Statistics Lecture 6.4: Sampling Distributions Statistics. Using Samples to Approx. Populations

[@vd1923]

if I was in his class I'd answer every question to show how grateful I am to have such an amazing prof like him. I'm gonna pass my class because of Prof Leonard and these kids are not even interacting with him

[@sj19991]

They are probably taking other classes also. Also, we are here voluntarily which makes us more attentive since we have a why.

[@husbandsamantha]

I am not one of your students but you have taught me all of statistics. I have watched every lecture as you use the same textbook as my college. I am an online student and without your breakdown of the problems, I wouldn't be passing. THANK YOU!!!!

[@a3production277]

Samantha King what book are you usng ?

[@Hany_AlShahhat]

what book are u using ?? is it Triola book ??

[@sanik1939]

Hi Thoraia. I'm following along with my textbook right now as well! Yep, its 5th edition Essentials of Statistics by Triola! He's a life saver!!

[@cleoliu8040]

I heard yawn in the class. Poor guy didn't realize how lucky he was to sit in the class. Good job, professor Leonard

[@extraordinaryblues8536]

On 11.50

[@zevlegend4267]

A trick : you can watch series on Flixzone. Me and my gf have been using them for watching a lot of movies recently.

[@lucianlewis5044]

@Zev Legend definitely, have been watching on flixzone for months myself =)

[@beckyh7949]

You are a great teacher and your videos are the only way I can understand what is supposedly being taught in my college course. Thank you for rescuing me. I would love to give you the money I'm giving my college for this course.

[@billzhangzitong]

Feeling the same way as you did Wonderful professior indeed

[@arjunsinghmadman]

I am an engineer and had learnt this. But I wish my profs in college would have taught the way you did (and of course I had paid the same amount of attention that I gave your lecture). Really amazing work. Keep them coming!!!

[@marynguyen6417]

You are a brilliant teacher! I've been watching many of your videos , and they have tremendously helped me with my statistical knowledge. I cannot thank you enough!!! All the best to you!

[@zemule5210]

You are a great professor. You converted me into another new religion known as STAT

[@VenujanSrithar]

Best lectures I ever had❤

[@nasrullahturke4480]

True teaching always has these characteristics of patience and making sure that concepts are understood. Really my heart goes with you Professor. Excellent and thank you so much for providing such a wonderful teaching.

[@lamisarusmeha9185]

Mans videos single handedly got me an A in both calculus and statistics! Thank you!!

[@joannaleigh2002]

It's my first time in your channel but I already love it. Your explanations we're very easy to understand which makes it easy for us to understand the whole concept. Thanks!

[@ismailumarukanneh6277]

Watching and listening to your lectures is one of the best experiences I have ever had in the world of mathematics. please upload lectures on correlation and regression for my understanding. Thanks

[@pallavisaxena7496]

Class strength reduced from 43 to 27. Feeling sorry for those students. You guys are so lucky to have such a great teacher.

[@AFarah-wu9ib]

I took this course 2017-2018 I pass it because of you thank you so much Professor 🤓

[@jameschan2404]

So far the best explanation of sample proportion vs sample mean.

[@waddywaddy7248]

Really thanks to you. I am in my first year in bachelor of biomedical science and i have to take statistics in my first year. Without you I will just only get credit... but now there is a high probability that i will get high distinction.

[@marianomanto]

Funny, I am from South America and watching this incredibly cool lesson for free :D

[@LC-pj5cz]

Thank you for your thorough explanation. This really helped me alot!

