Measures of Variation - Free Educational videos for Students in K-12

Measures of Variation - By Anywhere Math

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00:0-1	Welcome to anywhere . Math . I'm Jeff Jacobson .
00:02	And today we're going to talk about the measures of
00:04	variation . Let's get started If you watch the last
00:26	video , you remember we talked about the measures of
00:28	center which included mean , median and mode . Well
00:31	today we're going to talk about the measures of variation
00:34	and measures of variation is just a measure that describes
00:37	the distribution of the data . You can think of
00:41	it as how spread out as the data . Is
00:43	it really , is it clustered all together in one
00:46	area or is it really spread out ? Okay ,
00:48	so that's what we're talking about today . Let's get
00:51	to our first example . Alright , example , number
00:54	one find and interpret the range in length of burmese
00:58	pythons . So again today we're talking about measures of
01:01	variation and range is a way to do that .
01:06	Range is a way to find how spread out our
01:08	data is . So let's talk about how to find
01:10	the range . Well , it's pretty simple to find
01:13	the range . You just find the difference . So
01:16	we're subtracting difference between okay the greatest value and the
01:30	least value . Okay that's all it is . You
01:38	find the greatest value and you subtract the least value
01:41	and your difference is the range . Um So first
01:45	like always we always put our data in order from
01:49	least to greatest first this is no different . So
01:52	that's what we're gonna do . So I'm gonna do
01:54	that really quick . Okay I got my data in
01:56	order again before I do anything I would just want
01:59	to double check . So I'm going to count 123456789
02:03	10 123456789 10 . So I'm good so now it's
02:09	very simple . Find the range the difference between the
02:11	greatest value in the least value Here is my greatest
02:14	value 18.5 ft here is my least . So the
02:18	difference I'm going to subtract 18.5 Five would give me
02:23	a range of 13.5 ft . Mhm . Okay .
02:31	And that is my range . Here's one to try
02:33	on your own example to find the inter quartile range
02:45	of the following data set . Now before we do
02:47	that , let's talk about what our core titles .
02:50	Uh Well just like the word implies chortled . You
02:55	think of quarters and portals of a data set ?
02:58	They divide or split divide the data set in four
03:08	equal groups . Okay . For equal groups of quarters
03:15	. Right ? So we have a first quartile and
03:19	the third quartile and then we have our median .
03:22	So let's get started when we're doing this . The
03:25	first thing you're going to do Before you start doing
03:28	the 1st and 3rd quartile is you're gonna find the
03:30	media , right ? And remember median means middle ,
03:33	it's whatever number is exactly in the middle . In
03:36	this case though we have 123-456-789-10 . Which is an
03:41	even number . So we won't have a number exactly
03:44	in the middle . That's part of our data set
03:47	. So instead we're gonna have to in the middle
03:48	. So let's see 12345 and six . These two
03:53	numbers we have to find out exactly what halfway between
03:57	and you can do that in your head . We
03:59	don't have to add and divide by two . So
04:01	our media and then is 29 . That's our median
04:07	. Okay now the median splits it in half .
04:11	Right ? Here's half of our data . Here's the
04:14	upper half . Okay so let's kind of label that
04:17	that is our lower half of data . This is
04:24	our upper half of data . Okay so we split
04:31	in half . But remember we're talking about quartile .
04:34	So we need to split these in half so that
04:37	we have quarters . So to do that we do
04:40	the same thing . We find the median of the
04:44	lower half and we find the median of the upper
04:47	half . Well now this is nice . We've got
04:49	five numbers just like you got five fingers so ones
04:52	in the middle . So this 22 we call that
04:57	that is the first portal or you might see people
05:04	call it the lower portal same thing . Okay Now
05:11	up here we find the median of the upper half
05:13	of our data . That would be 32 right in
05:17	the middle . So that is our third Coretta .
05:23	Because if you want to you can kind of think
