Understanding the normal distribution - statistics help

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Dr Nic explains the characteristics of the normal distribution, and why it is so useful as a model for real-life entities.
0:00 Introduction
0:49 How the normal distribution is useful and the features
2:11 defining a normal distribution by the mean and standard deviation
3:14 Example of how multiple chance events lead to a normal distribution
4:47 How to find probabilities based around weights of ice creams
6:32 Why P(X=120) = 0
Understanding the normal distribution leads into understanding the central limit theorem: • The Central Limit Theo...
This video builds on other videos about random variables and distributions:
1. Understanding random variables: • Random Variables and P...
2. Discrete random variables: • Discrete Random Variab...
3. Probability distribution models: • Probability Distributi...
You may also find the following useful
The binomial distribution: • Understanding the Bino...
See creativemaths.net/videos/ for all of Dr Nic's videos organised by topic.
#DrNicStats #Statistics #Probability

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3 июл 2024

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Комментарии : 133

@tonygrant223 4 года назад

You've got a real gift for this. Thank you so much!

@notme7310 6 лет назад

Thank you, thank you, thank you! This was the best explanation I could find on YT for an introduction that is easy to understand :)

@karthikeyannarayanan6744 4 года назад

A simple yet comprehensive and articulate explanation! Wow!

@DrNic 4 года назад

Pleased it hit the spot!

@winstonmisha 5 лет назад

You are excellent at explaining this!

@isaacdengkolnyinmachar344 5 лет назад

Thanks a lot you who have offered to feed us online but am proud for doing bachelor degree of statistics and demography.

@nikki777yo 3 года назад

Thank you so much!! It's amazing how much I can learn when it's presented in a fun format like this. Also, the tapir joke actually made me laugh out loud so thank you for that.

@DrNic 3 года назад

Glad you enjoyed it and that it was helpful. There are many more for your entertainment and edification.

@subramanianchenniappan4059 4 года назад

I am a Java developer trying to learn stats and probability for machine learning. I have good hands-on in maths. Like physics, calculus, algebra and eggs maths. But not stats and probability. Hence seeing all your videos.they are good. Thanks a lot for your effort

@naosarang7265 7 лет назад

i really enjoyed watching your videos i am having a hard time in my statistics class thank you very much

@fifaham 3 года назад

One of the best doctors of the best on RU-vid - thank you for your efforts, Dr. Nic.

@DrNic 3 года назад

So nice of you

@mirceapauca8541 6 лет назад

Congratulations Dr. Nic for a good intro for newcomers! The"Many factors" argument may be qualified: it IS really that (Central Limit Theorem) but it applies only under certain conditions. In lay terms: - the effects of those factors add; (no multiplication, logical AND relationships...) - they are independent; - no one factor dominates the overall variation. There are plenty of unknown distributions in real life where it's VERY dangerous to assume a Normal shaped distribution - as financial and Insurance people found out. Especially if people/agents with opposed interests aim to exploit any holes. For beginners your lessons are great, but as a continuation you may "borrow" more from Nassim Taleb and show: the limitations of the Ludic Fallacy (that we fully know Rules for the Game so can deduce all their consequences); unknown unknowns... and some other cautionary lessons.

@yashgupta1530 5 лет назад

Thanks for such a helpful and nice explanation Probability has never been more fun😀

@ank2790 6 лет назад

Very very........... beautiful Presentation.I loved It . Excellent work

@amirestebari1470 5 лет назад

Very helpful. Thank you so much for this nice video!

@ArghyadeepPal 5 лет назад

Thank u ma'am!! The video was thorough and well-explained. Cleared all my doubts on Normal Distribution.

@DrNic 5 лет назад

Thank you Archyadeep. It is great to hear that my videos are helping you. It is so lovely to read comments like this.

@thlomayi 6 лет назад

Very detailed and helpful thank you very much

@shaileshkatariya2128 7 лет назад

really good ...enjoyed much and also my students.

@susansample4372 7 лет назад

These are great videos.

@muratcan__22 5 лет назад

nice point in getting the normal dist from non-normal!

@azar8538 6 лет назад

Thank you very much.

@nousgj4212 4 года назад

So clearly explained

@risausa4796 4 года назад

Thanks for sharing!

@isharaliyanage2364 5 лет назад

It was very helpful. Thnxx

@paurushgargtube 4 года назад

Awesome.. Best explanations by far

@DrNic 4 года назад

Thank you. I think really hard about explaining and then write scripts to make sure I do it well. It is great that you appreciate it.

