[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.52,0:00:02.82,Default,,0000,0000,0000,,Let's say I've got\Na set of numbers.
Dialogue: 0,0:00:02.82,0:00:08.71,Default,,0000,0000,0000,,2, say I've got three 3's, I've\Ngot a couple of 4's, and
Dialogue: 0,0:00:08.71,0:00:10.62,Default,,0000,0000,0000,,I've got a 10 there.
Dialogue: 0,0:00:10.62,0:00:14.21,Default,,0000,0000,0000,,And what we want to do is find\Nthe middle of these numbers.
Dialogue: 0,0:00:14.21,0:00:17.82,Default,,0000,0000,0000,,We want to represent these\Nnumbers with the center of the
Dialogue: 0,0:00:17.82,0:00:19.90,Default,,0000,0000,0000,,numbers, or the middle of the\Nnumbers, just so we have a
Dialogue: 0,0:00:19.90,0:00:24.35,Default,,0000,0000,0000,,sense of where these numbers\Nroughly are.
Dialogue: 0,0:00:24.35,0:00:27.36,Default,,0000,0000,0000,,And this central tendency that\Nwe're going to try to get out
Dialogue: 0,0:00:27.36,0:00:31.02,Default,,0000,0000,0000,,of these numbers, we're going\Nto call the average.
Dialogue: 0,0:00:31.02,0:00:34.99,Default,,0000,0000,0000,,The average of this\Nset of numbers.
Dialogue: 0,0:00:34.99,0:00:38.84,Default,,0000,0000,0000,,And you've, I'm sure, heard the\Nword average before, but
Dialogue: 0,0:00:38.84,0:00:41.11,Default,,0000,0000,0000,,we're going to get a little\Nbit more detailed on the
Dialogue: 0,0:00:41.11,0:00:44.27,Default,,0000,0000,0000,,different types of averages\Nin this video.
Dialogue: 0,0:00:44.27,0:00:46.89,Default,,0000,0000,0000,,The one you're probably most\Nfamiliar with, although you
Dialogue: 0,0:00:46.89,0:00:49.95,Default,,0000,0000,0000,,might have not seen it referred\Nto in this way, is
Dialogue: 0,0:00:49.95,0:00:58.29,Default,,0000,0000,0000,,the arithmetic mean, which\Nliterally says, look, I, the
Dialogue: 0,0:00:58.29,0:01:01.27,Default,,0000,0000,0000,,arithmetic mean of this set of\Nnumbers, is literally the sum
Dialogue: 0,0:01:01.27,0:01:03.42,Default,,0000,0000,0000,,of all of these numbers divided\Nby the number of
Dialogue: 0,0:01:03.42,0:01:04.21,Default,,0000,0000,0000,,numbers there are.
Dialogue: 0,0:01:04.21,0:01:07.44,Default,,0000,0000,0000,,So the arithmetic mean for this\Nset right here is going
Dialogue: 0,0:01:07.44,0:01:17.07,Default,,0000,0000,0000,,to be 2 plus 3 plus 3 plus 3\Nplus 4 plus 4 plus 10, all of
Dialogue: 0,0:01:17.07,0:01:19.23,Default,,0000,0000,0000,,that over, how many\Nnumbers do I have?
Dialogue: 0,0:01:19.23,0:01:22.87,Default,,0000,0000,0000,,1, 2, 3, 4, 5, 6, 7.
Dialogue: 0,0:01:22.87,0:01:24.72,Default,,0000,0000,0000,,All of that over 7.
Dialogue: 0,0:01:24.72,0:01:25.66,Default,,0000,0000,0000,,And what is this equal to?
Dialogue: 0,0:01:25.66,0:01:34.56,Default,,0000,0000,0000,,This is 2 plus 9, which is 11,\Nplus 8, which is 19, plus 10,
Dialogue: 0,0:01:34.56,0:01:35.52,Default,,0000,0000,0000,,which is 29.
Dialogue: 0,0:01:35.52,0:01:41.29,Default,,0000,0000,0000,,So this is going to be equal to\N29/7, or you could say it's
Dialogue: 0,0:01:41.29,0:01:43.54,Default,,0000,0000,0000,,equal to 4 and 1/7.
