In this set of video I’ll talk about
some ways of representing and visualizing data
that’s used very often
when one is looking for power laws
This is building towards the idea of
the cumulative distribution function
and ranked frequency plots.
But I am gonna start by talking about
a simple histogram first.
So let’s say we have some data
And in practice you would have a many points
But for this example I am gonna imagine
we would have only 10
And so we wanna know how are these distributed.
Are they distributed according to
power law or something else?
So a common thing to do
when you’re faced with the data
kinda get a sense of a big set of data
where does it live
where are most values
is to make histogram
So histogram
we just count the number,
frequency of occurrences, number of occurrences
of data points with in certain ranges.
So here’s a set of axes
Here’s those data points again.
And so I chose somewhat arbitrarily
10, 20, 30, 40, 50
And so each sort of range is gonna go
from 0 to 3 and thirds,
3 and thirds to 6 and two thirds and so on.
So that’s kind of a usual bin size
But that’s nothing wrong with that
And we are just fine.
So let’s think about
how we would build up a histogram.
Alright so there’s one value that is 5
So 5 would fall in this region.
So I would say there’s one in there filling that box
7,
7 is between 6 and two thirds and 10
So there is one in there.
10 and 13
We take the end point to go
towards the right bracket
and write something.
We would have two in this region to between
equal to 10 or greater but less 13 and a third
So that’s for 10,
That’s for 13
And I coup keep going
14
18 is in there
21 is a little to the right of 20
28
32
and 48 goes all the way over here.
Ok, so this is a way of visualizing this data set
Particular let’s see is there any central tendency
What’s the range of values and so on.
In practice one really wouldn’t do histogram
with this small amount of data.
You probably want a lot more.
And you wanna think about
what size you use for the bins as well.
But I’m trying just to illustrate
this general idea.
So this is the idea behind the histogram.
And we will see the next is another way
an alternate way of visualizing the same data
something called cumulative distribution function.
But before we go to
cumulative distribution function
I realized that one more thing
I want to mention about the histogram
So we can think of a histogram
as measuring in terms of counts.
But we can also turn this into a probability
by dividing by the number of the data.
So never data points.
So we have 10 measurements and
so I could interpret this as saying
There is one value between 3 and third
and 6 and two thirds.
It can also interpreted as saying
there is one in 10 change.
If I were to draw from this at random
that I would get something in that range or
that simply 10 percent of the data falls in here
So I could take this.
I am dividing by 10
0.1
0.2
And this I might think of as p of x
The probability of x.
There’s a subtlety with this interpretation
this is one of those places where in matters
if we’re thinking about the continuous
or discrete distribution
But in either case we can think of this
more or less as the probability
that’s a lowercase p
Ok so now let’s move on
to cumulative distribution functions.