# Estimation

• ### My k Nearest Neighbors

music and lyric by Cynthia Rudin

When I look around, I'd find you there in space, and I see that you are like me...
and the future is ours, the oyster, our world, where things far-away just don't matter.

‘Cause I can count on you, ‘cause you know me too well, you just sit right there by my side.
In a metric space, we can find our place...
for each other we truly decide.

My nearest neighbors
My k nearest neighbors

If I were missing a part, you would extend your heart, so that I could be whole once again.
And when clustering, I'd do anything so that I would be with you, my friends.

My nearest neighbors
my k nearest neighbors

And all the k of you, with k more than two, together we work as a team.
Case-based reasoning, can do anything, perform as you'd fathom to dream.

My nearest neighbors
my k nearest neighbors

• ### 99 Bottles of Beer

lyric copyright by Lawrence M Lesser and Dennis K Pearl
(based on Donald Byrd's idea to use the mid-20th century folk song in Mathematics Education)

100 bottles of beer on the wall,
plus or minus one beer:
If one of those bottles should happen to fall,
the M.O.E. won't cover them all!

99 bottles of beer on the wall,
plus or minus one beer:
If one of those bottles should happen to fall,
the M.O.E. won't cover them all!

etc...

• ### Dancing Sampling Error

Video explaining the statistical concept of sampling error  and standard error through dance.

(Teaching notes available to instructors logged into CAUSEweb)

• ### Meditation on Statistical Method

by J.V. Cunningham (1911 - 1985)

Plato, despair!
We prove by norms
How numbers bear
Empiric forms,

How random wrong
Will average right
If time be long
And errors slight;

But in our hearts
Hyperbole
Curves and departs
To infinity.

Error is boundless.
Nor hope nor doubt,
Though both be groundless,
Will average out.

• ### Capture-Recapture with Goldfish

Students use the capture-recapture method to estimate the size of a population of GoldfishTM crackers. The bias in the MLE versus a bias-corrected estimate is evaluated with computer simulations.

• ### The Probability of a Kiss

Students estimate the probability that a Hershey's KissTM will land on its flat base when spilled from a cup.  Almond and plain Kisses are compared.

• ### Capture-Recapture with Split Peas

Students use the capture-recapture method to estimate the size of a large population of split peas. Student worksheets and expository materials are included.