Statistics: Sample vs. Population Mean

The difference between the mean of a sample and the mean of a population.

[@mukulzaheer3304]

Thank you very much.learning statistic was my dream. At the age of 65 I joined a school to learn statistics but was really disappointed.no one had the patience to teach an old lady. Then I found your tutorials. Good bless you my dear. Thank you once again.

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I am 52 Zimbabwe

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I just wanted to thank you for all these videos. My professor mumbles, barely explains anything and never shows any work and often confuses himself. Myself and a few classmates are trying to teach ourselves, more or less, statistics to keep up. These videos are a godsend. Thank you.

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I agree my professor is an older gentlemen and he told us he does not lecture or basically teach. These videos are very helpful.

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I have a very cool professor and he explains very well, plus sends us emails with PDFs containing the courses. Yet these videos still help me very much, because you can rewatch them anytime you feel the need to whilst you can't do that with your professor.

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Benjamin Wilde , could you please send those PDF files ?

[@benjaminwilde152]

Alina Kvon I am from Romania and the PDFs are in my language. Sorry..

[@joefann227]

just learned more in 6 minutes than i did in my whole 3 hour lecture. Thanks a ton!

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kmsl

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My lecturer spent two hours going on about this and I had no idea what she was withering on about. You explained it in six and a half minutes. God bless you sir!

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[@nastenkaoo]

yeah

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Khan Academy delivers concepts crisp and clear.

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i like your explanations. u are a bit repeating and sligthly unorganised but very human. i finished the online dutch statistic course that is intensive and they speak with having the scenario on the backround so they don't repeat themselves. but your way makes me much more relax, like speaking to a friend over a cup of coffee while he is trying to explain me the homework

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Thank you for explaining how come the formulas are written the way they are. Usually, it’s not explained by others. I love your series.

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Refreshing my STATS knowledge after being out of high school for awhile -- these videos are perfect. Thank you!

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There is nothing wrong with schools making money but the reason why they cost so much is because the government backs them with various loan programs that neither the school nor the government ends up being liable for. College in the 1950s would cost about $800 per year and that would be for room and board. Now taking the worst case of inflation of 4% that means today it should cost around $8000. But since inflation is only 2.5% historically it should really cost $3500 today.

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So much better than school I don't understand why they confuse us with nonsense in public education

[@Traveler216]

Thank you for this wonderful, easy to understand explanation. I am in a class where the instructor cannot seem to get this concept and information across as simply and wonderfully as you have done. I was hung up on the equation and now I understand it! Thank you!

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Kahn... May the math gods bless you

[@themooseyoyos]

*Khan

[@mmftw]

Sal*

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I'm basically studying data science on my own. Thank you. These are great videos, specially the real life examples.

[@AWSKAR]

I'm taking this class as a winter course, and listening to these while playing world of warcraft is giving me a great idea of what to expect.

[@PraveenKambhampatiMyVideos]

One of the best presentations i have seen on Statistics !! Clear explanation and awesome examples !! Too Good!! Many thanks !! Much Appreciated !!

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I love you man. I was almost asking for privet tutor who charge me $ 70 per hour to explain what you've done but now I am so happy as I got the idea. Thankssss a lot

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I don't understand how my professor can take simple concepts, such as these, and make them so incredibly confusing. Thank you Khan Academy!

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I've literally never taken a statistics course before and I'm in my senior year of undergrad studying quantum mechanics now of which it is very much built upon statistics. Great!

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Ta for putting this online. I had no problems at all to stay concentrated and interested while watching your vids. A+ for online teaching.

[@V.Hansen.]

Yay! My first fancy symbol. This all makes sense and is interesting. I'm ready to not be afraid of math any more.

