Statistics 101: Sample Mean Proximity to Population Mean
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- Опубликовано: 8 авг 2024
- Statistics 101: Sample Mean Proximity to Population Mean.
How close is our sample mean to the actual population mean? How does sample size influence the approximation? In this video we inch towards confidence intervals by looking at how the standard error of the mean influences the sample distribution. We then compare several different sample sizes to see how each size influences the probability that our sample mean is within a certain distance of the population mean. Enjoy!
My playlist table of contents, Video Companion Guide PDF documents, and file downloads can be found on my website: www.bcfoltz.com
You literally just saved my academic life.
Not only did you simplify these concepts, you delivered the information with a moderately comical tone (a refreshing change from previous profs) and your encouraging pep-talks are genuinely assuring.
Kudos!
Please never stop with these series... Thank you so much from Italy, making the most of quarantine with those playlists..
At 25:25 the cumulative probability up to 3215 is .6508 and the cumulative probability up to 3185 is .3492. Therefore the probability in between is .6508-.3492 = .3016. I just rounded it to .302. Remember the probability will always be positive: upper boundary - lower boundary (in this case). Hope that helps! - B
Thank you Sir!
Oh my thank you so much for your very kind comments!!! So glad you find them helpful You are right however that I need to organize them better. I never imagined my channel would take off like it has so I never really set up a category scheme. And I skip around topics. But I am working on it! Best of luck in all things. - B
Thanks for the videos. They are wonderful.
Suggestion: In a couple of videos I have watched you refer back to earlier videos generically. It would be very helpful to try and use the video names when you do that for learners that are using your videos to fill in some gaps.
These videos have been so very helpful in my studies. You are an excellent teacher. I wish I would have found your videos first.
i have never been more interested in learning... im amazed by what a good teacher can do. Thank you so much!
This is one of the most substantive and elucidating statistics video I've seen. I wish I saw it 45 years ago when I was doing my statistics degree course.
Really love your videos. They are the best statistics videos Ive seen around and they are really helping me out in my classes. Thanks so much!!
Brendan, I can't thank you enough (though I don't wanna rush about it as I have so many other topics to cover)....I just couldn't resist it....You're amazing....Thank you so much....my gratitudes are with you and I literally bow before your teaching...Again thank you so much :)
Hi Zoraida! It is in Playlist #7 (PL07) on my channel.
Statistics PL07 - Sampling and Sampling Distributions
And thank you for your very kind comment. :) I am glad to know you find them helpful. Keep learning! - B
Hi Zoraida! You can learn how to find cumulative probabilities in my video: Statistics 101: A Tour of the Normal Distribution. You can find that video in my playlist #6: Continuous Probability Distributions. It is the 2nd video. Let me know if you have any problems finding it. Take care! - B
Thank you for the motivation at the beginning of the video. Very helpful.
Hello! All of my videos are ordered sequentially by playlist and then inside each playlist by topic. The easiest way to find that is to 1) go to my main channel page, 2) under my name click "Videos" and then 3) change the "Uploads" drop-down box to "Playlists". You will find everything there. Let me know if you have any problems! - B
Hello! Grrr...I feel frustrated that navigating my videos is causing problems. :((( I am not sure what else I can do. All my stats videos are organized by 1) playlist and then 2) internally by topic sequence. Do you all have any suggestions? I really do want to make my videos/channel as easy to use as possible. Thanks! - B
I am studying from your videos now when our uni closed a few days ago due to the coronavirus outbreak and it helps me very much to understand the material we are covering this semester (without teachers). Thank you!
You rock! This series is rigorous and complete! Thank you for having made this
Please give him a thumbs up or comment if he helped you like he helped me. I see constructive criticism saying he repeats information from previous videos, it can be redundant but it can also cement your learning. I like to watch those parts at 1.25x speed to refresh myself and watch the rest of the video at normal speed. THANK YOU BRANDON
Can't thank you enough in words Brandon, you made statistics very simple, stay blessed!!
You're explanations are crystal clear. You can really teach Stats!! I have watched so many of your videos. Thank you for your hard work. The production of these videos are expert.
Extremely helpful. I learn fro you more than I do my instructor! Thanks a lot.
The example is measuring the viscosity or flow of asphalt. I went over the problem more in depth in the videos leading up to this one. However 3200 is in the units of viscosity. It is a unit of measurement like any other.
Krttersnortyt, I agree with you. Numbering the videos would be of great help. Brandon's voice is calming. The slow pace is even better, even though I stop and write down the main ideas. I still can't find the numbering.
