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Exploring Statistics with Fathom 4: Sampling Distributions 127
© 2007 Key Curriculum Press
In this activity you’ll use Fathom to draw samples of size 5 from a collection of
rectangles many times to explore the sampling distribution of various summary
You will need
• Sampling
Rectangles.ftm
statistics.
EXAMINE DATA
1. Open SamplingRectangles.ftm. The collection named Rectangles contains
100 random rectangles.
Q1 Make a plot of Area and describe the distribution of Area in terms of shape,
center, and spread.
INVESTIGATE
Taking a Sample
2. With the collection selected, choose CollectionSample Cases. By default,
Fathom takes a sample of ten cases with replacement and places them in a new
collection named Sample of Rectangles. You’ll change this to fi ve cases without
replacement.
Notice that animation
is on by default. You
may want to change
this later.
3. Double-click the sample collection to
show its inspector. On the Sample
panel, change the settings to match
these. Click Sample More Cases.
Remember that you
can drag an attribute
from the Cases panel
of the inspector.
4. You now have a sample of 5 areas from
the collection of all 100 rectangles. Make
a dot plot of the attribute Area for your sample.
Choose GraphPlot
Value and type
!"#$%&. Then do
the same for the other
values.
5. You need to compute some summary statistics
for your sample. Plot the values for the mean,
median, and maximum of your sample.
Q2 In a moment, you are going to repeat this
sampling, say, 200 times, to create sampling
distributions of these summary statistics (or
measures). But fi rst, sketch distributions to
predict what you will get for the set of 200 mean, median, and maximum areas.
Introduction to Sampling Distributions—Random Rectangles
