Sorry, you need to enable JavaScript to visit this website.

# Summary Statistics

• ### Letterman on Percentages

USA Today has come out with a new survey - apparently three out of four people make up 75 percent of the population.

David Letterman (1947 - )

• ### Churchill on Statistics

The only statistics you can trust are those you falsified yourself.

Sir Winston Churchill (1874 - 1965)
(Attribution to Churchill is ironically falsified)

• ### Hailey on Statistics

Legal proceedings are like statistics. If you manipulate them, you can prove anything.

Arthur Hailey (1920 - 2004)

• ### Central Tendency

Well I [G] got me some data [C] to make me more [G] wise,
But the [C] data I [G] had to [D7] summarize,
Since my [G] Ed Psych 480 I did [C] mem-o-[G]-rize ,
I [C] knew just [D7] what to [G] do.

Refrain: Oh, the [D7] mode, the mean, and the [C] med-i-[G]-an,
For a [C] large set of [G] data you [D7] choose just one,
As a typical value we [C] have these [G] three
Measures [C] of Central [D7] Ten-den-[G]-cy.

Now the [G] mode is quite easy to [C] find, you [G] see,
But it [C] suffers from [G] insta-[D7]-bil-ity,
Yet for [G] categorical data use it [C] confident-[G]- ly,
There [C] just ain't no [D7] other [G] choice.

Repeat Refrain

If you [G] like to rank data use the [C] me-di-[G]-an,
It's so [C] much [G] fun to find the [D7] middle one,
But if [G] you have two middle values [C] not [G] one
Their [C] midpoint is [D7] what [G] you need.

Repeat Refrain

The [G] a-rith-metic mean may be [C] your best [G] bet,
And [C] you can be [G] sure that I'll [D7] never for-get,
It [G] reflects all the values of the [C] data [G] set,
[C] E-ven those [D7] quite [G] ex-treme.

• ### What's the Average?

Lyric copyright by Lawrence Mark Lesser
May sing to tune of "Love and Marriage" (Sammy Cahn and Jimmy Van Heusen)

What's the av'rage, what's the av'rage--
It's a question to be askin':
When it's in the media,

What's the av'rage, what's the av'rage?
Each kind has its own baggage--
Some try to fool the plebian
By choosing mean or median!

Bridge:
Are... there... outlier values
or lots of skewness?
Do we... want... middle or the total?
Let's review this...

What's the av'rage, what's the av'rage?
It's a question we must manage:
When it's in the media,
You gotta know, you gotta know,
You gotta know what it means t'ya!

• ### Stat 51: I Will Survive

Lyrics copyright by Sheila O'Leary Weaver
may sing to the tune of "I Will Survive" (Gloria Gaynor)

At first I was afraid; I was petrified.
I just hadn't realized my data was skewed to one side.
And now I'd spent so many hours finding the mean and the SD,
But now I see, just how misleading they can be.

So now I'll go; walk out the door.
I'll get an F in here; I may not stay in college anymore.
I should have dropped this stupid class; I should have bought the answer key.
I should have thought for just one second, office hours were for me.

But no, I'll try, a new technique.
I'll rank the data, and the middle is the median I seek.
The middles of the halves are called the Quartiles 1 and 3,
Add the min and max - that's the five number summary.

Stat 51, I will survive
As long as I can pass this class, I know I'll be alive,
I've got all my life to live,
One semester's time to give:
I will survive, I will survive,
Hey, Hey....

Dance Interlude

To put it in a graph, I'll draw a number line.
Make spacing even or interpretation's undermined.
Draw vertical lines at each number and connect the middle three,
And a boxplot will result to show the lack of symmetry.

And now I'll find the IQR.
It's Q3 minus Q1. If it's big, the data spreads out far.
If a number's more than 1.5 IQR from the box,
It gets a star, and you can call it an outlier.

And now I'm done. My summary,
Is more appropriate for data that is lacking symmetry
The mean and the SD may be affected by the skew.
But my way's strong: It's more robust and it's not wrong....

Stat 51, I will survive
As long as I can pass this class, I know I'll be alive,
I've got all my life to live,
One semester's time to give:
I will survive, I will survive,
Hey, Hey....