Brandon Fulton. You are a superb teacher. Thank you. Hope you continue to provide these instructional videos on more and more topics: all of statistics. Thank you so much.
Brandon Foltz thank you.
awesome videos, I must say! thanks Brandon for all the hardwork and great tutorials. These days, I watch your tutorials videos on desktop, mobile, ipad etc.
Thanks Brandon. Excellent Lecture
every vedio you made is quite helpful. I like all of them. Tanks for your vedios
Awesome! Great talk about statistics which help me a lot. Thanks
Sigma is the symbol for population standard deviation, true. But also remember that the sampling distribution itself ALSO has a standard deviation. That is why it is sigma-sub-x-bar. So one is applicable to the population itself and the other is for the sampling distribution. I cover this in my video on sampling distributions as well.
Thanks for the videos! You do a great job at explaining!
Yes you are on the right path. Sample Mean Proximity to Population Mean is the first video in playlist #8 (PL08) on Interval Estimation. Are you able to find the playlists section on my channel page? There should be "Playlists" section in the upper left. Let me know if you have any problems finding it. Thanks again! - B
Hi Brandon, It would be nice if you could please make a video on difference between Arithmetic mean -Harmonic mean and Geometric mean. And when should we use what. I have been a long time follower of your videos and they are amazing!
Thanks for your help!
I only ask when you say "they are in my previous or other videos" can you please reference PL#? I have watched several and I am lost on where these other videos are? Thanks...I still like your teaching style though.
Thank you so much! very helpful!
It's great that this information was here 10 years ago! 🤪. I seemed to feel every decibel that was rising, too close! 😂 Now that it seems that I have learned to differentiate the Quantum states of Man, I will be able to continue with this. 😁
11 years*
Brandon, a few comments. First, great videos. They help me to understand statistics much better. One suggestion. Use more graphics to explain your ideas. "A picture paints a thousand words."
Thank you!
Amazing lecture as always. I have one question though. When we talk about the sample size, are we talking about samples we take from the population that have the same size? or are we talking about the numbers of means we have? or do they have to be equal? Because I've been doing some simulations in excel using macros, and I've noticed that the only time I get a normal distribution around the population mean is when the sample size is closer to the sampling size, meaning that we take 10 samples each one of them has 10 data points in it. A further clarification would be very appreciated. Keep up the good work, and thank you so much.
Great video sir
I loved your video lessons. Honestly, I am struggling so badly in class. I'm a PhD student and before I even begin my research I've got to understand quantitative analysis and I feel like an utter dud who simply doesn't get it (given that I've gotten admission into a top university in Europe for a prestigious program that had very competitive admission requirements, I'd like to think I am actually smart). I'd really appreciate it if your videos were ordered/arranged so that a person like me could decide where I'd like to start from. As it stands I watched this one (Statistics 101: Sample Mean Proximity to Population Mean) and I totally "got" it but you keep referring to "in the previous video I've explained how..." and I can't for the life of me figure out which is the previous video. Do you have a list somewhere even if you can't rearrange these videos.
Many many thanks for your wonderful lessons - so lucidly and clearly explained.
Fantastic video
These are really amazing videos. Does anyone have any idea that how he calculated the probabilities of .302, .755 and .975? Or if someone has any idea of PREVIOUS VIDEOS to find these calculation of probabilities?
Thank you so so much
Great job with the videos. I have a question that’s been bothering me and don’t know where to look.
In this video it seems you looked at each sample (With n changing 15, 150;500) and showed how close each sample is to population mean for a given interval.
What about a sampling distribution and not just single sample which can take many samples (random variables)ranging from 1 to infinity. How do we measure how accurate the mean of sampling distribution is to the real population mean. The videos I have gone through state the expected value of sampling distribution is the mean of population, but sampling distribution can consist of variable amount of samples ranging from 1 to infinity.
awesome ...great
suresh kumar Thank you for your comment and for watching suresh! Best, B.
Thank you Brandon. As always your explanations are superb. I will always remember sigma-sub-x-bar. Thanks.
Could you please provide the video link on finding probability of regions of a normal curve using calculators?
Hi Brandn, these are really great lectures. can you please upload more videos on other topics in statistics?
+לירן זיידמן What did you have in mind? I have many videos on stats in other playlists.
Thanks
thank you very much
He is the dude!
+professorschuler my sentiments exactly
thank you ...
