Mean Absolute Deviation (MAD) | Math with Mr. J - Free Educational videos for Students in K-12

Mean Absolute Deviation (MAD) | Math with Mr. J - By Math with Mr. J

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00:0-1	Welcome to Math with mr J . In this video
00:05	, I'm going to cover mean absolute deviation . The
00:09	mean absolute deviation gives us the average distance between each
00:13	number in our data set and the mean . So
00:16	how far each number is from our mean , on
00:20	average . And think about it . I mean means
00:23	average absolute means we're going to be working with positive
00:28	distances and then deviation means something differs , it's different
00:33	than the usual . So the average distance that these
00:36	numbers differ from the mean . Now the mean absolute
00:40	deviation gives an idea about how much our data differs
00:45	, so how consistent or inconsistent it is . Does
00:49	the data differ greatly ? Is it all close in
00:52	value or somewhere in between ? This is a measure
00:56	of spread . It tells us how spread out our
00:59	data is . Let's jump into our example and see
01:02	exactly how we do this . The first step that
01:05	we need to do is find the mean . So
01:08	add up all of the numbers and then divide by
01:11	how many numbers we have . So let's calculate the
01:14	mean , three Plus three plus 5 plus eight plus
01:23	eight plus 12 . So we add all of the
01:28	numbers and then divide by how many numbers we have
01:32	and we have six . So three plus three is
01:36	six plus five is 11 plus eight is 19 plus
01:42	eight is 27 plus 12 , gives us 39 And
01:48	we divide by six . So 39 divided by six
01:52	, gives us six and 5/10 or 6.5 . So
01:58	that's our mean . Once we have that we can
02:01	move to the next step . So we need to
02:04	find how far each number is from the mean .
02:08	We do this by finding the absolute value of each
02:12	number minus the mean , we want the absolute value
02:16	. So we get positive distances . Now there are
02:19	different ways to do this step as far as set
02:21	up goes much like most things in math , I've
02:24	seen it set up vertically horizontally , or even in
02:28	tables , whatever works best for you , I'm going
02:31	to calculate this horizontally so side to side . So
02:34	let's take each number , subtract the mean and find
02:38	the absolute value of that . And we'll start with
02:41	three . So the absolute value of three -6 and
02:47	5/10 plus , I'm going to separate each of these
02:52	with an addition sign because looking ahead , our next
02:56	step , we're going to add these deviations . So
03:00	we have another three -6 and 5/10 And we will
03:08	continue our way through our numbers . So five next
03:14	now I'm running out of room so I'm going to
03:16	go to the next , lying down , so to
03:19	speak , And we have an eight , A couple
03:26	more here , so another eight and then lastly 12
03:39	, so let's find the absolute value of each of
03:42	these . Starting with three minus six and 5/10 .
03:47	That's going to give us a negative three and 5/10
03:50	. The absolute value is going to be a positive
03:54	three and 5/10 . So I'm going to make note
03:56	above and below these . So we have two of
04:02	the three minus six and 5/10 . So now we
04:06	have five minus six and 5/10 . That's going to
04:10	give us a negative one in 5/10 . So the
04:13	absolute value is going to be a positive one in
04:17	5/10 . Eight minus six and 5/10 gives us a
04:23	positive one in 5/10 . So the absolute value is
04:26	a positive one in 5/10 Same for this eight .
04:31	And then the 12 12 minus six and 5/10 gives
04:35	us a positive five and 5/10 . So the absolute
04:39	value is a positive five and 5/10 . So here
04:44	are all of our distances for the numbers within our
04:49	data set . So their distance from the mean ,
04:53	Once we have this information we need to find the
04:56	average of those distances . So we add them and
05:00	then divide by the number of numbers we have within
05:03	our data set . So those are steps three and
05:06	four . So let's add and divide . We'll start
05:09	by adding . So we have three and 5/10 plus
05:13	three and 5/10 plus one in 5/10 plus one in
05:19	5/10 Plus one in 5/10 Plus five and 5/10 .
05:27	So adding those , we're going to get a sum
05:30	of 17 , so that's our total amount of distance
05:35	from the mean , if we add all of our
05:38	distances . So once we have that , let me
05:41	write 17 here . So we got 17 , we
05:44	need to divide by the number of numbers within our
05:48	data set . And that's going to give us our
05:50	mean absolute deviation . So 17 divided by six .
05:56	So 17 divided by six is going to give us
05:59	an answer of 2.83 and that three is going to
06:03	be repeating . So I'm going to round to the
06:06	100th place , it's going to give us two and
06:10	83/100 . Again , the answer is going to be
06:14	2.83 and that three is going to be repeating .
06:18	So I'm rounding to the 100th place . So our
06:22	mean absolute deviation is two and 83/100 . That's the
06:28	average distance for each of our numbers within the data
06:31	set , as far as distance from the mean .
06:34	Again , this is a measure of spread . So
06:37	how spread out are the numbers in our dataset ?
06:41	Now , a very important note here when comparing or
06:45	looking at different mean absolute deviations . The higher the
06:49	mean absolute deviation is , the more spread out your
06:52	data is , The lower the mean absolute deviation is
06:56	, the closer your numbers are together , so there
07:00	you have it . There is how you calculate the
07:02	mean absolute deviation . I hope that helped . Thanks
07:06	so much for watching until next time . Peace .
07:11	Mhm . Yeah .

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