Hi, I’m Adriene Hill and Welcome back to Crash Course Statistics.
Last time we left off talking about different data visualizations. The ones we encounter every single day.
Whether it’s a chart on the subway telling us the prevalence of heart disease in different
age groups, or a histogram on Buzzfeed showing us how many times people use Lyft each week.
These visualizations allow us to get to know data with our eyes, and today we’ll dive
deeper into data visualization and make all sorts of beautiful graphs and talk about some
really extreme situations, like the person who watched Sandy Wexler on Netflix like 400 times.
Which seems like high.
INTRO
Last episode we looked at histograms which use the height of a bar to show how frequently
data occur.
We can also use this format to make a dot plot.
A dotplot takes a histogram, and replaces the solid bars which use their height to show
frequency... with dots.
There’s one dot for each data point contained in the bar, so we can just count the number
of dots to find out how many there are.
The dot plot for our olive oil data looks like this, unsurprisingly similar to the histogram
for that data.
Or check out this dot plot of how often this sample of people called their moms this month.
This gives us a nice way to explore the general shape of our data, but we still lose information
about the individual data values, just like with the histogram.
Occasionally we WANT that extra information.
Enter, the stem and leaf plot.
A stem and leaf plot is a cousin of the dotplot.
It also gives us information about data and their frequencies by stacking objects on top
of each other.
However, stem and leaf plots use values from the raw data ...instead of dots.
So we’ll turn our Olive oil dot plot into a stem and leaf plot.
And no, I’m not going to explain my olive oil fixation...
First, we need to split each data value into a stem, and a leaf.
Stems are related to the “bins” or bars in a histogram or dotplot.
Take our dotplot for example: each stack of dots might represent a range of 5oz, from
0-4 oz, 5-9oz, all the way up to a bar with all the data in the 80-84 oz range.
The stem for a “bin” of data is the digits that *all* the values in a “bin” have
in common.
For the 10-14 oz range, each value has a 1 at the beginning of the number so the stem
is ‘1’.
For the 80-84 oz range, the data all have an “8” at the beginning, so the stem would
be ‘8’.
We can have larger stems too!
If the data went all the way up to 2,006 oz, we could have a stem of “2-0-0”, but that’s
probably too much for our olive oil example.
Now that we have all of our stems, we can add the leaves.
Each stem, like in a real plant, can have multiple leaves.
They’re stacked on top of each other so that the height of the stack shows you how
frequently data appear in that bin, just like a dotplot.
The actual “leaf” is the rest of the digits that are not in the “stem”.
If one of our data points is 13, and the “stem” for that range is 1, that takes care of the
“1”, so the leaf is “3”.
Leaves appear in numerical order, from the stem out, so leaves that are smaller digits
are closer to the stem.
From a distance, stem and leaf plots look a lot like a dotplot or histogram.
If you squint your eyes, the leaves almost look like bars or dots, but unsquinting them
will allow you to see even more information than a histogram or dotplot will tell you.
You get to see what the individual values are and *how* they’re spread out within
a bar.
Stem and leaf plots are usually flipped on their sides so that the stems are listed vertically
and leaves extend horizontally.
Here’s a stem and leaf plot of the number of pieces of gum each of your extended family
members has chewed in the last month.
Now let’s talk about boxplots.
Boxplots use some of our measures of central tendency and spread to visually display our data.
A boxplot--is also called a “box-and-whiskers-plot” It has two major parts: the box and the whiskers.
The box is a rectangle that stretches across the inter quartile range of our data (from
Q1-Q3).
At the median, there is a line splitting the rectangle into halves.
If one one of those halves is larger than the other, that quartile is more spread out.
Since each quartile has the same number of data points, the smaller the quartile, the
less spread out that portion of the data is.
Imagine the difference between fitting 20 clowns in a car and fitting 20 clowns in a
regulation sized football field.
Same number of “clowns”, more space to make balloon animals.
Attached to either end of this box are the whiskers-- which help show the minimum and
maximum of all the data, as long as it's within one and a half times the Interquartile range
of the median.
This value sets our “fences.”
We use one and a half times the InterQuartile Range because *most* of the data will be within
this range, especially if your data is normally distributed.
We’ll get into this more in future episodes.
Most of the data will be inside the fences-- any data outside is flagged as a potential
“outlier”.
It can be tempting to think of outliers as data that’s “wrong” somehow, but that’s
not always the case.
Values outside the fences are less likely than data near the boxplot, but they’re
not impossible.
For example, It’s pretty unlikely that if you dial random numbers into your phone you’ll
call is a Domino’s Pizza, but it is possible.
Rare values do happen.
Keeping these rare-but-possible values can be important.
When the local news shows you a boxplot of local rents and decides that the bottom 1000
rent values are “outliers”, the graph they display could be misleading.
Those rents are real values that you could expect.
Taking them out will make your visualization less informative, and might lead you to think
that the average rent is higher than it actually is.
However, some values that are flagged as “outliers” may not be expected in your data at all.
Perhaps Neymar snuck into your amateur pick-up soccer game without you knowing.
