[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.96,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.96,0:00:03.14,Default,,0000,0000,0000,,Before, at the end of the last\Nvideo, I actually said that
Dialogue: 0,0:00:03.14,0:00:06.42,Default,,0000,0000,0000,,we'd talk about measures of\Ndispersion or how things are
Dialogue: 0,0:00:06.42,0:00:08.40,Default,,0000,0000,0000,,distributed, but before I go\Ninto that, I realize that I
Dialogue: 0,0:00:08.40,0:00:10.68,Default,,0000,0000,0000,,have more to talk about,\Nespecially the mean.
Dialogue: 0,0:00:10.68,0:00:15.59,Default,,0000,0000,0000,,And before I do that, I want\Nto differentiate between a
Dialogue: 0,0:00:15.59,0:00:16.82,Default,,0000,0000,0000,,sample and a population.
Dialogue: 0,0:00:16.82,0:00:23.15,Default,,0000,0000,0000,,
Dialogue: 0,0:00:23.15,0:00:26.25,Default,,0000,0000,0000,,I touched on this a little\Nbit in the last video.
Dialogue: 0,0:00:26.25,0:00:28.63,Default,,0000,0000,0000,,Let's say I wanted to\Nknow-- I don't know.
Dialogue: 0,0:00:28.63,0:00:31.59,Default,,0000,0000,0000,,Let's say I wanted to know\Nthe average height of all
Dialogue: 0,0:00:31.59,0:00:33.53,Default,,0000,0000,0000,,men in America, right?
Dialogue: 0,0:00:33.53,0:00:37.60,Default,,0000,0000,0000,,So let me make the set\Nof all men in America.
Dialogue: 0,0:00:37.60,0:00:39.18,Default,,0000,0000,0000,,So that's all men in America.
Dialogue: 0,0:00:39.18,0:00:42.74,Default,,0000,0000,0000,,I know there's 300 million\Npeople in the U.S., and half of
Dialogue: 0,0:00:42.74,0:00:45.24,Default,,0000,0000,0000,,them maybe roughly are men,\Nso this would be 150
Dialogue: 0,0:00:45.24,0:00:49.36,Default,,0000,0000,0000,,million men, right?
Dialogue: 0,0:00:49.36,0:00:53.12,Default,,0000,0000,0000,,And it would be nearly\Nimpossible, even if I was
Dialogue: 0,0:00:53.12,0:00:56.62,Default,,0000,0000,0000,,intent on doing it, to actually\Nmeasure the average height
Dialogue: 0,0:00:56.62,0:00:58.10,Default,,0000,0000,0000,,of every man in America.
Dialogue: 0,0:00:58.10,0:01:00.77,Default,,0000,0000,0000,,Frankly, you know, every few\Nseconds, one of these men is
Dialogue: 0,0:01:00.77,0:01:02.49,Default,,0000,0000,0000,,being born and one of\Nthese men is dying.
Dialogue: 0,0:01:02.49,0:01:04.59,Default,,0000,0000,0000,,So you know by the time I'm\Ndone measuring everything,
Dialogue: 0,0:01:04.59,0:01:06.95,Default,,0000,0000,0000,,someone would have died, and\Nsome new men would have
Dialogue: 0,0:01:06.95,0:01:09.76,Default,,0000,0000,0000,,been born, so it would\Nalmost be impossible.
Dialogue: 0,0:01:09.76,0:01:15.51,Default,,0000,0000,0000,,And if not impossible, it would\Nbe very tiresome to measure the
Dialogue: 0,0:01:15.51,0:01:18.93,Default,,0000,0000,0000,,average, or the mean, or the\Nmedian, or the mode of this
Dialogue: 0,0:01:18.93,0:01:20.86,Default,,0000,0000,0000,,entire population, right?
Dialogue: 0,0:01:20.86,0:01:24.24,Default,,0000,0000,0000,,So the best way I can get a\Nsense of this, because I'm
Dialogue: 0,0:01:24.24,0:01:27.57,Default,,0000,0000,0000,,interested in what the average\Nof the population is, maybe I
Dialogue: 0,0:01:27.57,0:01:30.04,Default,,0000,0000,0000,,can take the average\Nof a sample.
