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Measures of Center - By Anywhere Math

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00:0-1	Uh huh . Welcome to anywhere , Math . I'm
00:01	Jeff Jacobson . And today we're gonna talk about the
00:03	measures of center more specifically the mean , median and
00:08	mode . Let's get started . Before we get to
00:28	the first example , let's talk about what exactly a
00:30	measure of center is a measure . Center is just
00:33	a measure that describes a typical value for the data
00:38	set . In other words , if I gave a
00:40	test and I've got 100 students and I have all
00:45	the scores for all of the students on the test
00:47	and I'm wondering , well , how did they do
00:50	? How did my students do on that last test
00:53	? It's going to be really tough to tell when
00:55	I have 100 numbers , 100 grades . Uh ,
00:58	just looking at them all together . So instead we
01:01	use things like median mean and mode to get a
01:05	better idea of a typical value . So instead of
01:10	100 numbers , I might have The mean was an
01:14	85 , right ? That's the average . Okay ,
01:19	that gives me a better idea of how the students
01:21	did . So that's what measures of centers are .
01:24	They're just taking the data set and finding a typical
01:26	values kind of somewhere in the middle uh to give
01:30	you a better understanding of the data . So let's
01:32	get to example one . All right , here's example
01:35	one . What is the mean number of messages sent
01:38	? So here's our data . Uh So we're finding
01:41	the mean . That's gonna be the first measure of
01:46	center that we're going to talk about . So first
01:48	what is mean ? Another word for that is the
01:51	average . Okay . Finding the mean of a set
01:58	of data is the same thing as finding the average
02:00	of that data . And to do that , all
02:03	you do is you take the some of the data
02:08	divided by the number of values . Yeah . Okay
02:15	. So you add them all up , that's the
02:17	sum then . You divided by how many pieces of
02:20	data there are . So let's do that . Um
02:23	First thing what I like to do it's a good
02:27	thing when you're doing things like mean median mode .
02:29	The very first step is to put all the data
02:32	in order . So if I'm looking from least to
02:35	greatest well 82 is my least . Um Then let's
02:39	see Mm We've got 90 and the good point .
02:48	And finally on 25 just double check I checked them
02:53	all so I'm just gonna double check by counting them
02:56	. So I got 12345671234567 Perfect . Okay so I
03:03	got him off there in order . That's the first
03:05	step . Now I'm gonna add them , I'm gonna
03:07	find the song . I've got 721 as my son
03:14	. Now I just divided by the number of values
03:17	. Again there were 123-4567 . So 721 divided by
03:23	seven . When I divide , that's gonna give me
03:27	103 . So my mean is 103 text messages again
03:39	, that's like the average 103 Text messages . Here's
03:45	some to try on your own . Alright , example
03:54	to we're gonna have three parts of this example at
03:57	A B and C . So first a identify the
04:00	outlier . Well here's our data , the height of
04:03	ponies and inches . First what is an outlier ?
04:08	So an outlier ? Let's write this down . Boom
04:15	is a data value that lies kind of outside all
04:19	the other values . So what that means is an
04:21	outline is a data value that is either a lot
04:28	greater than all the other values or a lot less
04:31	. It's kind of outside the other ones that is
04:34	either a lot greater . Four left dandy the other
04:40	night . That's an outlier . Okay , so first
04:46	like always I'm gonna put my data in order and
04:48	that's going to help me see if there's any outliers
04:51	. Just to double check let's count . 123456789 10
04:57	12345 times two is 10 . Okay so I got
05:01	all my data in order . Now let's take a
05:02	look if I wanted to , I could make a
05:05	dot plot and that could help me see if there's
05:07	any outliers but hopefully looking here it should be obvious
05:12	. Can you see what the outlier is ? Well
05:15	if you notice we go from 28 all the way
05:17	up to 37 , 37 , 39 , 42 .
05:23	Here the data is all clustered pretty close together Except
05:28	the 28 , is quite a bit less than all
05:31	the other values , which means my outlier is 28
05:38	. Okay , let's try part B . Okay ,
05:41	Part B is just find the mean . So again
05:44	the mean is the sum of all your data values
05:46	divided by how many values there are . So if
05:49	we add all of this up and hopefully you get
05:52	379 , that's what I got . Uh So that's
05:57	the some I'm going to divide that by how many
05:59	there are . So 123456789 10 . There's 10 values
06:05	which is really nice because divided by 10 I can
06:08	just move the decimal place once to the left .
06:10	So my mean then is 37.9 . Remember my units
06:16	? All these values were inches , so 37.9 inches
06:22	. Okay , So the mean of the heights of
06:24	the ponies is 37.9 in . Let's try the last
06:28	part . Part C . All right , here's part
06:30	C . Of example to find the mean again .
06:32	But this time without the out letter . So if
06:35	we remember our outlier was 28 , so I'm gonna
06:39	find it without that that we're not going to include
06:42	that . Okay ? Um so now if again fined
06:46	the sum of all the data right ? 379 -28
06:51	because we took it away , I'm going to get
06:53	351 ah divided by . Now notice there's still aren't
07:01	10 values , we got rid of the outliers .