Dialogue: 0,0:01:43.54,0:01:45.24,Default,,0000,0000,0000,,If I got my calculator out,\Nwe could figure out
Dialogue: 0,0:01:45.24,0:01:46.48,Default,,0000,0000,0000,,the decimal of this.
Dialogue: 0,0:01:46.48,0:01:50.99,Default,,0000,0000,0000,,But this is a representation\Nof the central tendency, or
Dialogue: 0,0:01:50.99,0:01:52.45,Default,,0000,0000,0000,,the middle of these numbers.
Dialogue: 0,0:01:52.45,0:01:53.67,Default,,0000,0000,0000,,And it kind of makes sense.
Dialogue: 0,0:01:53.67,0:01:57.67,Default,,0000,0000,0000,,4 and 1/7, it's a little\Nbit higher than 4.
Dialogue: 0,0:01:57.67,0:02:01.07,Default,,0000,0000,0000,,We're kind of close to the\Nmiddle of our number range
Dialogue: 0,0:02:01.07,0:02:01.81,Default,,0000,0000,0000,,right there.
Dialogue: 0,0:02:01.81,0:02:03.59,Default,,0000,0000,0000,,And you might say, well, it's\Na little skewed to the right
Dialogue: 0,0:02:03.59,0:02:04.70,Default,,0000,0000,0000,,and what caused that?
Dialogue: 0,0:02:04.70,0:02:06.95,Default,,0000,0000,0000,,And well, gee, 10 is a little\Nbit larger than all of the
Dialogue: 0,0:02:06.95,0:02:07.84,Default,,0000,0000,0000,,other numbers.
Dialogue: 0,0:02:07.84,0:02:09.32,Default,,0000,0000,0000,,It's kind of an outlier.
Dialogue: 0,0:02:09.32,0:02:13.37,Default,,0000,0000,0000,,Maybe that skewed this average\Nup, the arithmetic mean.
Dialogue: 0,0:02:13.37,0:02:16.68,Default,,0000,0000,0000,,So there are other types of\Naverages, although this is the
Dialogue: 0,0:02:16.68,0:02:19.20,Default,,0000,0000,0000,,one that, if people just say,\Nhey, let's take the average of
Dialogue: 0,0:02:19.20,0:02:21.66,Default,,0000,0000,0000,,these numbers, and they don't\Nreally tell you more, they're
Dialogue: 0,0:02:21.66,0:02:23.94,Default,,0000,0000,0000,,probably talking about\Nthe arithmetic mean.
Dialogue: 0,0:02:23.94,0:02:30.27,Default,,0000,0000,0000,,The other forms of average,\Nthough, are the median, and
Dialogue: 0,0:02:30.27,0:02:32.29,Default,,0000,0000,0000,,this literally is the\Nmiddle number.
Dialogue: 0,0:02:35.97,0:02:38.36,Default,,0000,0000,0000,,If there are two middle numbers,\Nyou actually take the
Dialogue: 0,0:02:38.36,0:02:40.73,Default,,0000,0000,0000,,arithmetic mean of those\Ntwo middle numbers.
Dialogue: 0,0:02:40.73,0:02:43.31,Default,,0000,0000,0000,,You actually find the number\Nhalfway in between those two
Dialogue: 0,0:02:43.31,0:02:44.33,Default,,0000,0000,0000,,middle numbers.
Dialogue: 0,0:02:44.33,0:02:47.26,Default,,0000,0000,0000,,So the median of this set\Nright here-- let me just
Dialogue: 0,0:02:47.26,0:02:48.35,Default,,0000,0000,0000,,rewrite them.
Dialogue: 0,0:02:48.35,0:02:57.06,Default,,0000,0000,0000,,So I have a 2, a 3,\N3, 3, 4, 4, 10.
Dialogue: 0,0:02:57.06,0:02:59.69,Default,,0000,0000,0000,,So, let's see, we have seven\Nnumbers right here.
Dialogue: 0,0:02:59.69,0:03:02.80,Default,,0000,0000,0000,,The middle number, if\NI go 1, 2, 3, to the
Dialogue: 0,0:03:02.80,0:03:04.14,Default,,0000,0000,0000,,right, we're there.