Dialogue: 0,0:01:30.04,0:01:32.97,Default,,0000,0000,0000,,So what I could do is I can go\Nup to, you know-- and I'd try
Dialogue: 0,0:01:32.97,0:01:34.10,Default,,0000,0000,0000,,to be pretty random about it.
Dialogue: 0,0:01:34.10,0:01:37.37,Default,,0000,0000,0000,,I don't want to like-- you\Nknow, hopefully, my sample
Dialogue: 0,0:01:37.37,0:01:41.17,Default,,0000,0000,0000,,wouldn't be my college's\Nbasketball team because that
Dialogue: 0,0:01:41.17,0:01:44.20,Default,,0000,0000,0000,,would be a skewed sample, but\NI'd try to find random people
Dialogue: 0,0:01:44.20,0:01:46.93,Default,,0000,0000,0000,,and random situations where it\Nwouldn't be skewed
Dialogue: 0,0:01:46.93,0:01:48.02,Default,,0000,0000,0000,,based on height.
Dialogue: 0,0:01:48.02,0:01:50.86,Default,,0000,0000,0000,,And I'd maybe collect 10\Nheights, and I'd get, well,
Dialogue: 0,0:01:50.86,0:01:53.08,Default,,0000,0000,0000,,maybe-- you know, the more\Npeople I get the more
Dialogue: 0,0:01:53.08,0:01:55.36,Default,,0000,0000,0000,,indicative it is, but if I got\N10 heights, and those 10
Dialogue: 0,0:01:55.36,0:01:57.72,Default,,0000,0000,0000,,heights were-- I don't know.
Dialogue: 0,0:01:57.72,0:02:03.08,Default,,0000,0000,0000,,I'll do it in, you know, 5\Nfeet, 6 feet, 5 and a half
Dialogue: 0,0:02:03.08,0:02:09.09,Default,,0000,0000,0000,,feet, 5.75 feet, and, well,\Nlet's say I only do 6,
Dialogue: 0,0:02:09.09,0:02:11.14,Default,,0000,0000,0000,,or let's say in 6 and\Na half feet, right?
Dialogue: 0,0:02:11.14,0:02:14.14,Default,,0000,0000,0000,,Those are the five people that\NI'd sample, and we could talk
Dialogue: 0,0:02:14.14,0:02:17.06,Default,,0000,0000,0000,,more about what's a good way to\Ngenerate a random sample from a
Dialogue: 0,0:02:17.06,0:02:19.82,Default,,0000,0000,0000,,population so it's not skewed\None way or the other.
Dialogue: 0,0:02:19.82,0:02:22.15,Default,,0000,0000,0000,,But anyway, if I wanted to get\Na sense of it and if I was kind
Dialogue: 0,0:02:22.15,0:02:24.23,Default,,0000,0000,0000,,of lazy, so I only took\Nfive measurements, this
Dialogue: 0,0:02:24.23,0:02:25.13,Default,,0000,0000,0000,,is the way I would do it.
Dialogue: 0,0:02:25.13,0:02:28.03,Default,,0000,0000,0000,,This would be a sample.
Dialogue: 0,0:02:28.03,0:02:30.36,Default,,0000,0000,0000,,This would be a sample\Nof the population.
Dialogue: 0,0:02:30.36,0:02:33.96,Default,,0000,0000,0000,,So instead of taking the mean--\Nlet's say how I wanted to
Dialogue: 0,0:02:33.96,0:02:36.41,Default,,0000,0000,0000,,calculate the average by\Ntaking the arithmetic mean.
Dialogue: 0,0:02:36.41,0:02:38.54,Default,,0000,0000,0000,,Instead of taking the\Narithmetic mean of this entire
Dialogue: 0,0:02:38.54,0:02:41.89,Default,,0000,0000,0000,,group of 150 million people, I\Nmight just be happy taking the
Dialogue: 0,0:02:41.89,0:02:44.39,Default,,0000,0000,0000,,mean of this sample, and\Nthat'll be called
Dialogue: 0,0:02:44.39,0:02:46.19,Default,,0000,0000,0000,,the sample mean.
