Summary Statistics

  • 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
    Is gonna make your day
    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

  •  

    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
    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)

  • 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!

    Exchange Paradox
    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
    about expected value
    and avoid bias.

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

  • 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)

Pages