[@izabelaedmunds9746]

"Khan" maybe you can add a notation underneath the video to watch the next video with the correct formulas? Many thanks for the video and I love what are you doing "Khan Academy" :-)

[@meterotronic]

Sal, i congratulate u on all of ur accomplishments, i wish i was more like you, I must thank you for coaching me through pre-cal, cal, and now... statistics...i am on the way of obtaining my bachelors in Mathematics and i owe it all to u. My path to my masters will include you and i will keep u posted as i near my destined origing. -Namaste-

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You make things so easy !! ... thank you

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Yep, I needed that clarification!

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I just graduated from high school, and I must agree with you. The majority of my classes have tried to teach information rather than understanding, and that is a VERY serious flaw. High school shouldn't put someone in a position to perform, but rather in a position to both innovate and understand the world around them.

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You voice serenades me while teaching me stuff that my stupid teachers cannot.

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I love professors that makes math understandable..it does not have to be as hard as some professors make it!! thanx!!

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Thanks God you exist!!!!! You are doing a really important thing here. Thank you so much. Now I undertsnad that I'm not dumb , I just had really bad teachers before

[@bshmoove08]

Thanks ALOT!! Taking stats this summer and I was very intimidated after looking over the formula sheet for the first exam. Almost dropped the course lol. Keep it up!

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Thank u so much for this information and special thanx for differentiating between "mu" and "X bar "😊 I dream of u as my maths teacher 😅😄

[@rivariad]

aaah, hearing those things with a proper english felt like heaven, got it immediately

[@kathyho8927]

thanks man, this has been a confusing topic for me but now it is all fixed

[@sukimusk675]

this is very very good! If I have a prof. like this, stat. would be fun to learn.

[@Susyw123]

Great I wish i had a math teacher like you

[@ghostrideralex11]

i like how you use random situations

[@AmokBR]

Great series of lectures. Just want to point out that when you write the expression for the sample mean it's not correct and, more importangly, confusing to use small n for both the index of the summation and it's upper bound. Cheers.

[@mallubhai0MBBS]

YOU ARE AWESOME!!!! ONE OF THE BEST TEACHERS!!! Sorry for shouting...I was too excited....

[@camobanana1]

This helped so much! Thank you!

[@ameenalgamal.9741]

Countless thanks for all the videos

[@gianglearning3509]

This is a great video, you explained clearly. Thank you.

[@divyas4411]

Thank you so much for these videos ❤

[@kartofobelachka]

There is something I don't understand. When we are talking of the mean of a sample, we use x1, x2, x3.... as real numbers. But they are formally random variables (or even variates). That sais, they are not real numbers, but functions. And if you think of the domain of those functions? There might be some explanations there. Thank you!

[@TictactoeOP]

Umm... 1 question 🙋 , We can Write 5 over sigma and also in the denominator in the case of sample mean, So do we have to replace the base of x to 5 also? If you'll explain then it would be better 😊.

[@hithisismira]

Taking an online stats course and the professor basically just gives us homework and quizzes and gives us her notes. So we are basically teaching ourselves from the textbook

[@jillyburt]

all of the online classes I have taken are degree mills

[@hithisismira]

R. B. The school isn't online, just the class. It's the local community college, if the course is available online I'll go that route bc I'm a single parent and finding a sitter is difficult and expensive. Online schools like Post and Phoenix aren't trustworthy, but most of the time local colleges will offer an online option of their courses for students like me who can't attend regular days.

[@GLaDOShugger]

yeah i had to watch this just to learn the two different notations, the one for population mean and the one for sample mean i have seen both being used for mean and was very confused

[@AshkanTaherizadeh-x9m]

Thanks for providing videos. do these 67 videos cover from beginner to advanced level?

[@yoursports6910]

I’ve learned more from the internet then 7 years of school

[@jacksonkline2275]

Thanks for clearing this up for me!