Dialogue: 0,0:02:46.19,0:02:48.54,Default,,0000,0000,0000,,And I want to introduce you to\Nsome notation, even though it's
Dialogue: 0,0:02:48.54,0:02:54.14,Default,,0000,0000,0000,,kind of-- so in statistics\Nspeak, the mean, this mu, it's
Dialogue: 0,0:02:54.14,0:02:57.45,Default,,0000,0000,0000,,a Greek letter, essentially the\NGreek letter that later turns
Dialogue: 0,0:02:57.45,0:03:02.64,Default,,0000,0000,0000,,into m, but mu is the\Npopulation mean, and this is
Dialogue: 0,0:03:02.64,0:03:07.15,Default,,0000,0000,0000,,just a convention\Npopulation mean.
Dialogue: 0,0:03:07.15,0:03:09.66,Default,,0000,0000,0000,,
Dialogue: 0,0:03:09.66,0:03:14.90,Default,,0000,0000,0000,,And x with a line over it, that\Nis equal to a sample mean.
Dialogue: 0,0:03:14.90,0:03:17.93,Default,,0000,0000,0000,,
Dialogue: 0,0:03:17.93,0:03:20.15,Default,,0000,0000,0000,,And these are just notations\Nthat people might see, and you
Dialogue: 0,0:03:20.15,0:03:21.82,Default,,0000,0000,0000,,might have been confused\Nbecause sometimes you see
Dialogue: 0,0:03:21.82,0:03:24.50,Default,,0000,0000,0000,,something-- people talk about\Nmeans, and you see this mu, and
Dialogue: 0,0:03:24.50,0:03:28.24,Default,,0000,0000,0000,,sometimes you see this x with a\Nline over it, and it's nice
Dialogue: 0,0:03:28.24,0:03:29.02,Default,,0000,0000,0000,,to know the distinction.
Dialogue: 0,0:03:29.02,0:03:31.45,Default,,0000,0000,0000,,Here they're talking about\Nthe mean of a sample of the
Dialogue: 0,0:03:31.45,0:03:35.10,Default,,0000,0000,0000,,population, and here they're\Ntalking about the mean of
Dialogue: 0,0:03:35.10,0:03:37.50,Default,,0000,0000,0000,,the population as a whole.
Dialogue: 0,0:03:37.50,0:03:41.31,Default,,0000,0000,0000,,Now, the way you calculate\Nthem is essentially the same.
Dialogue: 0,0:03:41.31,0:03:43.18,Default,,0000,0000,0000,,If you want to figure out the\Npopulation mean, you'd go to
Dialogue: 0,0:03:43.18,0:03:47.73,Default,,0000,0000,0000,,all 150 million people at one\Nmoment and add up all their
Dialogue: 0,0:03:47.73,0:03:50.53,Default,,0000,0000,0000,,heights, and divide by 150\Nmillion to get the
Dialogue: 0,0:03:50.53,0:03:51.57,Default,,0000,0000,0000,,population mean.
Dialogue: 0,0:03:51.57,0:03:54.58,Default,,0000,0000,0000,,The sample mean, you just add\Nup the numbers in your sample
Dialogue: 0,0:03:54.58,0:03:57.57,Default,,0000,0000,0000,,and divide by the number\Nof data points you have.
Dialogue: 0,0:03:57.57,0:04:00.38,Default,,0000,0000,0000,,And the formulas I\Nwant to show you.
Dialogue: 0,0:04:00.38,0:04:03.00,Default,,0000,0000,0000,,I think you know how to\Ncalculate averages.
Dialogue: 0,0:04:03.00,0:04:05.84,Default,,0000,0000,0000,,It's a fairly straightforward\Noperation, and I want to show
Dialogue: 0,0:04:05.84,0:04:08.03,Default,,0000,0000,0000,,you how it's often written in\Nstatistics books, so that
Dialogue: 0,0:04:08.03,0:04:09.96,Default,,0000,0000,0000,,you're not intimidated\Nwhen you see it.