Love you videos. What is the next video after Point Estimator? I am trying to follow you in sequence.
what should be the ideal bucket size for the distribution of sample means?
At 23:20 he talks about referingg to some videos which talk about finding the probability that our sample mean is within a region. What video can i refer for that? I dont want to watch ALL the previous videos
thank you
HI Brandon, This is Rameez from India. I have been bitten by Data Science bug and have been trying hard to learn statistics to strengthen the foundation of data science. I have found your videos very interesting since it explain from the beginner's point of view. I have also come across your shorts video with R language. Since I am using python as my language of preference for learning data science and I believe there are many more like me, I think it will be more interesting if you could post videos on applying statistical concepts using python. Just wanted to know if there any chances of posting videos in python using data science tools
Thank you for your comment. I have so many ideas for videos, including those you mentioned, but there is so little time. But I will do my best.
Great Videos; Certainly a big help so far. And I apologize if this question has been answered previously...
When calculating the probability of the range (approx. min 25) what mean are you using - the desired population parameter of 3200? Or the sampling statistic (from previous video) of 3217? (Since the SEM is used, it would make sense to use the sampling statistic rather than the parameter, but I've tried calculating with a z score and table using both means and using standard error 38.7 have come up with .296 & .35 respectively. Obviously I'm missing something since you have .302 in the video. Also, the slide is labeled sampling distribution of x, but the distribution has the population mean at z=0. This seems to be misleading.
Hi sir, I really enjoyed the video and learnt a lot , can you pls share the slides
Great videos.I would like to ask a question about some of the methodology of Presidential polls. I noticed that when I read the actual sample size ,most seem too small (for example1000 or less) to be accurate. Also most polls like Rasmussen Monmouth Quinnipiac are weighing the data. What does a statement like the following actually mean and what impact does it have on the results?"After the surveys are completed, the raw data is processed through a weighting program to ensure that the sample reflects the overall population in terms of age, race, gender, political party, and other factors."Most are using population as defined by census not registered voters. Does anyone know what the formula is that they are using to weigh the data or where to find it? Does this process potentially make the sampling error greater for example in a year like 2016 where we have 4 candidates and people may not be voting across party lines?
Brendan, If time permits, can you please do a video on Factor analysis and principal component analysis?...If time permits...please..
Which video is related to 25:00? Where can I see how to calculate this?
Hi Brandon. I have been watching and studying your videos a lot, thanks. Here you talked about the effect of sample size which is bigger the sample size smaller the std error, got it. But what is the effect on the number of samples here? 9 sets of 15 samples= 135 observations in total. Why wouldn't I reduce the sets in order to enlarge the sample size say 5 sets of 27 samples or even 1 set of 135. which I think might change the sample mean but will give a narrower standard error. Is there any rules around number of samples vs the size of them? Thanks!
I had the same question.
thank you for the wonderful videos! pardon my stupidity, but why is the standard error of the mean equal to the standard deviation of the sampling distribution?
Hi Brandon, thanks for the great video. I have one query though. At one place it is said to use z-distribution if we know population standard deviation and t-distribution when not known. However, as per the Central Limit Theorem, the shape of any sample distribution will be a normal distribution irrespective of the shape of the population distribution. So, shouldn't we always use z-score to calculate the sample mean proximity to population mean as shown in the video in all scenarios, i.e., whether we know sigma or not?
My understanding is that knowing population standard deviation will only help with calculating the standard deviation of the sampling distributions with different 'n' values, that's all
What is the effect of changing the number of samples taken? Let's say if we took 100 samples of 15 specimens instead of taking 9 samples of 15 specimens? Also, what would happen if instead of taking many samples of a small number of specimens, we took a few samples of a large number of specimens - like 3 samples of 100 specimens?
Brandon
how do we know what is the reasonable sample size to use for each n?
Thank you very much for your great work! Can you please how did you get the probabilities in this video? I mean .975 probability ?
There should be a video on how to do that, it's some video in the series about z score
Is this playlist should be the second playlist?
which previous video were you referring to???
I found the next video by mistake as I do not see PL#7. Listening to Sample Mean Proximity to Population Mean right now. My lesson is on confidence intervals. Am I following the right path?
I don't know if I am missed the point where it is explained, but wasn't the original question if the sample of size 15 is sufficient to estimate the viscosity? It was answered YES but the only thing stated is, that error decreases with a larger number of samples. As I understand it, the probability of 30 percent for the sample mean to lay within the interval is pretty poor. Therefore I am struggling to understand why it was stated in the beginning that it would be sufficient.
