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# Summary Statistics

• ### Worry Lines

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.

• ### Empirical Rule

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

(Repeat Chorus)

• ### My Family's Mean

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.

• ### Don't Buy a Carpet

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]
• ### Spiegelhalter on Big Data

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 - )

• ### Which Measure Should I Choose

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

• ### Which Measure and Spread to Use

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

• ### Transformation Song

may sing to the tune of "BINGO"

When the data that you have goes through a transformation
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

• ### Describe the Distribution

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