@athrashandy7483 3 года назад

wow great work!! now i can finally understand!!! thanks so much

@DrNic 3 года назад

That is so nice to hear.

@mujaffershaikh9973 4 года назад

Fantastic explanation, thanks a lot.

@DrNic 4 года назад

You are welcome!

@AA-fb5fr 5 лет назад

you saved my life :) thank you

@DrNic 5 лет назад

You are most welcome - and not the first I have saved. ;) Tell your friends!

@YoShouresStar811 6 лет назад

Very Well explained. Thank you Dr. Nic.

@corradoblondi9792 3 года назад

Nice and clear!

@DrNic 3 года назад

Thanks!

@gyaneshwarprasad568 6 лет назад

It is probability distribution well explained.

@mariareyes9405 5 лет назад

Thanks, Dr Nic. I have been really struggling on 6th grade statics. Do you think you can make a video bout pie (3.14.....) with diameter and radii? It would REALLY be helpful. My math grade is rlly low but thanks 2 you my grade is going UP! God bless you and ur intelligence

@rudesaint4674 5 лет назад

Great !!

@luclloyd7809 6 лет назад

very nice you give a cocept map and an application. thanks a lot

@jerrysain7880 5 лет назад

I really enjoyed it ,thank you mam

@jerrysain7880 5 лет назад

Mam, your videos are really helpful and inspiring you are really doing a great job for students who struggles to study statistics...hats off

@jiboyoseo 3 года назад

Thank u so much!

@DrNic 3 года назад

You're welcome!

@EngRiadAlmadani 3 года назад

Great work

@DrNic 3 года назад

Thanks

@johnhammer8668 4 года назад

thanks so much

@DrNic 4 года назад

You're welcome!

@prodroma 5 лет назад

THIS CHANNEL IS A HIDDEN TREASURE. I INVITE EVERYONE WHO LIKED THE VIDEO TO SHARE IT TO OTHER SOCIAL NETWORKS. MILLIONS ARE LOOKING FOR THIS.

@DrNic 5 лет назад

Thanks, EMT ADVANCED. You are very kind. I really believe my videos can help people, so it would be wonderful if lots of people share them, subscribe and like them. That helps me to earn a little from them which in turn helps me make more.

@udaybhatnagar18 8 лет назад

How do I measure Consumer Purchase decision (Dependant variable)?

@chessnut9744 3 года назад

Excellent video. Just one thing I'm a bit confused about: why is the probability of an exact value (120 in this case) one over infinity? I get that there is an infinite amount of space from 119.9 to 120.1, but why is it one over infinity at exactly 120, I thought there is not an infinite amount of space at 120? And how does an ice cream being able to way 120g or 120.000001g illustrate that you can't find the probability of a specific point?

@DrNic 3 года назад

Good question. The thing is that it is never exactly 120. Or the probability of its being exactly 120 is one chance in infinity or not going to happen! There is no space at 120. It might read as 120 on a scale, but it is actually 120.000000000200000040000007000003 and so on.

@omarriadh1309 3 года назад

Thank you so much ! its very useful , I'd like to know why it is often preferred in statistical analysis that the data be subject to a normal distribution?

@DrNic 3 года назад

In traditional hypothesis testing we compare what we get from the sample from what we would get using probability distributions and often that assumes that either the values or the residuals are well-approximated by a normal distribution. Often this is valid, thanks to a the phenomenon described by the Central Limit Theorem. You may find this video helpful: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-_YOr_yYPytM.html

@adarshr6403 4 года назад

Hi, in your initial graph about the normal distribution the values in the axis range from negative 4 to positive 4. How is that possible.

@nandananilantha1622 2 года назад

Thanks to teach as eaaily underatand

@DrNic 2 года назад

It's my pleasure

@westla934 4 года назад

I am a math teacher in Los Angeles. I would really like to have access to your other videos. Thanks very much.

@DrNic 4 года назад

If you look at the website you can see all our videos. For access to the others you can become a channel member. creativemaths.net/videos/

@mandeeparora3417 7 лет назад

I really need to know about the other theoretical distributions.I didnt find any nice video of it on the youtube.could u plz help me out with it?.thnx fr this video.

@Rahulyadav-lt9cu 4 года назад

Mam how to use normal distribution table chart?

