Central Limit Theorem - Sampling Distribution of Sample Means - Stats & Probability

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This statistics video tutorial provides a basic introduction into the central limit theorem. It explains that a sampling distribution of sample means will form the shape of a normal distribution regardless of the shape of the population distribution if a large enough sample is taken from the population.
Introduction to Statistics:
• Introduction to Statis...
Introduction to Probability:
• Introduction to Probab...
Central Limit Theorem:
• Central Limit Theorem ...
Standard Error of The Mean:
• Standard Error of the ...
_____________________________________
Confidence Intervals & Margin of Error:
• How To Find The Z Scor...
Find The Z-Score Given Confidence Interval:
• How To Find The Z Scor...
How To Calculate The Sample Size:
• How To Calculate The S...
Student's T-Distribution:
• Student's T Distributi...
Confidence Interval-Population Proportion:
• Finding The Confidence...
Chebyshev's Theorem:
• Chebyshev's Theorem
_____________________________________
Hypothesis Testing - Null & Alternative:
• Hypothesis Testing - N...
Type I and Type II Errors:
• How To Identify Type I...
One Tailed and Two Tailed Tests:
• One Tailed and Two Tai...
Test Static For Means & Pop Proportions:
• Test Statistic For Mea...
Hypothesis Testing Problems:
• Hypothesis Testing Pro...
____________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

Опубликовано:

2 окт 2024

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Комментарии : 220

@TheOrganicChemistryTutor Год назад

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-UuHqq09nTAk.html

@m_abou 4 года назад

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@kevinkrzywulak8590 6 месяцев назад

This is ungodly complicated

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@clips.man356 4 месяца назад

00:02 Central Limit Theorem: Sampling distribution approximates a normal distribution. 03:05 Sampling distribution of sample means approximates a normal distribution. 09:49 The law of large numbers states that as the sample size increases, the mean of the sample gets closer to the population mean. 12:47 Increasing sample size decreases standard error 18:59 Understanding cumulative distribution function and probability calculations 21:52 Sampling distribution adds a standard deviation element and changes the mean notation. 28:01 Calculating probability for mean greater than 75 31:09 Understanding the distribution of mean exam scores for 50 students 36:57 Distribution for the mean of a hundred snackbars 39:47 Understanding population and sampling distributions in statistics. 46:24 Sampling distribution of sums in a normal distribution 49:32 Understanding the sampling distribution of sample means 56:00 Calculating the first and third quartiles using the Central Limit Theorem 59:08 Understanding the central limit theorem and solving associated problems.

@shahzodamirov3762 2 года назад

Very good explained about how to use CLT for solving problem examples, thanks a lot !

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@Celeste21yt 3 года назад

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@dilinijayasinghe8134 6 месяцев назад

Thank you so much. Your video helped to clarify something which bothered me a lot. Many thanks!!!

@Elite.79 6 месяцев назад

GURL why’d at 37:12 he divided by12

@emilyb9222 3 года назад

Love your videos! I watch them for chem and stats. You do such a great job explaining the how, the why, and providing helpful examples.

@matt_fs 2 года назад

All the great information you covered in this video, took 3 classes (3 hours each) to cover all this material and examples in my university statistics class a few semesters ago. Amazing compiled content here!

@racheltham8002 4 года назад

Thank you so much! This video really helped me clearly understand the Central Limit Theorem, especially with the practice examples. Keep up the wonderful work!! :)

@nanayu8040 2 года назад

Thank you for your explanations! very detailed. easy to und too!

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@jaypham3371 4 года назад

Best Stat teachers !!! Practical example

@benjaminchirwa5445 3 года назад

Am lost at 34:00 how did you get the Z value

@sudeshdugast4302 5 месяцев назад

I had this exact same question. So if you go to your normal distribution table there are values on the top and left edges. 0.0 all the way to 3.0 on the left and 0.00 all the way to 0.09 on the top. If we focus on the values populating the inside of the table for a moment it goes from 0.5000 to 0.9990 and its in this range that you look for the 0.80. So find the closest value within the tables to that 0.8. There is 0.7967 then 0.7995 then 0.8023 and so on. As he pointed out in the video 0.7995 is the closest in the tables to our 0.8 and if we find the corresponding values on the left and top of the tables we'll see that 0.7995 is on the 0.8 horizontal and 0.04 vertical so the final takeaway value is 0.84. Apologies for the clunky explanation but I hope this helps. Best of luck.