[@agh1750]

For the first example instead of thinking of rolling a "three sided die", it's a lot more understandable to imagine a pool containing x many bingo balls, one third of which are labelled "1", with another third labelled "2" and the remaining third labeled "5". Since the pool contains an equal quantity of each numbered ball, 2 of which are odd, we can say that for the population (all the balls in the pool) the proportion of odd numbered balls is 2/3, but what we want to consider are samples of 2 balls. Now how many possible outcomes are there when you randomly pull 2 balls from the pool? You can get either both 1s, both 2s, both 5s, a 1 and 2, a 1 and a 5, or a 2 and a 5. That's 6 possible outcomes, but notice how the probability of drawing any two different numbers is double that of drawing any 2 identical numbers because for example you can get a 1 and a 2 by drawing a 1 and then a 2, or a 2 and then a 1 but there's only one way you can get a 5 and a 5. In the video instead of bothering to sort out the probabilities, he defines either ordering of each pair of differently numbered balls as a distinct event so that all of the probabilities are the same, so for him there's 9 outcomes as opposed to 6. Also, instead of thinking about this as a "with replacement" scenario, we could equivalently consider it without replacement (which I think is more natural) by imagining that the pool contains infinitely many balls, the proportion off odd numbered balls would still be 2/3 for this infinite population so nothing changes. In addition, in the context of an infinite population the purpose and necessity of sampling is much more apparent so I truly believe that my explanation is a better way of thinking about this.

[@salumeserieca9593]

your students are so lucky to have you as their lecturer👍

[@Peter_1986]

"Peahat" is one of the enemies in the Zelda games; that thing that rests in the ground and then starts rotating really quickly and stalking Link.

[@johntindell9591]

Thank you very much from Thailand.

[@arbindrabogati9552]

Thank you so much for your post. You are awesome.

[@arunbm123]

brilliant explanation Proff.Leonard !!!

[@ryanwilson9555]

Assuming there are 27 people at your disposal, I’ve calculated that there are 80,730 potential *combinations* for creating a sample consisting of any 5 people (regardless of order) randomly picked from that entire population of 27 people. Likewise, there are also 9,687,600 potential *permutations* for creating that exact same sample (regarding order).

[@paristexas72]

i may actually pass my stats class thanks to you. My prof might as well be a text book

[@taekwondotime]

At 21:00 - 38:00, I'm surprised he didn't list out the possible samples of size n = 2. There are only 3. You don't have to fudge the numbers at all. It works just fine. (See below.) NCn is 3C2 = 3. If the population is S = {1,2,5}, then the valid samples of size n = 2 are: {1,2}, {1,5}, {2,5}. (You can't have repetition in a sample so an entry like 1,1 is not a valid sample. Also, order does not matter in a sample so we wouldn't consider different permutations of elements.) If you calculate the proportion for each of the three valid samples I listed above, you get: 0.5, 1.0, and 0.5. That means 50% of the numbers are odd in sample 1, 100% are odd in sample 2, and 50% are odd in sample 3. When you sum those up, 0.5 + 1.0 + 0.5 = 2.0. Then you divide by the total number of sample combinations: 2.0 / 3 = 2/3. Viola! You get the correct answer. Similarly, in his second example regarding the mean at 43:00.... The mean of {1,2} = 1.5. The mean of {1,5} = 3.0. The mean of {2,5} = 3.5. 1.5 + 3.0 + 3.5 = 8.0. 8.0 / 3 = 8/3 or 2.66666... Once again, you get the correct answer by examining the 3 possible combinations of sample size n = 2 from a population of N = 3.

[@taekwondotime]

Wow. Tough crowd! Posted this three months ago and haven't received even one like! Seems like the only comments that get liked on KZbin are one line comments involving praise.

[@rainerwahnsinn3262]

Can you explain, why we don't consider the samples with size 1 and 3?

[@taekwondotime]

@@rainerwahnsinn3262 If you did a sample of SIZE=1 then you would have: {1}, {2}, {5}. Three samples, each with one element in it. If you did a sample of SIZE=3 then you would have: {1,2,5}. One sample with three elements in it. In this case you have the entire population, so it's not a sample.