@minkatimijs8565 Год назад

Thank you. Amazing video. How did you get to the 3% at the end? Could you please elaborate on this? Thank you

@DrNic Год назад

I use Excel and find the p(X> 120.5) - p(X> 119.5) for the normal distribution with mean of 119 and a std deviation of 9. =NORM.DIST(120.5,112,6,TRUE)-NORM.DIST(119.5,112,6,TRUE) and the answer is 0.02736 which I round to 3%.

@Emina1008 8 лет назад

Hello! I find you explanations on medical statistics very usefull. I just started residency in surgery (Nigeria) and wish to be well grounded in medical statistics. How do I go about this

@DrNic 8 лет назад

+Bami Emina Hi. We do have a lot more videos that you can get access to for $25. If you go to course.statslc.com/ and scroll down to Statistics Videos (International), you can find out more about it there. This pdf summarises the content: course.statslc.com/pluginfile.php/28927/mod_resource/content/1/International_Info_2016.pdf

@rupalsharma6049 4 года назад

Hi Dr Nic. Can you help with what does the x-axis represent when you explained about the ice-creams per 2,3 and further customers. Thanks in advance. :)

@DrNic 4 года назад

It is the total number of ice creams ordered by that many customers. If you have two customers, one might buy two ice creams and the other one buys three ice creams. That is a total of five ice creams for the two customers. 3:44 In the simulation about 130 lots of two customers bought a total of five ice creams. Let me know if you need more explanation.

@merahikefyalew6776 2 года назад

I have never seen so engaging video like this and statistician with real knowledge. how on earth can we do same kind of presentations? Dr. Nic or anyone, please help me. waiting....

@DrNic 2 года назад

Glad you liked it. I'm not sure what you are asking.

@merahikefyalew6776 2 года назад

@@DrNic Again thank you for replying. What i wanted to ask was that what kind of software is used to prepare such animated presentation like your. And if u allowed me to ask one more thing, i am not very clear with my inferential statistics lectures. I was wondering if u can make more videos on complex formulas we use in paired t test, z test, chi squared.... or is there any way that we can conceptually understand the formulas for hypothesis testings like one sample t-test, z-test, paired t test, etc which i will also recommend to my friends in Ethiopia? Thanks in advance.

@DrNic 2 года назад

@@merahikefyalew6776 I use Premiere Pro from Adobe Creative Cloud to edit the videos. If you look at our website I think you will find useful videos: creativemaths.net/videos/

@merahikefyalew6776 2 года назад

@@DrNic Thank you for replying doc! I am glad to review your website.

@javedsaifi8871 5 лет назад

Mam, I didn't understand how probability is 9% for less than 100gm? I didn't understand how you calculate that.

@gosiama480 4 года назад

Same me.. ☹️

@jamesacosta6090 3 года назад

Excellent. I really enjoyed this video. Is there another video where we can see the math behind it? thanks!

@DrNic 3 года назад

Glad you liked it. I tend to stick to conceptual explanations as other channels do the mathematical stuff.

@jamesacosta6090 3 года назад

@@DrNic thank you. I have a presentation soon, and this made it so much easier to understand the concept! Have a good one.

@Isurender1966 6 лет назад

Can you please explain what is mean , median, and mode

@DrNic 6 лет назад

Maybe you should watch this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-rAN6DBctgJ0.html

@adarshr6403 4 года назад

Hi, in your graph about the normal distribution the values in the axis range from negative 4 to positive 4 for the sizes of the apples, but how can the size be negative.

@DrNic 4 года назад

The graph that goes from negative 4 to positive four is the standard normal distribution, which shows the number of standard deviations below and above the mean. Let me know if you would like more explanation.

@adarshr6403 4 года назад

@@DrNic got it, thank you taking your time to reply

@gauru2303 6 лет назад

Mam at 3.43, it is difficult to comprehend Distribution of Ice Creams per 2 Customers" graph. Can you please elaborate. Also thank you for your Videos, watching it here from India...Lots of Love

@DrNic 6 лет назад

I can see your confusion. It is a rather odd thing to model, now that I think of it. Say two customers arrived at the same time, independently. What is the most likely number of ice creams that the two of them would buy? As each customer is most likely to buy one or two ice creams, then between the two of them it is most likely that they buy two, three or four ice creams. You can see that in the graph. Let me know if you need more explanation.