A larger sample size reduces the SEM up to the point - We will talk about it in later videos. Please tell me which video is it? THank you
What is intution of central limit theorem when it comes to regression ang hypothesis testing??
So we calculate standard error from one sample but that standard error is of the whole sampling distribution I.e a distribution of all sample means ??
I think I am missing something. Can you direct me to a video on how to find the cumulative probability up to a certain number or are you using a chart? Is this the video on the region that you mentioned?
Brandon how did you get to .302 in your sample mean proximity video? I tried 3185 - 3215 and that gave me -.30.
Hi Brandon. I have question about the data at 19:54. Shouldn't there be a sample rather than population mean at z=0. At previous slides it is said that 3200 is our population mean, but formula x_bar +/- 3 sigma(x_bar) suggests that the sample is actually at the center, not population mean
Great videos. My only criticism is how often you repeat yourself, or say the same thing 5 different ways. Forces me to watch at 1.5x speed most of the time. At least for me, the repetitions are more of a distraction not a positive.
For people like me who are new to stats, this is very much required. If anything the few times where he doesn't rephrase things can confuse me
@brandonfoltz Please don't stop repeating things. Its very helpful for people learning this stuff for the first time. Its better to have some people need to watch on 1.5x than to have a huge chunk of people struggling to keep up and getting further demotivated to study this subject.
How did you find out that the probability mean for n=135 within 15 is having population mean of .755? How did you calculate .755?
Hi Brandon is this the explanation for central limit theorem? Am im correct?
What videos teaches: "How to find probabilities of the regions on the normal curve." ?
Hi I wonder If you can tell me why the standard error of the mean is always smaller than the standard deviation of the population.
I would appreciate it if you can answer that,
thanks,
Jacob
Hi Brandon: Question: Sigma is the standard deviation of the population, but earlier you mentioned that it was the standard deviation of the sample distribution. Confused.
so the intervals?
At 17:58 he said 3167.3 instead of 3161.3, right?
Brandon, is it a true statement to say that all confidence interval and hypothesis test operations are conducted in reference to the sampling distribution, as opposed to either the sample or population distribution?
Hello! Well, that is a very hard statement to unpack and make sense of mainly because of the ambiguity of "in reference to." The truth is that they are all related. Confidence intervals depend on the sampling distribution which is related to sample size. All sample statistics are done in reference to the populations they seek to estimate and that of course ties into hypothesis tests which are often stated using population parameters. So the way it is worded, it is very difficult to answer.
***** Sorry, it looks like I was being too vague. But for example in this video when you were establishing interval estimations for various sample sizes, the distribution on the screen which you were making the measurements on was always the sampling distribution. It seems like in general we pull some information from a given sample distribution in order to "build" the sampling distribution, then perform operations on the sampling distribution in order to make inferences about the population.
So whenever I see a confidence interval or a hypothesis test results in ANOVA, regression, or anywhere else, can I assume that the sampling distribution was invoked in the same general role as I described above?
If it's still not clear I'll drop it, and assume I'm going down a rabbit hole :0)
The sampling distribution is at the heart of all confidence intervals since all samples of the same size will have the same standard error. That in turn sets the confidence interval for our estimation of the population parameter (that is why larger samples sizes, up to a point, generate a "better" i.e. narrower confidence interval; the larger sample is more representative of the population. So the sampling distribution is invoked inasmuch as it is related to the sample size leading to a better approximation of the underlying population. That help at all? LOL :)
Why did we take 3200 as the mean and not the x (bar) like 3217?
Brandon, in this video you ask "what is the probability that the sample mean is within 15 of the population mean of 3200." What does 15 represent? Within 15 what? 15 samples?
Why you use 3200 as center point. It should be average of means of each sample?
Who is the best ? Brandon!
Sigma-sub-x-bar goes by another name: the standard error of the mean.
First of all, I have to say You are an amazing tutor!
BUT when it comest to probability calculation of regions, You decide to not show it, however there is load of info that you repeat throughout all videos.
Im trying to figure out this problem for ages! :( please show how you got 0.3 % when the sample is 15.
+Linda Elena Zālīte i also have some difficulties. Under the norm.dist function in excel 2013 i get the following awnser: P(3185
+Tim van Wessel You used the population standard deviation in your calculation, instead of the standard error (which is the mean of the sample distribution). Since you are evaluating sample means, it doesn't make sense to use the population SD (like Brandon has previously mentioned, they measure two different things). Hope this helps!
Have you ever thought of making a book?