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”)
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
What made it so clear
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)
Video explaining the statistical concept of frequency distributions through dance.
(Teaching notes available to instructors logged into CAUSEweb)
Video explaining the statistical concept of variance through dance.
(Teaching notes available to instructors logged into CAUSEweb)
Students make measurements on oranges for use in a unit on descriptive statistics.
by Lawrence Mark Lesser
At our next infant wellness visit,
the pediatrician plots
our only child’s weight on
paper ruled
by increasing bands
with concavity ill-suited
for extrapolation.
Kilograms or pounds,
it’s 40th percentile, down
from the 60th percentile.
Having delivered well
into “advanced maternal age,” my wife
frowns (“we aren’t feeding him enough!”).
I say it just fell
half a sigma and
we’re still well
within the fat
part of the bell curve –
it’s normal –
this won’t be one
of our worries.
lyric © 2017 Lawrence M. Lesser
may sing to the tune of “Material Girl” (Peter Brown and Robert Rans, popularized by Madonna)
Data values normally are
no more far away
Than 3 standard deviations
from the mean displayed.
And within 2 deviations, 19 of 20 lie, that’s right!
And within 1 deviation, 2/3 are confined,
CHORUS:
‘Cause we are living in an empirical world
and I need an empirical tool.
You know that we are living in an empirical world
and I use the empirical rule!
If I think a population
looks bell curve to me,
The rule helps tag outliers like a
z-score more than 3.
But if the population may not
take the normal shape (no way!),
Frequencies that you expect can
help you ascertain
(Repeat Chorus)