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Summary Statistics


  • 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)

  • 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!

    [REPEAT OPENING VERSE] 
  • 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 - )

  • Lyrics © Mary McLellan
    may sing to the tune of Journey's "Faithfully" 

    How do I know what measure to use
    Sometimes there’s symmetry
    Sometimes there’s skew

    When there’s skew, when there’s outliers
    All I know is that I need resistance
    The measure of center that is resistant to the skew
    The measure of spread that is resistant too
    Are the measures that I should choose to use
    I guess that I should choose then
    Interquartile range and median.

    Symmetry, symmetry 
    Standard deviation and mean
    Symmetry, Symmetry
    Standard deviation and mean

  • Lyrics © Mary McLellan
    may sing to the tune of ABBA's "Dancing Queen"

    If you have skew,
    then you must choose to use median and IQR ooh
    Symmetry, standard deviation and mean
    If you have skew,
    then you must choose to use median and IQR ooh
    Symmetry, standard deviation and mean

  • Lyrics © Mary McLellan
    may sing to the tune of "BINGO"

    When the data that you have goes through a transformation
    Addition and subtract, addition and subtract
    Addition and subtract
    Affects the center only

    When the data that you have goes through a transformation
    Multiply and divide, multiply and divide, multiply and divide
    Affects them both

  • Lyrics © Mary McLellan
    may sing to the tune of Fun's"We Are Young"

    Give me a second now
    I need to get my words straight
    I need to learn the vocab that is all about the data’s shape
    Uniformed, symmetrical, skewed to the right and the left
    Will there be an outlier or is the shape regular
    I know I then choose the center, though…
    Do I pick mean or median?
    So that I don’t get confused the spread that I choose to use is IQR or standard deviation

    When the AP test approaches and I want to get a 5, I know what to do:
    Describe the distribution
    Shape and outliers
    Center and spread
    Describe the distribution
    Shape and outliers
    Center and spread
    When the AP test approaches and I want to get a 5, this song will help me to thrive

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