Summary Statistics

  • 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,  

    ‘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)

  • Lyrics & Music © 2016 Amy Adler

    I'm looking at the ages of my living family
    I'm 29, my mom's 50, and Dad is 53
    The median is 50, and the mean is 44
    But if I added in my grandma, the mean would be much more.

    My grandma, she is 80, and now our group has four
    The median is different when we brought her aboard
    When this happens, it's the halfway point between the middle folks
    It's only 51.5, but the mean jumps up real close.

    Let's try a bigger group now, let's add my cousins, too
    They're 4, 13, and 16, 29, and 32
    Since we added younger people to the group to calculate
    Will the mean and median change much, what do you postulate?

    Our new median is 29, much lower than the last
    But the mean is now 34, it dropped, but not as fast
    'Cause my grandma and my parents keep the mean declining slow
    Yet more younger than the older, made the median drop down low.

    When you have a group of people who are mostly young in age
    The mean, it is affected by a few who are quite gray
    Since the median is simply the middle of the crew
    It doesn't change if Grandma were 100 or 82.

  • Music and Lyrics © 2015 Tom Toce (Retrograde Music)

    Don't buy a carpet for half a room
    Half a room
    Half a room
    Don't buy a carpet for half a room
    On the other half
    the floor will be bare.

    You see, the surface grows twice as fast,
    Twice as fast
    Nice and fast
    One side may double;
    Don't be aghast
    That the area grows just like –
    The area grows just like –
    The area grows like –
    The square.

    Variance grows like area
    Area grows like variance
    Area grows like variance
    Variance grows like area!

  • There are a lot of small data problems that occur in big data.  They don't disappear because you've got lots of stuff.  They get worse.

    David J. Spiegelhalter (1953 - )