His off-the-charts-agility-scores are not representative of the population you are interested
in since he is Neymar...not an amateur.
Or maybe you made a typo in your spreadsheet and wrote 500 pounds instead of 5 pounds for
your data on the weights of pet teacup pigs.
That’d be a giant teacup… pig.
The problem is you may not always know the difference between a point that’s valid-but-rare and one that’s
a mistake.
Since we still need a way to decide, it is useful to have a pre-set cut-off for when
we discard data .
To see how boxplots can help us look for these outliers and compare data from two samples,
Let’s jump to the Thought Bubble.
Justin Timberlake has a new album.
This American born singer and songwriter has had quite the career.
I mean, he did bring sexy back.
Our writer, Chelsea wanted wanted to know how going solo affected the songs he wrote,
specifically, the number of unique words he used per song.
To satisfy her curiosity she made a boxplot for a sample of Justin Timberlake’s songs
once he’d gone solo, and one for a sample of songs he sang with *N’SYNC.
The first thing we might notice, is that the medians-are pretty different.
The median number of unique words in a Justin Timberlake song is higher than the median
number of unique words in an *N’SYNC song!
JT has a median of 129 words vs a median of 89 back in his *N’SYNC days.
Guess we shouldn’t be surprised coming from a band that had a song titled “Bye Bye Bye.”
So it seems like JT may have developed a larger lyrical vocabulary when he went solo.
...Maybe Lance Bass was holding him back…
Anyway...you might also notice that the box part of the *N’SYNC boxplot is a lot smaller.
The squished nature of the boxplot shows us that *N’SYNC songs have a relatively similar
amount of unique words.
The boxplot also shows you some potential outliers to look at, shown by the points that
are outside the fences of our boxplot.
Let’s look at a song that’s marked as a potential outlier in the Justin Timberlake
Boxplot.
The song is “Chop Me Up” and it has 257 unique words which is a lot, since the median
number of unique words for a JT song is 129.
It’s definitely outside the fences.
Thanks Thoughtbubble.
We don’t want to throw out data just because it is extreme.
And Chop Me Up isn’t part of some super-experimental Christmas album... so it’s hard to tell
if this is a valid data point.
To get around this uncertainty, we apply our pre-set rule.
There isn’t one set rule for handling these extreme values, there are many.
For now, we’ll use our boxplot method, and get rid of the “Chop Me Up” data because
it’s outside the fences .
Remember, statistics is all about uncertainty.
I’m not sure if the number of unique words in Chop Me Up is just a rare value, or whether
it’s the lyrical equivalent of Neymar in a pick-up soccer game.
We still have to make decisions.
For all the Nerdfighters out there, you may have heard of Hank’s annual Nerdfighteria Census.
And while you’re interested in taking it, you may wonder how long it takes to fill out...you
don’t have all day...so you use your new data viz skills to create a boxplot of the
data...and wahwhah.
I can’t even see the box or the whiskers through all those extreme values--it looks
like some Nerdfighters were very thorough...or very distracted by other things.
8000 minutes is 133 hours.
This plot isn’t wrong….per se...but it’s not very informative since we can’t get
much useful information from it.
We don’t have any better idea of how long it’s gonna take to fill out Hank’s survey.
When you make or see a data visualization it’s important to remember that its job
is to actually give you information.
If it doesn’t do that, its not worthwhile.
Now, let’s go back to frequency plots and talk about one last method for visualizing
quantitative data: the cumulative frequency plot.
Cumulative Frequency Plots are like histograms but instead of the height of a bar telling
you how much data is in that specific bin, it tells you how much data is in that bin
AND all previous bins.
That’s why it’s called “cumulative.”
It’s the frequency of all the points we’ve accumulated up to this point.
It’s like a small fish getting eaten by a bigger fish, which gets eaten by an even
bigger fish, and so on.
Each fish is now full of the fish it ate.
And the fish that fish ate.
And side note.
Your odds of being killed by a shark--are about one in 3 point 7 million.
Back to our cumulative frequency plots... these plots have their moment to shine when
we want to answer a question like “How many JT songs have 160 unique words or fewer?”
The cumulative frequency plot looks like this:
Here’s the bar that answers our question.
We could also get this information by counting all the songs in the bars that are 160 or
less on our histogram, but that’s more work.
Now that we’ve seen some good graphs and some bad, we can apply our newfound knowledge
anytime we see data visualizations...which will be all the time.
“This I Promise You”.
I mean...like... "until the End of Time".
On the bus, in your health app, or during your bosses annual company-wide meeting, you’ll
know that graphs are only as good as the information they communicate.
If you see a bad graph out there.
“Say Something” Ask questions.
Be skeptical.
I’m coining a new DFTBA today: DFTBAQ.
Don’t forget to be asking questions… it’s another way of being awesome.
“I Want it that way” The world wants it that way.
And remember...it’s not just gonna be you…”it’s gonna be me” too.
Allright. I’m “Gone” See you next time.
And yeah, I know "I want it that way"was Backstreet Boys.