Dialogue: 0,0:03:04.14,0:03:06.47,Default,,0000,0000,0000,,If we go 1, 2, 3 to the\Nleft, we're there.
Dialogue: 0,0:03:06.47,0:03:09.85,Default,,0000,0000,0000,,The middle number is\Nthat 3 right there.
Dialogue: 0,0:03:09.85,0:03:13.36,Default,,0000,0000,0000,,I just listed them in order, and\NI said, well, look, 3, you
Dialogue: 0,0:03:13.36,0:03:16.64,Default,,0000,0000,0000,,could think of it as the fourth\Nnumber from the right,
Dialogue: 0,0:03:16.64,0:03:19.55,Default,,0000,0000,0000,,and it's also the fourth\Nnumber from the left.
Dialogue: 0,0:03:19.55,0:03:21.36,Default,,0000,0000,0000,,3 is the middle number.
Dialogue: 0,0:03:21.36,0:03:23.94,Default,,0000,0000,0000,,And this case, it\Nis the median.
Dialogue: 0,0:03:23.94,0:03:29.28,Default,,0000,0000,0000,,So in this case, 3, if you use\Nthe median, is our average.
Dialogue: 0,0:03:29.28,0:03:30.36,Default,,0000,0000,0000,,And that also makes sense.
Dialogue: 0,0:03:30.36,0:03:32.03,Default,,0000,0000,0000,,I mean, it's literally the\Nmiddle number, and if you look
Dialogue: 0,0:03:32.03,0:03:35.67,Default,,0000,0000,0000,,at this set of numbers, it kind\Nof does represent the
Dialogue: 0,0:03:35.67,0:03:37.79,Default,,0000,0000,0000,,central tendency of this set.
Dialogue: 0,0:03:37.79,0:03:40.88,Default,,0000,0000,0000,,Now just to be clear, it was\Nvery clear what the middle
Dialogue: 0,0:03:40.88,0:03:45.35,Default,,0000,0000,0000,,number was, because I had an\Nodd number of numbers.
Dialogue: 0,0:03:45.35,0:03:48.56,Default,,0000,0000,0000,,I had three on each side of the\Nthree, so it was very easy
Dialogue: 0,0:03:48.56,0:03:50.79,Default,,0000,0000,0000,,to figure out the median,\Nthe middle number.
Dialogue: 0,0:03:50.79,0:03:53.80,Default,,0000,0000,0000,,But if I had a situation-- let's\Nsay I have the situation
Dialogue: 0,0:03:53.80,0:03:57.85,Default,,0000,0000,0000,,where I have 2, 3, 4, and 5.
Dialogue: 0,0:03:57.85,0:04:01.51,Default,,0000,0000,0000,,Let's say that's my\Nset of numbers.
Dialogue: 0,0:04:01.51,0:04:04.35,Default,,0000,0000,0000,,Well, here, there is no\None middle number.
Dialogue: 0,0:04:04.35,0:04:07.46,Default,,0000,0000,0000,,The 3 is closer to the left\Nthan it is to the right.
Dialogue: 0,0:04:07.46,0:04:10.04,Default,,0000,0000,0000,,The 4 is closer to the right\Nthan it is to the left.
Dialogue: 0,0:04:10.04,0:04:12.22,Default,,0000,0000,0000,,There's actually two middle\Nnumbers here.
Dialogue: 0,0:04:12.22,0:04:17.38,Default,,0000,0000,0000,,The two middle numbers here\Nare the 3 and the 4.
Dialogue: 0,0:04:17.38,0:04:20.64,Default,,0000,0000,0000,,And here, when you have two\Nmiddle numbers, which occurs
Dialogue: 0,0:04:20.64,0:04:24.43,Default,,0000,0000,0000,,when you have an even number\Nin your data set, there the
Dialogue: 0,0:04:24.43,0:04:27.63,Default,,0000,0000,0000,,median is halfway in between\Nthese two numbers.
