Statistics Frequency Distributions and Features

Hi and welcome back to www.educator.com.0000

We are going to be talking about frequency distributions again but now we are going to be going a little more into detail about their features.0003

In the last lesson we covered how to look at the data in Excel.0013

There is a checkmark on top of that one and we talked about how to go from data to frequency tables using our count if function.0017

From frequency table to visualization.0026

We are going to take another look at those same examples that we looked0029

at before except now we are going to be talking about the features of these distributions.0033

In particular we are going to be looking at their shape.0037

There are couple of shapes you should know after this.0040

One is uniform distributions.0043

Another one is going to be called unimodal.0047

Yet another is called bimodal.0054

Especially we are going to be looking at called normal.0059

We are also going to be talking about center.0065

We are not going to be talking about how to calculate the center of the distribution.0068

We are going to be talking about how to think about the center conceptually in three different ways, mean, median and mode.0072

We are not going to talk about how to calculate it yet.0080

We are also going to be talking a little bit about spread.0084

How spread out is this distribution.0086

Finally we will also mention outliers, gaps and clusters whenever they are relevant.0090

Recall example 1, here we looked at a data set of a 100 www.facebook.com friends0098

and we looked at whether more of these friends are born in a particular month or another.0103

Note here that it really seems to be that no particular month is super popular.0108

This is what we call the uniform distribution.0113

If you sort of squint and blur your vision a little bit, it is almost like there is a flat line here.0116

Everybody is hovering close to that line.0125

No one month is more frequent in births than any of the other months by a lot.0130

Some of these months are a little more frequent but only by a little bit.0136

You could see there is relatively little change from month to month here.0143

Other uniform distributions also look like this sort of rectangle or flat shape0147

and these distributions might be anything from deaths occurring on days of the week.0155

Is there any reason to believe that one particular day is more favorable to die on than the other?0160

Or in rolls of a six sided dice, is there a particular reason to believe that one side might come up more frequently than another?0165

Not if it is a fair sided dice.0174

Remember this is now example 2, in example 2 we look at the same data set again and we looked at the age distribution in the sample.0181

Here we do not have a uniform distribution.0191

No matter how much you squint your eyes you are not going to see sort of a flat shape.0193

You will see a peak right here and because of that, this peak often called a mode the most frequent value.0197

This peak makes this a unimodal distribution.0208

I’m not going to call it example 2 anymore, I’m going to call it a unimodal distribution.0213

We will add on to that.0220

Not only that but this shape is what we call skewed.0222

If I decide to just draw a light little sketch over this guy, we see that it has this long what we call tail.0226

This tail goes out towards the right side, the larger values because it is skewed and the tail is to the right we call is skewed right.0242

It is not only unimodal but it is also skewed right.0256

You often have a skewed distribution when you have some sort of minimum or maximum value that these values are all bumping up against.0263