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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.
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I'm in grad school and you do a better job at teaching in-depth and letting me understand the problems than my professor. I should've watched your videos instead of their lectures
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!
JG, u are really a great tutor...u have often made my day in mathematics, so precise and concise a tutor! U are wah... To me. I just yearn to look at your JG. U have made me understand calculas and all Probability... Thanks so much for your questions and answers...so much...may the Lord in heavens above award u more and more...
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!! :)
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!
At 42:00, in a Uniform Distribution, In this example, you did not have to calculate the height of the uniform distribution. Since we know that the area of a uniform population distribution is always 1, In this example, the end points of the distribution are a=21 and b=29 You can get the probability of a single snack bar being between 24 and 26 by simply taking (26-24) and dividing it by (B - A) = (26 - 24)/(29 - 21) = 2 / 8 = 0.25 Your method f(x) = 1/8 when 21
you are the BEST!! thank you soo much for helping so many lost students like mee.. I visit your channel whenever i have a problem in understanding the concepts like these.. you make it soo easy.. Bless you..!
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.
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?
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.
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?????
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.
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
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 :)
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
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 ?
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Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: th-cam.com/video/UuHqq09nTAk/w-d-xo.html
Honestly from the bottom of my heart you saved me throughout Middle school, high school and college. Thank you so much. I hope u get rich and nothing bad ever happends to you
YOU DO STATS TOO!! Ive been watching your math videos for years now and recently physics and now I need help with stats and you've got this too 😭😭😭😭 Bless you I swear you're the best!!!! I literally recommend you to all my friends because you're that awesome.
Yeah ikr he even does biology which is great!
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I got help on chemistry too
dont recommend to your friends so you can brag :)
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.
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I'm in grad school and you do a better job at teaching in-depth and letting me understand the problems than my professor. I should've watched your videos instead of their lectures
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!
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JG, u are really a great tutor...u have often made my day in mathematics, so precise and concise a tutor! U are wah... To me. I just yearn to look at your JG. U have made me understand calculas and all Probability... Thanks so much for your questions and answers...so much...may the Lord in heavens above award u more and more...
been watching your videos since high school and I'm in my third year of college now. I freaking love you man.
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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!! :)
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At 42:00, in a Uniform Distribution, In this example, you did not have to calculate the height of the uniform distribution.
Since we know that the area of a uniform population distribution is always 1,
In this example, the end points of the distribution are a=21 and b=29
You can get the probability of a single snack bar being between 24 and 26 by simply taking (26-24) and dividing it by (B - A)
= (26 - 24)/(29 - 21)
= 2 / 8
= 0.25
Your method
f(x) = 1/8 when 21
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you are the BEST!! thank you soo much for helping so many lost students like mee.. I visit your channel whenever i have a problem in understanding the concepts like these.. you make it soo easy.. Bless you..!
Thank you for the help! It was especially helpful to have the time stamps to go where exactly I needed!
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This is the best video for understanding sampling dist.
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Am lost at 34:00 how did you get the Z value
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.
why did you divide by square root of 12 at 37:15?
@11:08 you write n^ the mean of the sampling dist. -> mu are you referring to n here as the number of samples and not the sample size like above?
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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
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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?
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.
Thank you Organic Chemistry Tutor!!
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?????
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.
I cannot thank you enough for this
I’m passing with A- in my statistics class because of you!!!!!!!
What's the difference between sample mean and mean of sample distribution. I don't get it
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
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Pretty clear explanation. Thank you so much!
Hey, quick question here, how does the Z score at 50:58 correspond to .95818?
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GURL why’d at 37:12 he divided by12
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Best Stat teachers !!! Practical example
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 :)
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
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 ?
45:54 shouldnt it be 0.666 plus 0.333 instead of minus?
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22:46 shouldn't it be a instead of x?
yaa you are correct it should be a
at @25:51 is x=65 ?
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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
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