05:26	of it . Here's our first the media is kind
05:28	of the second I guess you could say . And
05:30	uh this would be the third quarter to or again
05:35	you can call it the upper . Mhm chortled same
05:39	thing . Okay so now we have Our court trials
05:46	. Okay . 20-29 is our median and then 32
05:50	. Uh Now let's talk about how to find the
05:52	inter quartile range . Well inter quartile that just means
05:57	within the core tiles , the range of within those
06:01	quartz out . So to do that . I'm just
06:04	gonna call it . I like you are inter quartile
06:08	range . All we do is subtract or find the
06:12	difference of the third quarter . Hell in the first
06:14	quarter mile . Okay so pretty simple . 30 to
06:18	minus 22 . Well give me an intercourse . A
06:22	range of 10 and that is my final answer .
06:27	So that's inter quartile range . Let's try another example
06:30	. Alright example number three finding and interpret the inter
06:32	quartile range of the data . So we're doing the
06:35	same thing as example . To remember the first step
06:38	when we're finding the inter quartile range is to find
06:41	the median . We've got 12 . These are all
06:45	top speeds of 12 different sports cars so we've got
06:48	12 . So there's two in the middle 123456 the
06:52	6th and 7th . So right in the middle of
06:55	those two would be 247.5 . That's gonna be my
07:03	median . And if you can't do that in your
07:06	head remember you can add them together and divide by
07:08	two . So here is my lower half . Okay
07:15	and here is my upper half of the data .
07:22	Mhm . So now I gotta find those portals .
07:25	My first quartile I'm gonna find the median of these
07:29	pieces of data . So we got 123456 And even
07:33	number again . So let's see . 123 and four
07:37	it would be right here . 235 is my first
07:42	quartile . I'll just put uh yeah I'll just put
07:46	Q . One . How about that Q . One
07:49	? That's the first quarter , top 123 and four
07:55	Right there which would be 255 would be my third
08:01	quartile so now I can find the inter quartile range
08:05	. Remember to do that we just find the difference
08:08	. uh so so I'll say inter quartile range is
08:14	going to be 255 -235 which would give me a
08:21	range of 20 and that's MPH . 21 mph .
08:29	Okay so that's my inner core to arrange , let's
08:33	interpret what that means . Well remember this is the
08:38	middle half of our data from first quarter mile to
08:41	third quarter , that's the middle half of our data
08:44	. So that means that the range in top speeds
08:48	of the middle half of these cars is no more
08:52	than 20 mph . Okay , that's how we can
08:55	interpret that . Let's try one more example . All
08:58	right , here's our last example . Check for outliers
09:01	from example three . So I left all of our
09:03	work , we've got our inter quartile range here which
09:06	was 20 . Now for outliers a lot of times
09:09	it's gonna be obvious if you have an outlier but
09:11	if it's not obvious and you're not sure we have
09:14	formulas that we can use to tell us if we
09:16	have outlier , so these are them . Uh you
09:21	won your first quartile -1.5 times your inter quartile range
09:26	that result . If you have any values that are
09:29	less than that , it would be an outlier .
09:32	Same thing here . You take your third quartile and
09:35	you add 1.5 times the inter quartile range that result
09:39	. If you have any values that are greater than
09:42	that , those would be outliers as well . So
09:45	let's check real quick . Uh So here . Corta
09:48	one with 235 -1.5 Times 20 which was my inter
09:56	quartile range . So that's going to be 235 -30
10:02	is 205 . So do we have any data values
10:08	that are less than 205 and we don't to 20
10:11	was our lowest . So we're okay on this side
10:14	. No outliers down here let's check up here ,
10:18	Chortled three is 255 . We're going to add 1.5
10:25	times the intercourse a range which was 20 . So
10:29	that's 255 plus 30 which gives us to 85 .
10:36	Do we have any data values that are greater Then
10:39	to 85 and no 2 70 was the greatest value
10:44	. So there are no outliers . Okay ? Here's
10:48	some to try on your own . Thank you so
10:57	much for watching . And if you like this video
10:59	please subscribe . Mhm .

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