@roberte.6892 4 года назад

I feel like this is a good video, but a rare miss. You're pulling formulas from the ether a little too quick. At 43:30, why is the mean 25? Are you averaging the 24.9 and the 25.1? Where do you get Standard Dev = 2.3094 from? Wasn't that from a uniform distribution formula?? (b-a / square root of 12?) But in part D there are 100 snack bars, so that isn't a uniform distribution, right? At around 49:00 what is going on with these "sum of" formulas? Where are they coming from? Where are you getting their values from?????

@alephkasai9384 2 года назад

The mean is 25 because when N is equal or more than 30 the mean of the sampling distribution is the same as the population distribution. Standard deviation is 2.3094/sqrt(n). Aka 0.23094. You can see he already inputted it in but he simply didn't show the step to actually calculate the standard deviation of the sampling distribution. And yeah the sums thing I'm guessing he forgot to show earlier on in the vid. Technically the questions like those are rare, I've never seen one myself in fact, but you can find the equations he uses elsewhere.

@aradarbel4579 5 лет назад

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I was studying this now as well!!!

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man carried through my whole undergrad

@ComplexOri 2 года назад

Thank you for the help! It was especially helpful to have the time stamps to go where exactly I needed!

@amrhelmy5795 2 года назад

Thanks alot, your video was so helpful, you always clarify my doubts, I just wanted to ask, why in 57:06 we should use the (-z) table for 0.25, arent we supposed to use the positive one?

@AkshatJha Год назад

I think what he meant was that you just look up the standard normal distribution table, and find the Z value(Which in this case will be negative) for probability value=0.25. The Z value as per the table comes to -0.675.

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@alexandrawalker2469 9 месяцев назад

Thank you for the video

@eadvm 4 года назад

minute 21:05: you call mu xbar the stdev of sample means but in another video you named it mean of sampling distribution? May you clarify? I appreciate your videos. They are wonderful to work through and you excel at teaching :)

@Sk8erMorris 4 года назад

it's practically the same thing tho, mean st.d of sample is the same as mean of sampling distribution, the key term here is "Sampling mean" which is different from normal mean if n isn't large enough .. if it is then mean will be the same for sampling data and for normal data

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@odaigassan5330 2 года назад

Anybody else is annoyed that every time you want to like the video then find out that you already did

@laurenorourke2442 Год назад

thank you so much for this! my whole stats class was confused when we learned this today, and I understand this way more than when my professor taught it!

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@veronika4307 5 месяцев назад

why did you divide by square root of 12 at 37:15?

@shrutimankotia8537 4 года назад

List the conditions necessary for the CLT to hold. Make sure to list alternative conditions for when we know the population distribution is normal vs. when we don’t know what the population distribution is, and the when the sample size is barely over 30 vs. when it’s very large

@light006bs2 5 лет назад

Your videos are the best

@calebkayyeboah893 6 месяцев назад

At 21:03, did you intend to say the mean of the sampling distribution or the standard dev of the sample mean? I'm a lil confused here

@kwenakomape1545 5 лет назад

can you upload hypothesis testing(Stats)...im writing this friday

@ОйдинИногамова 3 года назад

thank you so much!

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@michaelw6902 3 года назад

The answer to Question 1 (d) seems too small. Mike

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you've been helping me for almost 2 years now

@ibrahimjklahai3781 3 года назад

Please help me to solve this problem "(a)The masses of certain pharmaceutical have a mean value of 4 g with a standard deviation of 0.2 g. Assuming that the masses are normally distributed and a pharmaceutical is chosen at random, what is the probability that (i) it has a mass between 3.55 and 3.85 (ii) differs from the average by less than 0.35 g (b) If 1000 of the pharmaceutical from (a) above are taken, how many may be expected to weigh more than 3.7 g?"

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@p2p2p2p2p2p 3 года назад

can you please make a stats final review?

@subarnasubedi7938 Год назад

We dont know what the population is then how can you have value of meu and standard deviation i thought that we take samples and estimate population mean

@rubytrinity8187 3 года назад

And im here right before an exam to catch up! Thank you!

@whit9250 Год назад

You ask a baby, who is less than a year old, their age... Lol

@auntorhossain7145 3 года назад

At 10:19 you said " if you ask a baby who's like less than 1 year old it's going to affect the average big time". Now the question is HOW TO ASK A 1 YEAR OLD BABY ABOUT HIS AGE?????? please help!!!!!