[@gaylelim6672]

he got a helluva mic cuz i hear absolutely EVERYTHING lol

[@rainerwahnsinn3262]

From 21:00 - 38:00 why do you take no samples with size 1 and 3? {1} or {5} is also a valid sample, no?

[@benjaminkolbeck]

Sample size is defined to be 2.

[@tatakim2517]

I think this topic is the hardest so far... I have been understanding all your previous lectures perfectly fine but this one is rlly hard to grasp😭

[@amoghchaube2927]

is there no poisson distribution in this playlist ?

[@wigdanahmed1989]

Thank you so much for the great work, is good that I still see new comments I'm starting statistics this fall. I just want to have an idea before my class starts.

[@theillustriousjohn]

I am confused. At 34:00 we are calculating the sampling proportion (based on every possible combination of n=2). With no surprise the result is the same as the population proportion. What is confusing me is that Prof. Leonard uses the u (or mean of the population) in the equation. Shouldn´t the equation be named P(pop. proportion) not u (pop. mean)?

[@jeffc5780]

at min 34:32, the calculation would be 1 * 9 / (9*4) + (18*4) / by average mean 9 = 1 / 12. i dont get the calculation, can somebody explain thanks

[@jeffc5780]

or 9/12, how come its 2/3?

[@TarunSingh-je9my]

You are incredible Professor. Please upload videos on Correlation and Time Series. pls pls pls

[@jayjayf9699]

I’m studying for an actuary exam and your a good teacher

[@xgamer2443]

unknown slayer thank you for helping me🔥🔥🔥

[@nyawirawaithaka4993]

Thank you Professor Leonard!

[@marccepeci2980]

If you took these proportions/averages from samples that DID NOT have a repetition (so if you used one number then you can not use it again) would the mean of the means still be the same as the population mean?

[@leonben3921]

the guy yawning 5-6 times within 15min, please stahp lol

[@namra2184]

SO good! Thank you so much!

[@lovedieyoung2846]

Thank you!!! Awesome lecture ever!!

[@TheZakev]

You're the best!

[@Dee-cq5rk]

a stat exam brought me here .. thank you!

[@joshuawalker8297]

Such good instruction.

[@a3production277]

does anyone knows the book name that the professor is using ??

[@AJ-et3vf]

Awesome video! Thank you!

[@hanman5195]

Thank you very much Sir Leonard

[@CamiloDS]

Sir you are a monster. 10/10

[@mechanical4642]

Sir, Which text book are you following? Thanks.

[@mariegitsas5510]

What text do you use

[@poojashedge266]

You are such a amazing , good looking , funny teacher..

[@probono2876]

Great Lectures.

[@anitamahapatra1847]

Which book do you refer?

[@akkineni1947]

Thank You

[@teachermcholo6976]

sorry prof... may you help me to derive the population parameters with and without replacement?? i.e mean,varience and proportions

[@krystal373]

I was looking for this part of the lecture too! I can't find it.

[@dabrutte]

Hope all is well. Does anyone know, which textbook he’s referring too?

[@uzmahafeez5911]

Elementary Statistics By Mario F. Triola, 11th Edition

[@bradleycassity1845]

All the dislikes for these videos are probably students who failed his class. The sample size would be the dislikes on this video and the population size would be all dislikes on all of his videos. I am learning!

[@Gregsmom]

I think the dislikes are from "That Tutor Guy" who is hating in the ads about how much more helpful a tutor is than a professor lol

[@wesleydunow222]

@@Gregsmom HAHAHAHA im dying... you both are hilarious.

[@shaikhatifanees5431]

you are brilliant

[@mikkolodeon7053]

please help.. if the population is only 3, why there is 1,1 2,2 and 5,5? would it be 1,2 1,5 2,1 2,5 and 5,1 and 5,2 combination? thanks!

[@sebastianantelo1824]

Because since you are sampling with replacement. It could happen that you draw a random number, say 5, then you put it back into the "hat"; draw again, and it could be a 5 again. In that case, you would have 5,5. same for the others

[@naomidiaz5272]

Are you using the Triola book????? I think you are!!!

