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For more information, please see full course syllabus of Statistics
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Lecture Comments (13)

0 answers

Post by Mohamed E Sowaileh on July 10 at 08:49:28 AM

Hello Dr. Ji Son,
I hope you are very well.

I am a student who is extremely weak in math. In order to be very strong in math, specially for engineering field, could you provide me with sequential order of mathematical topics and textbooks. With what should I begin so that I can master big topics like calculus, statistics, probability ... etc.

Your guidance is precious to me.

Thank you so much.

0 answers

Post by Saadman Elman on August 31, 2014

It was very helpful! She clarified it very nicely.

0 answers

Post by Oliver Barry on May 2, 2014

Is there anywhere where we can get more examples to work through?

0 answers

Post by Ryan Hughes on February 10, 2014

Where does one ask questions from their class work that they would like help answering?

0 answers

Post by Abdihakim Mohamed on November 25, 2013

This is not specific, I feel like I am lost. I understand early part but the examples don't make sense. I mean basically I am lost in the examples.

0 answers

Post by Manoj Joseph on June 27, 2013

what do you mean by measured conclusions?

1 answer

Last reply by: Gayatri Arumugam
Tue Jan 8, 2013 11:48 PM

Post by Jameelah Hegazy on October 22, 2012

Great lecture.

Is it possible for members to save your lecture slides?

0 answers

Post by Matthew Manning on September 17, 2012

Just to make sure I'm understanding this correctly, Descriptive Statistics is basically exact information (the type of information that we desire from a population, but are unable to obtain. Inferential statistics is the information that we gain from samples, and we then use that info in order to come to conclusions.

0 answers

Post by Matthew Manning on September 16, 2012

What specific areas of Math on Educator.Com should I brush up on in order be successful at Statistics, I have obtained an override to bypass lower level classes. But I need to know specifically what I need to review in order to do well. Please be very specific, Thanks

0 answers

Post by Daniel Goff on April 18, 2012

great lecture...very informative

0 answers

Post by M Holland on December 1, 2010

Extra example 2 has errors in the finding the probability of the first item

0 answers

Post by Abraham Hsu on February 11, 2010

***Column "Yes" total =/= 279, but 379, therefore 178/379

Descriptive Statistics vs. Inferential Statistics

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Roadmap 0:10
    • Roadmap
  • Statistics 0:35
    • Statistics
  • Let's Think About High School Science 1:12
    • Measurement and Find Patterns (Mathematical Formula)
  • Statistics = Math of Distributions 4:58
    • Distributions
    • Problematic… but also GREAT
  • Statistics 7:33
    • How is It Different from Other Specializations in Mathematics?
    • Statistics is Fundamental in Natural and Social Sciences
  • Two Skills of Statistics 8:20
    • Description (Exploration)
    • Inference
  • Descriptive Statistics vs. Inferential Statistics: Apply to Distributions 9:58
    • Descriptive Statistics
    • Inferential Statistics
  • Populations vs. Samples 12:19
    • Populations vs. Samples: Is it the Truth?
    • Populations vs. Samples: Pros & Cons
    • Populations vs. Samples: Descriptive Values
  • Putting Together Descriptive/Inferential Stats & Populations/Samples 17:10
    • Putting Together Descriptive/Inferential Stats & Populations/Samples
  • Example 1: Descriptive Statistics vs. Inferential Statistics 19:09
  • Example 2: Descriptive Statistics vs. Inferential Statistics 20:47
  • Example 3: Sample, Parameter, Population, and Statistic 21:40
  • Example 4: Sample, Parameter, Population, and Statistic 23:28

Transcription: Descriptive Statistics vs. Inferential Statistics

Hi welcome to the first lesson in statistics course.0000

Today we are going to talk about descriptive statistics versus inferential statistics.0005

Here is the road map for today, first we need to distinguish how statistics is different from other mathematics.0012

We will talk about how descriptive and inferential statistics separate.0018

Finally we are going to talk about populations versus samples and then we are going to put all of those ideas together0024

and look at how population, samples, descriptive, and inferential statistics all fit together.0030

First things first, how is statistics different from other specializations in mathematics such as trigonometry, geometry, calculus, linear algebra.0037