Dialogue: 0,0:04:27.63,0:04:31.07,Default,,0000,0000,0000,,So in this situation, the median\Nis going to be 3 plus 4
Dialogue: 0,0:04:31.07,0:04:35.67,Default,,0000,0000,0000,,over 2, which is equal to 3.5.
Dialogue: 0,0:04:35.67,0:04:37.61,Default,,0000,0000,0000,,And if you look at this data\Nset, that's not what our
Dialogue: 0,0:04:37.61,0:04:44.43,Default,,0000,0000,0000,,original problem was, but if\Nyou look at this data set
Dialogue: 0,0:04:44.43,0:04:47.77,Default,,0000,0000,0000,,right there, you're actually\Ngoing to find that the
Dialogue: 0,0:04:47.77,0:04:52.07,Default,,0000,0000,0000,,arithmetic mean and the median\Nhere is the exact same thing.
Dialogue: 0,0:04:52.07,0:04:53.23,Default,,0000,0000,0000,,Let's calculate it.
Dialogue: 0,0:04:53.23,0:04:55.47,Default,,0000,0000,0000,,What 's the arithmetic\Nmean over here?
Dialogue: 0,0:04:55.47,0:05:00.24,Default,,0000,0000,0000,,It's going to be 2 plus 3 plus\N4 plus 5, which is what?
Dialogue: 0,0:05:00.24,0:05:09.49,Default,,0000,0000,0000,,5 plus 9, which is equal\Nto 14, over 4.
Dialogue: 0,0:05:09.49,0:05:10.91,Default,,0000,0000,0000,,And what's this equal to?
Dialogue: 0,0:05:10.91,0:05:16.74,Default,,0000,0000,0000,,14/4 is 3 and 2/4, or 3 and\N1/2, the exact same thing.
Dialogue: 0,0:05:16.74,0:05:19.31,Default,,0000,0000,0000,,So for this data set, they\Nwere the same thing.
Dialogue: 0,0:05:19.31,0:05:24.02,Default,,0000,0000,0000,,For this data set, our median\Nis a little bit lower.
Dialogue: 0,0:05:24.02,0:05:28.09,Default,,0000,0000,0000,,It's 3, while our arithmetic\Nmean is 4 and 1/7.
Dialogue: 0,0:05:28.09,0:05:30.08,Default,,0000,0000,0000,,And I really want you to think\Nabout why that is.
Dialogue: 0,0:05:30.08,0:05:32.84,Default,,0000,0000,0000,,And it has a lot to do with this\N10 that sits out there.
Dialogue: 0,0:05:32.84,0:05:37.19,Default,,0000,0000,0000,,All of these other numbers are\Npretty close to whichever
Dialogue: 0,0:05:37.19,0:05:39.59,Default,,0000,0000,0000,,average you want to pick,\Nwhether it's the arithmetic
Dialogue: 0,0:05:39.59,0:05:42.56,Default,,0000,0000,0000,,mean or it's the median.
Dialogue: 0,0:05:42.56,0:05:47.86,Default,,0000,0000,0000,,But this 10 is kind of\Nan outlier, or it
Dialogue: 0,0:05:47.86,0:05:50.65,Default,,0000,0000,0000,,skews the data set.
Dialogue: 0,0:05:50.65,0:05:53.79,Default,,0000,0000,0000,,Maybe it's so much larger than\Nthe other numbers, that it
Dialogue: 0,0:05:53.79,0:05:57.68,Default,,0000,0000,0000,,makes the arithmetic mean seem\Nlarger than maybe is
Dialogue: 0,0:05:57.68,0:05:59.67,Default,,0000,0000,0000,,representative of\Nthis data set.
Dialogue: 0,0:05:59.67,0:06:01.50,Default,,0000,0000,0000,,And that's something important\Nto think about.
Dialogue: 0,0:06:01.50,0:06:07.57,Default,,0000,0000,0000,,When you're finding the average\Nfor something, most
Dialogue: 0,0:06:07.57,0:06:09.74,Default,,0000,0000,0000,,people will immediately go\Nto the arithmetic mean.