Dialogue: 0,0:04:09.96,0:04:12.39,Default,,0000,0000,0000,,The population mean, they'll\Nwrite it as-- so just to do,
Dialogue: 0,0:04:12.39,0:04:13.90,Default,,0000,0000,0000,,you know, the convention.
Dialogue: 0,0:04:13.90,0:04:17.30,Default,,0000,0000,0000,,Each member of a-- well, let\Nme do the sample first.
Dialogue: 0,0:04:17.30,0:04:20.50,Default,,0000,0000,0000,,Each member of a sample, say\Nthis is the first sample.
Dialogue: 0,0:04:20.50,0:04:22.43,Default,,0000,0000,0000,,They'll call that x sub 1.
Dialogue: 0,0:04:22.43,0:04:24.89,Default,,0000,0000,0000,,They'll call this x sub 2.
Dialogue: 0,0:04:24.89,0:04:29.58,Default,,0000,0000,0000,,They'll call this one x\Nsub 3, x sub 4, and this
Dialogue: 0,0:04:29.58,0:04:31.75,Default,,0000,0000,0000,,one x sub 5, right?
Dialogue: 0,0:04:31.75,0:04:33.37,Default,,0000,0000,0000,,And this is just a way\Nof referring to each
Dialogue: 0,0:04:33.37,0:04:34.31,Default,,0000,0000,0000,,of the samples.
Dialogue: 0,0:04:34.31,0:04:36.26,Default,,0000,0000,0000,,So in a sample mean, they'll\Nsay, do you know what you do?
Dialogue: 0,0:04:36.26,0:04:38.35,Default,,0000,0000,0000,,You take the sum\Nof these numbers.
Dialogue: 0,0:04:38.35,0:04:41.07,Default,,0000,0000,0000,,And you know how to do that,\Nbut the fancy way of writing
Dialogue: 0,0:04:41.07,0:04:43.40,Default,,0000,0000,0000,,it is to say, let's\Nwrite a capital Sigma.
Dialogue: 0,0:04:43.40,0:04:45.73,Default,,0000,0000,0000,,That means the sum.
Dialogue: 0,0:04:45.73,0:04:49.38,Default,,0000,0000,0000,,Sum of every x sub n, right?
Dialogue: 0,0:04:49.38,0:04:51.97,Default,,0000,0000,0000,,Take the sum of each of\Nthese numbers, right?
Dialogue: 0,0:04:51.97,0:04:58.45,Default,,0000,0000,0000,,This is x sub 1, x sub 2, where\Nn goes from 1 to-- I mean, you
Dialogue: 0,0:04:58.45,0:05:01.16,Default,,0000,0000,0000,,could say to the size\Nof the population.
Dialogue: 0,0:05:01.16,0:05:04.70,Default,,0000,0000,0000,,You know, sometimes-- you know,\Nin this case it would be 5, or
Dialogue: 0,0:05:04.70,0:05:07.90,Default,,0000,0000,0000,,sometimes they'd write a big--\Nthey'd write an n like that.
Dialogue: 0,0:05:07.90,0:05:11.03,Default,,0000,0000,0000,,And you'd divide it by the\Nnumber of members there are
Dialogue: 0,0:05:11.03,0:05:15.11,Default,,0000,0000,0000,,in that population,\Nso divided by n.
Dialogue: 0,0:05:15.11,0:05:16.92,Default,,0000,0000,0000,,You know, when you see this in\Na book, you're like, wow, this
Dialogue: 0,0:05:16.92,0:05:18.48,Default,,0000,0000,0000,,is advanced mathematics.
Dialogue: 0,0:05:18.48,0:05:20.54,Default,,0000,0000,0000,,But essentially, they're saying\Ntake the sum of all the data
Dialogue: 0,0:05:20.54,0:05:22.94,Default,,0000,0000,0000,,points, just sum up these\Nnumbers, and divide by the
Dialogue: 0,0:05:22.94,0:05:23.93,Default,,0000,0000,0000,,number of numbers there are.
