In this video, we're going to talk about how
to visualize data.
In particular, we're going to use something called a stem
and leaf plot.
And what's useful about this is it essentially allows you
to show all of your data and show a lot of detail about all
of the numbers in your data set, while at the same time
having a good sense about how those numbers in your set are
distributed.
Right here, I have a set of numbers.
And when I just look at this, it really doesn't make a lot
of sense to me.
It's just a bunch of numbers to me.
I have no sense are more of them closer to 20 or 30?
Are more of them closer to 80?
Is their median or their mode 30 or 40 or 84?
I have no idea, just looking at this list of numbers.
But using a stem and leaf plot, hopefully, some of this
will become a little bit more apparent.
And the idea here is to list the most significant digit in
each of those numbers in the stem.
So when we talk about the most significant digit, these
numbers right here, they range-- let's
see, we have a 2 here.
That looks like-- we have a 1.
That looks like our lowest number.
And it goes all the way up to 84.
It has a bunch of numbers in between in the teens, in the
twenties, in the thirties, forties, fifties, sixties.
so on and so forth.
So it looks like the most significant digit here is the
tens digit.
So let's write it right here.
Let's write our tens digit.
And the tens digit could be a 0, 1, 2, 3, 4-- let me write
this a little bit bigger.
0, 1, 2, 3, 4, 5, 6, 7 or-- let me scroll down a little
bit-- an 8.
These digits will represent our stem.
So I'm going to draw this little line around here.
This is going to be a our stem right there in the
stem and leaf plot.
For a number like 1, the tens digit is 0.
You could imagine it as 01.
For a number like 84, the tens digit is obviously 8.
So what I'm going to do is rewrite all of these numbers
here using the stem and leaf plot.
And the technique here, and I'm just going to show you by
example, let's go through each of these numbers.
Let's say I want to write 35.
So 35-- let me cross it out.
35, so it has a tens digit of 3.
I'll put a 5 right here.
That tells me that 35 is one of my numbers.
Then I have 42.
Cross it out, let me know I used it.
42, I'm writing the ones digit as leaves.
You're going to see what I'm going to do.
Let's see.
38.
Well, I have a 30.
I'm going to write an 8 here.
So I didn't have to rewrite the 30.
I'm just saying, look, I have a 35 and I have a 38.
I'm just writing the ones digits within the three stem,
within the tens place, within the thirties place, however
you want view it, the thirties bucket.
Then we have a 57.
We have a 2, which you could just view as 02.
We have a 2.
We have 24, 27, 36.
We have a 35, a 38, and a 36, 45, 60.
I think you get the idea, but just for the sake of
completion, let's finish all of these.
38, 40, another 40, a 44, a 1, another 44, a 48-- there's a
lot of things in this forties bucket-- 48, an 84, a 38, a
20, a 4-- put that right there, 04-- a 2.
It's getting a little monotonous, but
let's just finish it.
48, another 48 right there, a 58, a 3.
Stick it up there.
It's 03.
Then we have a 20, a 6, a 40, 22, 26, 17.
That's our first number in the teens bucket.
An 18, a 40-- a lot of things in the forties-- a 51, 62, 31,
27, 48, 35-- almost done-- 27, 37, 58 and 21.
And we have our 21.
And just like that, it was a little monotonous, but we
essentially just rewrote this list of numbers down here.
I have every number represented.
We haven't lost any information here.
I know every number.
I could go start with this, and I could tell you every
number that I had in my original list. I have a 6, I
have a 27, I have a 38, a 35.
So we haven't lost any information.
But what's neater about this representation is when the
numbers are written this way, we actually save ink, because
you don't have to rewrite the 40 to 45.
You just write the ones digit.
But more importantly, we kind of understand how the numbers
are distributed, that we have a bunch of numbers in the
forties and thirties and twenties.
That's where most of the numbers are.
We have very few numbers up in the eighties.
We have no numbers in the seventies.
We have very few.
We have a lot in the ones, but still, most of them are
focused in this range over here.
So this is just one of many, many, many ways to visualize
data that you will run into in your mathematical or
statistical futures.
But I just wanted to expose you to this.