Statistics is different because it is the science of classifying, organizing, and interpreting or analyzing data.0048

You might be thinking to yourself - "Hey science? I thought this was mathematics." Right?0055

Its link implies much of science and because of that it is important in mathematics.0063

Let me explain that link to you in just one second.0069

First I want to step back and think about high school science firmament.0073

A lot of high school science is concerned with measurement, we go around measuring things and measuring how fast people run0077

and how fast things are dropped and how much things grow and how much things way.0084

How big things are and we are gathering a lot of data on measurement.0089

Then we find patterns within those measurements and that is basically the fundamentals behind high school science.0095

Those patterns can often be described as mathematical formulas.0104

I do not know if you have this experience that some of you may have had the experience of trying to derive the gravitational constant.0110

To some of you this equation might look familiar, D= ½ gt2.0117

(D) stands for distance, (g) stands for the gravitational constant and (t) stands for time.0126

Some of you may have had the experience of dropping things off a building and timing them0138

and putting in these numbers to try and figure out what (g) is.0143

(g) theoretically is supposed to be 9.8 m/sec2.0149

But rarely do you calculate exactly 9.8 when you put in distance and time into this equation.0159

Often, science students think I'm terrible at science, I’m not getting the right answer0167

but it is because all of these measurements are inherently a little bit sloppy.0173

Granted that high school students might be sloppier scientists than other scientists but in actuality all science experiments0178

have measurement error and there is variance that comes with measurement.0186

There is always a little bit of jiggle in that data and often we do not pinpoint the exact right data even when you look at something0191

like measuring someone's height, you might have 10 people measure the same person's height and come up with slightly different answers.0199

It is not because they are trying to cheat but that person might that a deep breath or slouch a little bit0207

or maybe they read the tape measure at their hairline instead at their actual height.0213

There are always different reasons for measurement error.0222

All science is fought with measurement error.0225

While because all experiments, even the good ones at SERV, MIT and Caltech, all experiments will have a little bit sloppiness.0230

That is because we are dealing with measuring the physical world.0242

It is not bad which we are looking at terrible scientist or just real messy0250

it is just that inherently in measuring the world we are going to have a little bit of sloppiness.0256

Now because of that sloppiness, even the best experiment will produce a scatter of numbers.0262

Even best experiment as well as the worst experiments they will produce a scatter of values or measurements.0269

That is where the problem is right?0289

You will not get just one number like nice 9.8 gravitational constant, you will instead get this scatter of numbers.0290

How do we deal with that scatter and that is where statistics come in.0299

Statistics is the math of distributions then you could see how the math part and the science part fit together.0305

Statistics is invented because we want to do better in science.0311

We even have a special name for the scatter of measurements and that is called a distribution.0317

Not only that but we are going to look and see how we can go from frequencies of these values0330

in order to get probability distributions of these values.0337

Those are also going to be called probability distributions.0341

One thing that should come to your mind is that when you have a scatter of values or a whole bunch of different probabilities0360

predicting different values then you are not going to have just one number, you are going to have a whole set of numbers.0366

Because of that we are going to have to deal with the mathematics a little bit differently.0373

We are not just computing one number at a time and looking at one number and adding things to it, subtracting things to it, doing things to it.0378

Instead we are looking at entire distributions.0385

How do we treat these distributions?0389

How do we interpret them?0390

That is the question behind statistics.0392

You might think working with whole distributions that sounds problematic.0395

Sometimes it might seem like it.0400

It might seem like these equations are pretty complicated because we have to deal with the whole distribution.0403

Also you will get some great stuff out of working with distributions.0408

One reason is because distributions are often much more predictable than individual values.0412

Distributions are more predictable than individual values.0419

Models of distributions or theories of distributions can often predict the mathematical nature of randomness.0435

Is it not great?0444

They are predicting randomness.0445

That is what statistics is a little bit about, it is dealing with that randomness and teaming it.0448

How is statistics different from other specializations in mathematics?0456

It is born out of the science of classifying, organizing, and interpreting data, distributions of data to be more precise.0460

And because of that statistics is the mathematics of distributions.0469

Statistics is fundamental in all science in both natural and social sciences.0474

