# Summary Statistics

• ### Trimmed Mean

Lyric by Dennis Pearl
may sing to the tune of the KitKat jingle by Michael Levin and Ken Shuldman

Gimme a break
Gimme a break
Break me off the ends of that
Whole x-bar

Gimme a break
Gimme a break
Break me off the ends of that
Whole x-bar

That robust taste
And everywhere you go
You hear the people say

Gimme a break
Gimme a break
Break me off the ends of that
Break me off the ends of that
Break me off the ends of that
Whole x-bar

• ### X-bar 12-bar Blues

Music and Lyric © 2018 Lawrence M. Lesser

When learnin’ ‘bout the mean, we wanna set a high bar;
Like the symbol for sample mean, we need a high bar!
More than procedure, here’s what its features are!

No bigger than the max, no less than the min;
Never past the max, or less than the min.
That makes a window x-bar is always in!

A value that equals 0 is part of the dataset.
If a value equals 0, it’s still in the dataset,
And sways calculation of the x-bar you get.

The mean might not have a value in reality,
Might not be a data point or value that could be:
Don’t know no household holdin’ 2.53!

Lay all the data points on a number line,
Lay all the data points on a weightless number line:
You’ll find at x-bar, it’s balanced fine!

Redistribute values so they’re all the same,
Level off the values so they’re all the same:
This fair share value the mean attains.

Take a deviation of each value from the mean,
Take a deviation of each value from the mean:
They all sum to 0: the proof is routine.

(Repeat Verse 1, changing “here’s” to “we know”)

Watch the video

• ### Variation

Variation
Lyric © 2022 Lawrence M. Lesser
may be sung to the tune of "Vacation" by the Go-Go's

Can’t seem to get my mind off of mu
But I think more is needed to view
Temperatures here
Are either near
40 or 100.

[CHORUS:]
Variation in the distribution
Variation – how the data lays
Location’s not enough alone
Variation – it is all around us
Variation links to chance of things
Variation – something we need to know

With a shift of values, what’s undone?
SD and IQR won’t run!
But a change of scale
Will make them both sail
But not percentiles
Or a z-score (Repeat Chorus)

• ### Expected Value Haikus

by Lawrence Mark Lesser

Deal or No Deal
The banker offers
less than expected value,
as was expected.

62% Shooter’s 1-and-1
Expected number
of points is 1, the outcome
that is least likely!

Dogs swap bowls and beds,
sure the other’s better like
Monty’s other door.

Negative Expected Value
Lottery tickets,
extended car warranty,
or health insurance.

Expectation in the Balance
Where distributions
balance like a see-saw with
one’s child more distant.

Unbiased
It is hard to speak
and avoid bias.

The Point
I could reduce a
distribution to EV,
but that would be mean.

• ### Dancing Frequency Distributions

Video explaining the statistical concept of frequency distributions through dance.

(Teaching notes available to instructors logged into CAUSEweb)

• ### Dancing Variance

Video explaining the statistical concept of variance through dance.

(Teaching notes available to instructors logged into CAUSEweb)