Dialogue: 0,0:06:09.74,0:06:13.52,Default,,0000,0000,0000,,But in a lot of cases, median\Nwill make a lot more sense, if
Dialogue: 0,0:06:13.52,0:06:16.97,Default,,0000,0000,0000,,you have these really large or\Nreally small numbers that
Dialogue: 0,0:06:16.97,0:06:18.46,Default,,0000,0000,0000,,could skew the data set.
Dialogue: 0,0:06:18.46,0:06:21.53,Default,,0000,0000,0000,,I mean, you can imagine, if this\Nwasn't a 10-- or let's
Dialogue: 0,0:06:21.53,0:06:22.79,Default,,0000,0000,0000,,imagine adding another\Nnumber here.
Dialogue: 0,0:06:22.79,0:06:27.81,Default,,0000,0000,0000,,If I added the number 1 million,\Nif I added 1 million
Dialogue: 0,0:06:27.81,0:06:30.39,Default,,0000,0000,0000,,to this data set, if that was\Nthe eighth number, the
Dialogue: 0,0:06:30.39,0:06:32.26,Default,,0000,0000,0000,,arithmetic mean is going\Nto be this huge number.
Dialogue: 0,0:06:32.26,0:06:36.40,Default,,0000,0000,0000,,It's going to be much larger\Nthan what is representative of
Dialogue: 0,0:06:36.40,0:06:38.47,Default,,0000,0000,0000,,most of the numbers\Nin this data set.
Dialogue: 0,0:06:38.47,0:06:40.24,Default,,0000,0000,0000,,But the median is still\Ngoing to work.
Dialogue: 0,0:06:40.24,0:06:43.73,Default,,0000,0000,0000,,The median is still going to be\Nabout 3 and a half, right?
Dialogue: 0,0:06:43.73,0:06:47.75,Default,,0000,0000,0000,,If you had 1 million here,\Nit would be 1, 2, 3, 4.
Dialogue: 0,0:06:47.75,0:06:49.20,Default,,0000,0000,0000,,The middle two numbers\Nwould be that.
Dialogue: 0,0:06:49.20,0:06:50.58,Default,,0000,0000,0000,,It would be 3 and 1/2.
Dialogue: 0,0:06:50.58,0:06:53.90,Default,,0000,0000,0000,,So the median is less sensitive\Nto one or two
Dialogue: 0,0:06:53.90,0:06:58.43,Default,,0000,0000,0000,,numbers at the extremes that\Notherwise would skew the mean.
Dialogue: 0,0:06:58.43,0:07:01.13,Default,,0000,0000,0000,,Now, the last form of average\NI want to talk
Dialogue: 0,0:07:01.13,0:07:02.84,Default,,0000,0000,0000,,about is the mode.
Dialogue: 0,0:07:05.40,0:07:08.00,Default,,0000,0000,0000,,It has nothing to do\Nwith ice cream.
Dialogue: 0,0:07:08.00,0:07:10.91,Default,,0000,0000,0000,,The mode is literally the\Nmost frequent number.
Dialogue: 0,0:07:16.80,0:07:19.88,Default,,0000,0000,0000,,And in this data set, it's\Npretty clear what the most
Dialogue: 0,0:07:19.88,0:07:21.13,Default,,0000,0000,0000,,frequent number is.
Dialogue: 0,0:07:21.13,0:07:25.82,Default,,0000,0000,0000,,I only have one 2, I have three\N3's, I have two 4's, I
Dialogue: 0,0:07:25.82,0:07:28.44,Default,,0000,0000,0000,,have one 10, and even if want to\Ninclude the million, I only
Dialogue: 0,0:07:28.44,0:07:29.71,Default,,0000,0000,0000,,have one million there.
Dialogue: 0,0:07:29.71,0:07:31.99,Default,,0000,0000,0000,,So here, the number\Nthat occurs most
Dialogue: 0,0:07:31.99,0:07:35.36,Default,,0000,0000,0000,,frequently is the 3.
Dialogue: 0,0:07:35.36,0:07:38.33,Default,,0000,0000,0000,,So, once again, the mode seems\Nlike a pretty good measure of
Dialogue: 0,0:07:38.33,0:07:41.26,Default,,0000,0000,0000,,central tendency or a\Npretty good average
Dialogue: 0,0:07:41.26,0:07:43.30,Default,,0000,0000,0000,,for this data set.