I’m a social science professor, a psychology professor by trade but even in the natural sciences all these discoveries that you have heard of0480

they only come about through rigorous applications of statistics in physics, biology, economics, psychology,0490

you name it statistics have left its math there.0497

There are two skills that you need to know when to enter into statistics.0502

The first is the skill of data description or what you can think of that as exploration.0506

Often you could think of it as just an open-ended examination of the data.0512

Let us look and see what is there.0516

We are looking for patterns and often it is helpful to make a graph or to look at averages0518

and standard deviations that are called summary values when you are looking for patterns.0524

These are tools that help us see patterns better.0535

The problem with just exploring or describing data is that you are not able to come to any conclusions.0540

You have to rain yourself from making conclusions when you are just doing descriptive statistics that is inferential statistics will come in.0548

When you make inferences in statistics you are doing a much more strict examination of the data according to set rules.0557

Then you will judge whether these patterns that you find through description are likely or not according to theories0566

and different models that you may have set up.0575

At the end of inferential statistics you should be able to make measured conclusions.0579

Often in science we do not say statistics has proven this theory or completely disproven this theory.0585

Instead we make much more measured and qualified conclusions.0593

Those skills of description and inference applied directly to descriptive statistics and inferential statistics.0601

This thing that is different now is you want to think about those skills and how they apply to distributions.0611

Here is how descriptive statistics applies to distributions.0619

These are the concepts and tools that you need in order to analyze sample distributions.0624

Use to describe or explore sample distributions.0637

We just have taken the same concepts of what describing data means and we have applied it to sample distributions.0653

Distributions that we have plucked out and a set of data that we plucked out.0660

In inferential statistics what we need to do is then apply inference to distribution.0666

Here it is the concepts and tools to reason from sample distribution.0674

To make some inference to reason from a sample distribution to a larger population distribution.0694

In inferential statistics what we are doing is using those skills of inference to go from sample distributions0715

but not only just to understand the sample but to make some inferences about a greater larger population.0721

Just to go beyond our actual data.0728

In descriptive statistics we just stay with our sample.0731

We do not make any inferences beyond what we have.0735

It behooves us to figure out what is the difference between the population and the sample distribution?0743

Here it might be helpful to just think of the population a sort of like the truth.0751

This is where we are interested in.0756

Is it the truth? This is the truth.0759

This is the thing that we want to get at.0765

If you think about the gravitational constant, this is that magical value that is out there in the world.0767

The sample is not the truth, it is like a little bit of that truth.0775

When we drop our objects from the top of the building and measure how fast they come down, we are getting samples.0781

From those samples we are trying to get at the truth.0791

The sample is not the whole truth but the sample does provide a window to the truth.0794

It is important to realize that the sample is not the actual truth itself.0803

This is not what we want to know about.0808

We want to know about the population but we are using the sample in order to know about the population.0812

Some pros and cons.0819

Some pros of the population is this because it is the truth if you happen to have all the information0822

about the real population it will be absolutely 100% accurate.0828

However here is the con, it is almost impossible to get.0836

It is almost impossible to get the truth, the real population true.0847

For instance let us say you just want to know what the real average height of every person in the United States is.0853

In order to do that you would have to get measurements from every single person in the United States.0861

All of those measurements would have to be 100% accurate.0868

Let us say I will give that to you, you will even do that.0872

By the time you are finish recording all of those measurements, some people would have died and new people will have been born.0874

All of a sudden your measurements would not be accurate anymore.0881

It is almost impossible to get the entire population.0885

Often in statistics, they will pick a small population like they will say consider all the people who attend your school0890

and to shrink down the population that you could think about it without feeling like your mind is being blown.0897

In the real world it is basically impossible to get the real truth.0905

On the other hand, the sample has the pro of being convenient.0910

It is easy to get data from just a sample of the population.0917

You do not have to get the whole population, you just have to get a sample of it and it is convenient and easy to get.0923

Here is the big con that you need to worry about.0929

The con is that the sample might be what is called biased.0933

By biased they do not necessarily mean like the sample like racists or prejudiced in some way,0938

I just mean that the sample may not be representative of the population.0944

The problem with that is when we look at our sample we are going to use our sample to try to get on the truth.0960