Dialogue: 0,0:05:23.93,0:05:27.40,Default,,0000,0000,0000,,So this would just be 5\Nplus 5 plus 5.5 plus 5.75
Dialogue: 0,0:05:27.40,0:05:30.05,Default,,0000,0000,0000,,plus 6.5 divided by 5.
Dialogue: 0,0:05:30.05,0:05:31.82,Default,,0000,0000,0000,,That's all this is telling you.
Dialogue: 0,0:05:31.82,0:05:33.68,Default,,0000,0000,0000,,For the population mean,\Nit's the same thing.
Dialogue: 0,0:05:33.68,0:05:36.16,Default,,0000,0000,0000,,They just use a slightly\Ndifferent notation.
Dialogue: 0,0:05:36.16,0:05:42.06,Default,,0000,0000,0000,,They'll say that's equal to the\Nsum from n is equal to 1 to a
Dialogue: 0,0:05:42.06,0:05:46.24,Default,,0000,0000,0000,,big N-- and I'll explain why\Nthey write a big N-- of each
Dialogue: 0,0:05:46.24,0:05:49.65,Default,,0000,0000,0000,,data point in the population,\Nnot just the sample, all
Dialogue: 0,0:05:49.65,0:05:52.56,Default,,0000,0000,0000,,that divided by big N.
Dialogue: 0,0:05:52.56,0:05:54.82,Default,,0000,0000,0000,,And this is just a way of,\Nwhen they're at big N,
Dialogue: 0,0:05:54.82,0:05:57.14,Default,,0000,0000,0000,,they mean 150 million.
Dialogue: 0,0:05:57.14,0:05:59.96,Default,,0000,0000,0000,,They mean, you know, we want\Nyou to get every data point
Dialogue: 0,0:05:59.96,0:06:01.38,Default,,0000,0000,0000,,in the entire population.
Dialogue: 0,0:06:01.38,0:06:03.85,Default,,0000,0000,0000,,So that's what they mean by--\Nand then divide by the number
Dialogue: 0,0:06:03.85,0:06:05.09,Default,,0000,0000,0000,,of the entire population.
Dialogue: 0,0:06:05.09,0:06:07.62,Default,,0000,0000,0000,,While the small n, they're kind\Nof-- it's just the convention,
Dialogue: 0,0:06:07.62,0:06:11.35,Default,,0000,0000,0000,,the notation, that they say,\Nhey, we just want you to get
Dialogue: 0,0:06:11.35,0:06:13.70,Default,,0000,0000,0000,,some smaller number, not\Nthe entire population.
Dialogue: 0,0:06:13.70,0:06:16.09,Default,,0000,0000,0000,,But the way you calculate\Nthem is, you know, they're
Dialogue: 0,0:06:16.09,0:06:18.54,Default,,0000,0000,0000,,essentially equivalent.
Dialogue: 0,0:06:18.54,0:06:21.97,Default,,0000,0000,0000,,Anyway, I wanted to leave you\Nwith that just because this is
Dialogue: 0,0:06:21.97,0:06:24.71,Default,,0000,0000,0000,,something that if you don't get\Nit clarified early on-- it's a
Dialogue: 0,0:06:24.71,0:06:27.63,Default,,0000,0000,0000,,fairly simple concept-- later\Non, it becomes very confusing
Dialogue: 0,0:06:27.63,0:06:29.26,Default,,0000,0000,0000,,when people want to\Ndifferentiate between the
Dialogue: 0,0:06:29.26,0:06:31.17,Default,,0000,0000,0000,,population and the sample mean.
Dialogue: 0,0:06:31.17,0:06:33.26,Default,,0000,0000,0000,,And you see these formulas\Nwritten slightly different.
Dialogue: 0,0:06:33.26,0:06:36.56,Default,,0000,0000,0000,,Sometimes you'll see a mu, and\Nsometimes you'll see an x with
Dialogue: 0,0:06:36.56,0:06:38.61,Default,,0000,0000,0000,,a line over it for\Nthe sample mean.
Dialogue: 0,0:06:38.61,0:06:41.23,Default,,0000,0000,0000,,Anyway, I'll see in\Nthe next video.
Dialogue: 0,0:06:41.23,0:06:41.40,Default,,0000,0000,0000,,