Dialogue: 0,0:07:43.30,0:07:45.95,Default,,0000,0000,0000,,Now the mode, it's a little\Ntricky to deal with, and you
Dialogue: 0,0:07:45.95,0:07:49.07,Default,,0000,0000,0000,,won't see it used that often,\Nbecause it becomes a little
Dialogue: 0,0:07:49.07,0:07:52.92,Default,,0000,0000,0000,,ambiguous when-- you know,\Nlook at this data set:
Dialogue: 0,0:07:52.92,0:07:55.27,Default,,0000,0000,0000,,2, 3, 4, and 5.
Dialogue: 0,0:07:55.27,0:07:56.37,Default,,0000,0000,0000,,What is the mode there?
Dialogue: 0,0:07:56.37,0:07:59.20,Default,,0000,0000,0000,,All of these numbers are\Nequally frequent.
Dialogue: 0,0:07:59.20,0:08:01.36,Default,,0000,0000,0000,,So if you have a situation\Nlike this, then you might
Dialogue: 0,0:08:01.36,0:08:03.93,Default,,0000,0000,0000,,just-- the mode really\Nloses its meaning.
Dialogue: 0,0:08:03.93,0:08:06.35,Default,,0000,0000,0000,,It might force you anyway to\Ntake the median or the
Dialogue: 0,0:08:06.35,0:08:07.53,Default,,0000,0000,0000,,mean in some form.
Dialogue: 0,0:08:07.53,0:08:10.70,Default,,0000,0000,0000,,But if you really do have\Nnumbers that one shows up a
Dialogue: 0,0:08:10.70,0:08:14.64,Default,,0000,0000,0000,,lot more than the other, then\Nthe mode starts to make sense.
Dialogue: 0,0:08:14.64,0:08:18.22,Default,,0000,0000,0000,,So, hopefully, this has given\Nyou a pretty good overview of
Dialogue: 0,0:08:18.22,0:08:25.40,Default,,0000,0000,0000,,how to represent the central\Ntendency of a data set.
Dialogue: 0,0:08:25.40,0:08:26.43,Default,,0000,0000,0000,,Very fancy word.
Dialogue: 0,0:08:26.43,0:08:28.18,Default,,0000,0000,0000,,But it's just saying, look,\Nwe're trying to represent with
Dialogue: 0,0:08:28.18,0:08:30.20,Default,,0000,0000,0000,,one number all of this data.
Dialogue: 0,0:08:30.20,0:08:31.81,Default,,0000,0000,0000,,And you might say, hey, why do\Nwe even worry about that?
Dialogue: 0,0:08:31.81,0:08:34.06,Default,,0000,0000,0000,,It only has seven numbers here\Nor eight numbers here.
Dialogue: 0,0:08:34.06,0:08:36.77,Default,,0000,0000,0000,,But you can imagine if you had 7\Nmillion numbers or 7 billion
Dialogue: 0,0:08:36.77,0:08:39.44,Default,,0000,0000,0000,,numbers, and you don't want to\Nshow someone all of that data.
Dialogue: 0,0:08:39.44,0:08:42.21,Default,,0000,0000,0000,,You just want to give someone a\Nsense of what those numbers
Dialogue: 0,0:08:42.21,0:08:45.34,Default,,0000,0000,0000,,are on average.
Dialogue: 0,0:08:45.34,0:08:49.42,Default,,0000,0000,0000,,And as we said, the arithmetic\Nmean is what I see being used
Dialogue: 0,0:08:49.42,0:08:53.17,Default,,0000,0000,0000,,the most. But in situations\Nwhere you might have numbers
Dialogue: 0,0:08:53.17,0:08:55.94,Default,,0000,0000,0000,,that would skew the arithmetic\Nmean, because they're so large
Dialogue: 0,0:08:55.94,0:08:58.67,Default,,0000,0000,0000,,or they're so small,\Nthe median might
Dialogue: 0,0:08:58.67,0:09:00.48,Default,,0000,0000,0000,,make a lot of sense.