If our sample is different from the truth then it might lead us astray and that is called being biased.0965

When we describe the population in terms of numbers and we get some summary values for the population,0975

those descriptive values are going to be called parameters.0982

A friend of mine who teaches statistics with a help of the population parameter.0988

On the other hand, for samples you would use what is called statistics.0996

This word for statistics is the same word as the word for the class.1006

But statistics covers all of statistics, descriptive, inferential, population, sample, all that stuff.1010

This is the sort of smaller use of that word.1018

Population and parameter, specific sample for statistics.1024

Now let us put all those ideas together.1033

How do we put together descriptive and inferential statistics with populations and samples?1036

It helps us to ground ourselves by starting off with the idea that what we are interested in, in knowing about is the entire population.1042

We want to know about the real population.1052

Let us deal with one population at a time for now.1056

Often we do not have the population's entire data in front of us, we only have a sample of that data.1060

This is our wish to go from sample to the population but remember the sample can be biased, that is problematic.1069

Here is where statistics comes in.1080

From samples we compute statistics and from populations we could know the parameters.1083

But we often do not have this link either because we do not know anything about the actual population.1097

Here is where we are, what inferential statistics will help us do is make this link.1106

How do we go from statistics of the sample to population parameters?1114

This jump, this inferential jump is going to be made through inferential statistics.1119

However in order to go from the sample to statistics we will use descriptive statistics.1134

This is how it all fits together.1147

Let us try some examples.1150

Here is example 1, a pollster asks a group of voters how they intend to vote in the upcoming election for governor.1153

In this example is the individual pollster primarily using descriptive statistics or inferential statistics.1161

What he or she computes parameters or samples.1171

Here the pollster is just asking a group of voters how they intend to vote.1175

A poll is often just a sample of the entire set of voters so I would say the pollster is probably going to compute some sample statistics.1180

We should say statistics not samples.1194

I would say the pollster is probably calculating statistics.1202

If the pollster just got an answer such as this sample of voters is going to vote for the governor 75% of them are going to vote for the governor1208

and only 25% are not that would be counted as descriptive statistics.1219

Once this pollster actually uses that information to then make some inferences and predicts and then I predict the governor will win,1225

that would be inferential statistics.1236

But so far, it does not say that.1238

It seems that only descriptive statistics is being used here.1242

Example 2, a teacher organizes his classes test grades into distribution from best to worst and compares it to the test grades of the entire school.1248

In this example is the individual primarily using descriptive statistics or inferential statistics.1259

First he is definitely using descriptive statistics in order to organize his classes data.1265

He is using this but then he is comparing it to the test grades that the entire school.1273

He is getting his sample, his class and looking at how they are relative to the entire school.1279

That leap is going to be inferential statistics.1290

I would say he is using both descriptive and inferential.1294

A statistician is interested in the choices of majors of this year’s entering freshmen at a university 10% of randomly sampled.1302

What is the population? what is the sample? What is the parameter? What is the statistic?1311

The population seems to be all freshmen at the University, right? but the sample is this 10%.1317

That is the population and the sample so what is the parameter?1337

The parameter is what are the real major choices of all the students.1342

Maybe he will look at it as you know maybe 50% are engineering and 20% are science and 30% are humanities.1355

Majors picked by freshmen.1374

What is the actual statistic?1383

The statistic that is going to be made up of the majors picked by the sample.1386

In order to go from this to this, you will need to use inferential statistics.1401

Example 4, a group of pediatricians are trying to estimate the rate of increase in obesity in young children in their city.1410

They begin a research project for every four years a group of 8 year-old children are randomly sampled from the city and weighed.1418

What is the population? What is the sample? what is the parameter? what is the statistic?1425

The population looks like young children in the city, whichever city this happens to be.1431

The sample is the group of 8 year-old children, group of selected to be in this study.1446

What is the parameter?1469

The parameter would really be the actual rate of increasing obesity and they do not know what that is, they can not get that data.1474

By looking at the different groups of 8 year-old children every four years they could look at the rate between the samples.1490

The statistic would be the rate among the sample, the samples every four years.1503

In that way they will try to use this rate in order to estimate this rate.1521

That is the end of lesson one for

Thanks so much for watching.1530