## 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
- Roadmap
- Statistics
- Let's Think About High School Science
- Statistics = Math of Distributions
- Statistics
- How is It Different from Other Specializations in Mathematics?
- Statistics is Fundamental in Natural and Social Sciences
- Two Skills of Statistics
- Descriptive Statistics vs. Inferential Statistics: Apply to Distributions
- Populations vs. Samples
- Populations vs. Samples: Is it the Truth?
- Populations vs. Samples: Pros & Cons
- Populations vs. Samples: Descriptive Values
- Putting Together Descriptive/Inferential Stats & Populations/Samples
- Example 1: Descriptive Statistics vs. Inferential Statistics
- Example 2: Descriptive Statistics vs. Inferential Statistics
- Example 3: Sample, Parameter, Population, and Statistic
- Example 4: Sample, Parameter, Population, and Statistic

## Mathematics: General Statistics

## Transcription: Descriptive Statistics vs. Inferential Statistics

*Hi welcome to the first lesson in www.educator.com 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 together *0024

*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 run *0077

*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= Â½ gt ^{2}.*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 them *0138

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

*(g) theoretically is supposed to be 9.8 m/sec ^{2}.*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, Iâ€™m not getting the right answer *0167

*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 experiments *0178

*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 something *0191

*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 bit *0207

*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 messy *0250

*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 values *0330

*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 probabilities *0360

*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

*Iâ€™m a social science professor, a psychology professor by trade but even in the natural sciences all these discoveries that you have heard of *0480

*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 averages *0518

*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 theories *0566

*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 distributions *0715

*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 information *0822

*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 school *0890

*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 governor *1208

*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 yearâ€™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 www.educator.com.*1527

*Thanks so much for watching.*1530

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.

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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

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Post by Daniel Goff on April 18, 2012

great lecture...very informative

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Post by M Holland on December 1, 2010

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

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Post by Abraham Hsu on February 11, 2010

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