[@aspenscript]

Which Triola book do you think it is... there's a few on Amazon? I'd like to buy it. Thanks.

[@anastaciamahoff1869]

Professor leanord, Do you have chapter 9-12 ?

[@paristexas72]

Ever thought of teaching Chemistry and Physics :-)

[@ericgrosch8073]

I took his claim about sample-variance as a challenge and I found it didn't seem to work. If anyone can find where I've erred, I'd like to know.: Example 3: sample-variance Population is 1, 2, 5. Population-variance = Sum (x - mu)[2]/n {(3/3-8/3)[2] + (6/3-8/3)[2] + 15/3-8/3[2]}/3 = {(-5/3[2] + (-2/3[2] + (7/3)[2]}/3= (25/9 + 4/9 + 49/9)/3 = 78/27 Samples x-bar probability S[2] (sampvar) varXprob 1, 1 1.0 1/9 (3/3-8/3)[2]/2=25/18 100/72 1, 2 1.5 1/9 (9/6-16/6)[2]/2=(-7/6)[2]/2=49/72 49/72 1, 5 3.0 1/9 (9/3-8/3)[2]/2=(1/3)[2]/2=1/18 4/72 2, 1 1.5 1/9 (9/6-16/6)[2]/2=(-7/6)[2]/2=49/72 49/72 2, 2 2.0 1/9 (6/3-8/3)[2]/2=(-2/3)[2]/2=2/9 16/72 2, 5 3.5 1/9 (21/6-16/6)[2]/2=(5/6)[2]/2=25/72 25/72 5, 1 3.0 1/9 (9/3-8/3)[2]/2=(1/3)[2]/2=1/18 4/72 5, 2 3.5 1/9 (21/6-16/6)[2]/2=(5/6)[2]/2=25/72 25/72 5, 5 5.0 1/9 (15/3-8/3)[2]/2=(7/3)[2]/2=49/18 196/72 Sum 468/72 117/18 varxprob 117/162 sigma[2], population-variance does not equal any single S (sample-variance), but find products of S and probability of each, add them and that’s P = (watch this space). Leonard claims: sample-variances target (estimate) the population-variance. Leonard claims also, sample standard deviation is not a good estimator of population-standard-deviation. It’s systematically a dressmaker (phonetic). [What did he say?]

[@TheMuslimKidd]

Best of best thank you

[@madinakakar8378]

I whant part 2 chp 14 survey sampling and sampling distribution

[@vade248721]

Great professor. As a teacher I'd relax a little on being condescending. Other than that a fantastic teacher.

[@SummumBonum.]

One more criticism for now, when you mention the population of the US and the population of the classroom in consecutive sentences, then you ask "what is our population"? Some students are left wondering which population you are asking for. When you do this, and then seem a little frustrated that they aren't sure which population you are asking, it is a bit demoralizing to me. I have been critical, but some of your explanations are good. I presume the main factor for my puzzlement is due to my ability to understand these concepts. Thank you for making your videos available for learning and criticism.

[@SummumBonum.]

It isn't possible to roll a 3 on a 3 sided dice that only has the numbers 1,2 and 5.

[@abigailnkromah3107]

Omg..they're so lucky

[@petergriffin4405]

30:00

[@SomeOfOthers]

Badass shirt

[@raggaelover8974]

I need a tutor. I shall pay you with food.

[@demetrasiountris8260]

Do these students seriously not know how to find the average of two numbers? Why are they taking a college-level statistics class?

[@reflectedcrosssite2848]

You do not realize how awkward it is to speak out in class :D

[@SummumBonum.]

The population of numbers on a three sided dice is three. There is something causing confusion in your explanation.

[@studyingchallenge6192]

.you are a super hot professor and super cool I wish if you were my husband.

[@rolaf438]

Your videos are too God damn long