[@ravikrishnarpan]

u r amazing bro !! million thanks

[@stargazer_373]

sorry I am a little rusty, haven't done math in 7 years. I got 5.75 in sample mean and 6.6 in population mean. I added everything together sample mean and then divided by 5 because there are 5x's and for population mean I added everything together then divided by 150,000,000 and got 6.6

[@xxxsc2xxx]

u have quite a way with words/ teaching

[@AA-hy6nb]

Thank you very much for this vieolectures! Why it is so easy&understandable, when you explain it, and so difficult&boring, when teacher tells about it in the lecture?

[@narancauk]

Excellent explanations .Thank you.

[@Austinator430]

Are you using a tablet with a pen or a pc with a mouse? If you're using a mouse, that's ridiculously neat.

[@jitendrapatel1110]

You are doing great and I love it

[@sanchitstriker]

hey Sal your videos have really helped me understanding the materials. I was looking for the tutorials on Methods of Moments and Maximum Likelihood estimators which I am having some trouble with. Are there videos on youtube ? Thank you for your great work. Thumbs UP!!

[@TheAkizo]

you should put annotations to the next video in the set.

[@shubhamranjan9495]

"new man would have borned" every time i'm done measuring :) Lol Hey btw great videos and thanks for making it freely accessible

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Where were you when Khan Academy uploaded this

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I like these videoes,they helped me a lot ,thanks

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(Applause) You just helped me out so much!

[@Jearhby]

I am 30 years old and I never understood mean meeting and mode until just now

[@elshad82]

Very clear explanation, but I am still confused. Isn't the population mean is the sample mean of 150M samples? If yes, and if the arithmetical calculation is the same for both, then what is the point in naming a regular mean (average) in two different names? If the population mean is used as a benchmark for comparing with the sample mean, then I suppose that the population mean was calculated somehow by somebody using a big number of samples, which again makes it a sample mean. I am lost.

[@AliKhalaf-k2p]

شكرا جزيلا thank you very much

[@kingsofleondrummer]

ur da best Tom Hanks!

[@jackmakson9798]

The quality control department of Atherton Mills specifies that the mean net weight per package of cereal should not be less than 20 (μ=20) ounces. Experience has shown that the weights are approximately normally distributed with a standard deviation of 1.5 (σ=1.5) ounces. A random sample of 15 (n = 15) packages yields a mean weight of 19.5 (x̅=19.5) ounces. Is this sufficient evidence to indicate that true mean weight of the packages has decreased? Hint: (H0: μ≥20, HA: μ

[@DosPerspectiva]

u r like a god to me Tomorrow is my test thanx

[@wilmersolis966]

thanks man you are good explaining

[@SznoopedCastGaming]

You could easily find the mean of the population by reversing the T-formula.

[@COJAZZ3]

Great explanation!

[@PratapO7O1]

I think there is a typo at 6:00 , it will be xi not xn ps thanks man

[@schrodingerscat3912]

favorite subject ever

[@luhlvi]

THANK YOU SO MUCH IT HELP ME A LOTTTT

[@shreyansbathiyan805]

Would you please share the notes of this videos.That addition will be very helpful. Thanks,

[@cupidus47]

GOD BLESS YOU!THANK YOU!

[@saswatsnayak102030]

i can't thank you enough sir

[@nicolasb3362]

Sum over n, ''Wow this is advanced mathematics''. Oh lord I wish...

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He knows how to teach well

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Thank you very much.

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SAVED MY LIFE THNK U! :')

[@Waranle]

Thank you Sal

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Terry Dean is that you

[@mikkelholm1770]

Where is this on the official khan academy website? I can't seem to find it under statistics and probability.

[@melaniegruben7486]

bless u Sal

[@Shkencetari]

Thank you very much

[@thedeserteagle9059]

Would that random sample (specifically referring to their height) chosen from the total number of American population be called as random variables? Because each of the person's height would follow a probability distribution?

[@MrUvikram]

After 12 years watching

[@MihaiBordeianu]

Awesome! Thanks a lot !

[@jjepsuomi]

Mathematics consists of proving the most obvious thing in the least obvious way. George Polya