@laxminiharika4116 2 года назад

At 46.50, isn't standard deviation for n = sqrt(n)* standard deviation for 1?

@TossiCS Год назад

45:54 shouldnt it be 0.666 plus 0.333 instead of minus?

@TheUsworldwide 2 года назад

HACK: Open another youtube tab and play some Bach or Beethoven or Mozart softly in the background while you watch this. It becomes a movie!

@slimeminem7402 Год назад

10:19 Me: Hey how old are you? Baby: gougougaga Me: Wait, that's an illegal move

@reamabdulsalam524 Год назад

Here I have a question if we do know the population mean from the beginning and we are taking samples from the population how do you know that these sampling mean or the results are equal to the population mean ? If we take n more than or equal 30 ? This question in my head for long time

@ama19128 11 месяцев назад

Can you explain the Simpson Paradox theorem for me l need your explanation because all your videos are easy to understand

@odaigassan5330 2 года назад

Anybody else is annoyed that every time you want to like the video then finding out that you already did

@y.x3476 3 года назад

Thanks a lot ! You always give amazing valuable class ！！

@kingpook3053 4 года назад

literally has 0 dislikes, and that's for a reason

@destroyriri 3 года назад

It has 15 now sad bro

@sherkhan2416 4 года назад

Man I really hope you get millions of subscribers

@benson4225721 4 года назад

Pretty clear explanation. Thank you so much!

@saraazzinnari5359 Год назад

Why can't the base be 23 and 27 ? Then the height would be 3 times 1/8 ?

@Lexyvil 2 года назад

So a Gaussian distribution is also called the Normal distribution? It makes so much sense now.

@rspmusic796 3 года назад

I am confused why the denominator of Standard error of Sampling distribution has √n. As per what I understood n is the size of a single sample whereas SE of Sampling distribution should have the number of such samples taken. Can you/anyone explain ?

@boyifudont Год назад

i can't believe i wasn't subscribed i'm such a fake fan omg

@CebolenkhosiTsabedze 10 месяцев назад

The 🐐

@reamabdulsalam524 Год назад

Hi you always ease the problems and describe the example and solve it in logical way , but every time I go and answer the question my tutor at uni gives she said wrong !!!!you said when the sample is large enough more than 30 we can use the normal distribution to calculate our problem like CI confidence level or hypothesis tests but I have surprised when my tutor gave an example with a n=120 and she said that I have compute the mean wrong I should not use the normal distribution or Z table she said I should use t table !!!! And in stat that is confusing me and make me loosing conference in any solution I made and that is made me also hate statistic because every time they use different way and every time they are saying something opposite I have exam after tomorrow and I don’t think that I can pass !!!!!

@rodelgabriel7248 Год назад

Hi I am a bit confused in example 1 and 2 when the value of N = 1. I thought population is bigger than the sample. How can we get 1 as our population.. Thanks...

@omartrkzi 2 года назад

You know Sir, @ 14:35 I felt like RU-vid was *literally waiting* for you to draw the graph for n=100 to get you a censorship 😭🤣😭 .

@penumbraproductions7516 Год назад

Hey, quick question here, how does the Z score at 50:58 correspond to .95818?

@boyinalabcoatboyinalabcoat393 3 года назад

jesus dude, what fuck is wrong with my teacher?

@halofanaticboy 2 года назад

for 1a. we don't use divided by sqrt(n), but for 1b, we use it. Why is that? Because of the large sample size?

@ym3816 2 года назад

HOW MANY CLASSES CAN YOU TUTOR! MY WIFE IS DOING NURSING; SHE WATCHES YOUR VIDEOS. I DO ENGINEERING; I ALSO WATCH YOUR VIDEOS FOR MULTIPLE CLASSES. THANKS A LOT FOR YOUR SERVICE

@jokatech Год назад

There is some law in college against stating things plainly or even truthfully at times. Some of these formulas were not stated plainly at all in my textbook or by the professor.

@carllawrencesaycon5769 3 года назад

ladies and gentlemen my brain just commited suicide

@reamabdulsalam524 Год назад

Can you please post a video of approximating Binomial distribution to normal ? I have exam and o could not understand my tutor she confuse us of many unnecessary notations