference of Gulliver's thumb. The Lilliputians then used the following well-known Lilliputian “Rule of Thumb”:

The circumferences of each body part are related as in the following equations:

\(\text{Wrist} = 2 \cdot \text{Thumb}\text{,}\) \(\text{Neck} = 2 \cdot \text{Wrist}\text{,}\) and \(\text{Waist} = 2 \cdot \text{Neck}\)

1.

By gender, gather thumb, wrist, and neck measurements, in centimeters, for at least 20 adults. Measure the thumb between the knuckles. Measure the wrist on the arm just above the wrist bones. Measure the neck just below the chin. Put your data in Table 3.3.3.1.

2.

Graph the data for (Thumb, Wrist), one graph each for females, males, and entire data set. Use a different color for each data set.

3.

Draw lines that best fit each data set. Explain why you think each line is a reasonable fit.

4.

Test the Lilliputian “Rule of Thumb” for:
(a)

The female sample

(b)

The male sample

(c)

The entire sample

6.

Were the Lilliputians lucky that Gulliver's coat fit or were they quite clever? Explain.

Table 3.3.3.1. Thumb, Wrist, and Neck Data
Female Male
Thumb Wrist Neck Thumb Wrist Neck
           
           
           
           
           
           
           
           
           
           
           

Functions for Females:

\begin{align*} W(T) \amp = \fillinmath{XXXXXXXXXX}\\ N(W) \amp = \fillinmath{XXXXXXXXXX}\\ N(T) \amp = \fillinmath{XXXXXXXXXX} \end{align*}

Functions for Males:

\begin{align*} W(T) \amp = \fillinmath{XXXXXXXXXX}\\ N(W) \amp = \fillinmath{XXXXXXXXXX}\\ N(T) \amp = \fillinmath{XXXXXXXXXX} \end{align*}

Functions for Entire Sample:

\begin{align*} W(T) \amp = \fillinmath{XXXXXXXXXX}\\ N(W) \amp = \fillinmath{XXXXXXXXXX}\\ N(T) \amp = \fillinmath{XXXXXXXXXX} \end{align*}

A Word about Function Notation.

When you were asked to record the functions you found for Gulliver Graphs, did you find the notation a bit strange? Notice that the notation gives important information about the columns of data being related to each other. \(W(T)\) indicates that we want to know the wrist measurement in terms of the thumb measurement, instead of just using \(W\text{.}\) We read the symbols, \(W\) of \(T\text{.}\) What do you think \(N(W)\) represents? \(N(T)\text{?}\)

If we want to be very specific, we could indicate \(W_F(T_F)\) to indicate the that we want to know the wrist measurements for females in terms of the thumb measurements for females. How would we write the wrist measurement for males in terms of the thumb measurements for males? We are not using subscript notation in Gulliver Graphs, instead opting to use headings to make clear which data sets are being related.

From this point on, we will use function notation to avoid ambiguity in cases where it is necessary to make clear which quantities we are relating.