More Dancing

• ### Statistition

Music: Superstition (Stevie Wonder)

Very statistitious, bell curve on the wall,
Very statistitious, so empirical,
Normal distribution, centered 'round the mean
Standard deviations, most fall within three

When they deceive with things that you don't understand
Distort the numbers
Statistitions lie all day

Very statistitious, probability
Mind your p's and q's, they're complementary
Median or mean, central tendency
Make a distribution, show the frequency

So you'll believe in things that you don't understand
They twist the numbers
Statistitions fabricate

(Scream) MUUUUUUUUUUUUU...

Very statistitious, show significance
With an estimation, know your confidence
Gettin' inferential, hypothesis test
Linear regression, the line that fits the best

When they deceive with things that you don't understand
Invent the numbers
Statistitions know the way

• ### Pick the Mode Jack

may sing to the tune of "Hit the Road Jack" (Percy Mayfield/Ray Charles)
(italicized words are sung by male soloist. Remaining words sung by female singers.)

Pick the mode Jack and don't you keep track of no mu, no mu, no mu, no mu.
Pick the mode Jack and don't you keep track of no mu.
What you say?
Pick the mode Jack and don't you keep track of no mu, no mu, no mu, no mu.
Pick the mode Jack and don't you keep track of no mu.

Woah Woman, oh woman, won't ya give me my mean,
You're the meanest old woman that I've ever seen.
I guess if you say so
I'll have to take x-bar and go.
(That's right)

Pick the mode Jack and don't you keep track of no mu, no mu, no mu, no mu.
Pick the mode Jack and don't you keep track of no mu.
What you say?
Pick the mode Jack and don't you keep track of no mu, no mu, no mu, no mu.
Pick the mode Jack and don't you keep track of no mu.

Well baby, listen baby, don't ya treat me this-a way
It's just a summary stat to say.

Don't care what you say 'cause it's understood
You ain't got no data for my likelihood.
Well, I guess if you say so
I'll have to take x-bar and go.
(That's right)

Pick the mode Jack and don't you keep track of no mu, no mu, no mu, no mu.
Pick the mode Jack and don't you keep track of no mu.
What you say?
Pick the mode Jack and don't you keep track of no mu, no mu, no mu, no mu.
Pick the mode Jack and don't you keep track of no mu.

Well!!
Don't you keep track of no mu.
Uhh what did you say?
Don't you keep track of no mu.
I did not understand it
Don't you keep track of no mu.
I came to talk it over
Don't you keep track of no mu.
I thought we had a better understanding
Don't you keep track of no mu.
Oh baby don't be so common
Don't you keep track of no mu.
Don't you want a hat on pi? x2
Don't you keep track of no mu.
Oh baby it isn't fair
Ooh yeahh

• ### Totally Average Woman

Lyric and music copyright by Carla Ulbrich

I got a totally average woman stands about 5'3"
I got a totally average woman she weighs about 153
Yeah she's a mean, mean woman by that I mean
statistically mean
Y'know average

When she walks down the street some people notice some don't
When she walks down the street some people notice
But in general most people won't
Some guys will whistle just as many won't

She takes all my money invests it in a mutual fund
She takes all my money invests it in a diversified dividend-producing mutual fund
We'll probably retire in a style to which we are accustomed

Make a blind man hear
Make a deaf man see
She could have any guy who is no better or worse than me

I got a totally average woman got an IQ of 103
She's a mean, mean woman statistically

Every night she beats me Lord she beats me so bad
Every night she beats me Lord
You wouldn't believe how she beats me so bad
She is the toughest scrabble partner that I have ever had

I asked her for some water she said ice or no ice?
I asked her for some water and she said,
"do you want a cup or a glass and ice or no ice?"
Then she brought it to me ... that was nice

She can let a sleeping dog lie
Send a dead man to his grave
When she was a young child she would usually behave

I got a totally average woman she's about 5'3 point 7
Yeah she's a mean, mean woman
By that I mean statistically mean
Y'know average
Baby I would walk over room temperature coals for you

• ### Mean

May sing to the tune of "Mean" (Taylor Swift)

You.......with your words like mean & mode & symbols that you use against me.
Mu........stands for a population mean and x bar for the sample.
Who.....knows what symbol to use for other measures of data location.
You......pickin' each time the mean.
But it can get pulled off by just one single point,
And you don't know what you don't know....

CHORUS:
Sometimes data have a real asymmetry
Or values that are really quite extreme.
In those cases, better use the median
If the middle is what you need - that's not gonna be the mean!

That won't be the mean with outliers, just forget it,
Do you see just what I mean & mean & mean & mean? (repeat chorus)