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)

• 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)

• Descriptive Statistics with Oranges

Students make measurements on oranges for use in a unit on descriptive statistics.