@vailaish1 4 года назад

@@DrNic I have the exactly same confusion. Also if two customers would buy close to 200 icecreams, why would 11, 12, 13 customers would buy almost 0 icecreams? Many thanks

@vailaish1 4 года назад

I got that now, probably giving more clarity on X and Y axis description would make this video even more comprehensive. Thanks again.

@DrNic 4 года назад

@@vailaish1 Sometimes struggling a little to understand helps to make it clearer. I'm glad you got there. I will be more careful in my axis labeling in future.

@abhaykumar-tf6gy 6 лет назад

Mam, i couldnt get it how it 3% wii be 120 gm?

@DrNic 6 лет назад

You have to use a calculator or spreadsheet or tables. You want to find P(119.50

@abhaykumar-tf6gy 6 лет назад

Statistics Learning Centre ,thankx a ton mam for replying.

@baradep 5 лет назад

If my coefficient of variation is 86% then what Sigma we should use to smooth the curve.

@DrNic 5 лет назад

Hi Prashant Barade Thanks for your question. I'm not sure what context you are talking about. Can you tell me more about what you are trying to do, and what the curve is.

@baradep 5 лет назад

Curve is normal distribution curve .... I am trying to use mean to standard deviation ratio i.e coefficient of variance to calculate safety stock

@DrNic 5 лет назад

Sorry - this is outside my expertise. I do not understand why you would want to smooth a normal distribution curve, as it is a model, and naturally smooth. Perhaps you are trying to find a better fit for your data than a normal distribution.

@baradep 5 лет назад

Thank you

@ExplaineRKhaN 5 лет назад

which software you use

@DrNic 5 лет назад

In this video I have used Excel. I also use iNZight.

@ExplaineRKhaN 5 лет назад

@@DrNic thank you so much

@VK-sp4gv 2 года назад

I love the brief visual comments. Not that pdf, hahaha.

@DrNic 2 года назад

That's great. I hope they entertain rather than distract.

@GraceCreatesLivingSpace 4 года назад

Where did she get the 9% for the ice creams? It was just look at the graph, bam that looks like 9%, what's the math? Can anyone show the work?

@DrNic 4 года назад

If you mean at 6:13 then you use tables or a calculator or spreadsheet to get 0.091. Then multiply by 100 to get 9%. Then the graph shows that you can see that it is about 9% which is the number you just found out.

@GraceCreatesLivingSpace 4 года назад

Dr Nic's Maths and Stats after more reading i realized this wasn’t a “calculation” we do but some kind of universal chart. I was panicking for a bit. My paper was due tonight. Than you so much for the help!!

@ajaykamath6783 5 лет назад

0:05 warning jumpscare !!!

@DrNic 5 лет назад

Lol - Not THAT scary!

@jakirajam 5 лет назад

in NORMAL distribution left tail and right tail never touch to X axis. please correct it

@DrNic 5 лет назад

Thank you for your concern. It is important in terms of the theoretical normal distribution to be mathematically correct. In practical terms, the area outside the three standard deviations either way is pretty minimal.

@jakirajam 5 лет назад

@@DrNic thanks..for clarification... Any how video is good

@joaodecarvalho7012 4 года назад

Why the customers are so sad?

@DrNic 4 года назад

That is a very good question! Maybe they know they are going to get ice creams in their faces?

@eimyrame 4 года назад

Wao! Go to my college and be my professor. Please

@lizgoldstein4256 4 года назад

I love how all your 'a's are 'e's. I know this has nothing to do with a normal distribution. Maybe among Aussies or Kiwis, though!

@lostforevercici9217 4 года назад

your subtitle is not right please change it soon

@DrNic 4 года назад

Thank you for letting me know. I have done a quick fix and will check again later.

@davidbalakirev5963 3 года назад

Why are these people so sad when they are lining up for ice-cream :)

@DrNic 3 года назад

It’s a very long line.

@corradoblondi9792 3 года назад

One thing doesn't satisfy me: the fact that the probability of having an ice cream that weighs exactly 120g is 0. Mathematically speaking is 0, in reality is low, so low that we can consider it zero, but it's never 0 actually. But maybe that's just a philosophical curiosity.

@DrNic 3 года назад

I agree - it does your head in really. It IS a philosophical thing as we can only ever measure to a finite level of accuracy. However it is important to know as it means that P(x< k) = P(x ≤ k).

@corradoblondi9792 3 года назад

@@DrNic Interesting! Thanks.