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.