Summary Statistics

  • 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
    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)

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