07:03	So now there's only nine values , so I'm dividing
07:05	by nine And let's see nine into 35 Goes three
07:11	times . Then there's 8 81 39 . Uh and
07:16	that's again 39" . So that is my uh ,
07:22	I mean without the outlier and notice they're different .
07:26	And the reason if you think about the outlier was
07:29	a lot less than the rest of my values .
07:33	So when I included the outlier in , when I
07:36	was calculating the mean , you can think of it
07:38	as it's bringing down that mean it's bringing down the
07:41	average if we don't include the outlier notice are mean
07:47	was was greater , it was hired . So keep
07:51	that in mind . When you're calculating mean , the
07:54	outlier , if there are some can really affect your
07:58	mean , they can either make it a lot greater
08:01	than it probably should be or a lot less than
08:04	it probably should be depending on where that outlier is
08:07	. Okay , here's some more to try on your
08:09	own . Okay , Example , three find the median
08:19	and mode of the bowling scores . So we've already
08:21	talked about one measure center , which was the mean
08:25	the other two we're going to talk about today are
08:27	the median and the mode . So first let's discuss
08:31	what exactly is the median ? And the median is
08:35	just the value in the middle . When you have
08:38	all the data in order from left from least to
08:41	greatest . The value that's exactly in the middle is
08:44	called the median . Okay . So yeah , so
08:46	let's write down the value in the middle when the
08:51	data is in order from least grades . Okay .
09:00	So let's write that down . And and I always
09:02	remember it median is the only one out of mean
09:04	median . And mode that has an eye . And
09:07	I think I for middle also has a nice .
09:09	So that can maybe help you remember ? Um Good
09:12	. So that's the median . Well , how about
09:15	the mode ? Mode is pretty simple . The mode
09:20	is just the most common value . Right ? Most
09:24	common value . And again mode has an O .
09:27	I think . Oh for most most and mode .
09:31	Uh So most common value . You can have one
09:34	mode right ? You can have more than one mode
09:37	. If there's a couple that are both occur the
09:41	same amount of times that are much more than the
09:43	others . You can also have no mode . And
09:45	no mode would be where there is exactly one of
09:49	each value . Right ? Not nothing is more than
09:52	the others . Then you would have no mode .
09:54	Um So that's what we're finding first . The very
09:59	first step . Remember put the data in order .
10:02	That's always our first step . So let's double check
10:04	. 123456789 10 12345 times two is 10 . Yes
10:11	. Okay . Now all I need to do for
10:15	the median is find the number that's exactly in the
10:17	middle . If you have an odd number of data
10:21	values right ? It's very easy because there's going to
10:25	be one of those values that are exactly in the
10:27	middle . Think about your hand , right ? Your
10:29	fingers , you have five fingers , which is why
10:32	you have a middle finger , right , odd number
10:36	. This one is right in the middle , you
10:38	got to to the left and you got to to
10:40	the right . Uh So if you have an odd
10:43	number is very easy . You can find the one
10:45	that's right in the middle . Some people like to
10:47	kind of cover up as they go from outside to
10:49	inside or cross off work their way in the middle
10:53	. Um But if you have an even number ,
10:57	we won't have a data value that's exactly in the
10:59	middle . So this is what we're gonna do Right
11:03	? We've got 10 here . So if I'm crossing
11:05	them off work my way to the middle notice now
11:13	I've got two values left . So in this case
11:17	what I'm gonna do is I'm going to find the
11:19	value that's exactly in the middle of those two .
11:22	And to do that sometimes you can do some mental
11:25	math and just know another way is just to adam
11:28	and then D . Vitamin too . So 100 and
11:31	35 plus 1 45 Uh is to 80 , Divide
11:40	that by two . And I get 1 40 right
11:44	? And if you look 135 and 1 45 .
11:47	Yeah 1 40 is exactly in the middle of those
11:50	two . Uh So 140 is my median exactly in
11:56	the middle . Okay let's check out the mode .
12:00	Now again the mode is the number that occurs the
12:03	most often the most common number . So notice all
12:07	of these ones only happened once , but then we
12:09	get to 160 and there's 2 160s . So that
12:14	is my mode . Mode is going to be pretty
12:16	quick . So the mode is 160 . Also with
12:22	motives kind of nice because that's the only measure of
12:25	center that you can use when you have data .
12:28	That's not numbers . So if you have , if
12:31	you're doing a survey and you're thinking , okay ,
12:32	what are students favorite colors ? Uh , and they
12:36	give you all their favorite color is blue and green
12:38	and purple and things you can't find the mean of
12:41	all the colours . You can't find the median of
12:43	all the colors , but you can find the mode
12:46	which one occurs the most often . So keep that
12:49	in mind when you're thinking of kind of what measure
12:52	of center to use when , Okay , uh ,
12:55	here's some to try on your own . Thank you
13:04	so much for watching . And if you like this
13:05	video , please subscribe . Mhm .

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