Quartiles | Lower Quartile, Median, and Upper Quartile | Math with Mr. J - Free Educational videos for Students in K-12

Quartiles | Lower Quartile, Median, and Upper Quartile | Math with Mr. J - By Math with Mr. J

Transcript


00:0-1	Welcome to Math with Mr J . In this video
00:05	, I'm going to cover quartile so the lower quartile
00:09	, the median and the upper quartile chortled divide data
00:13	sets into quarters . Simply put we break the data
00:16	up into four equal parts . The lower quartile will
00:20	give us the 25th percentile So the 25% or 1
00:25	4th mark . The median gives us the 50th percentile
00:29	, so the middle of our data and then the
00:32	upper quartile will give us the 75th percentile , the
00:36	75% or 3/4 mark . All of this information helps
00:42	us understand and interpret data chortled zara building block for
00:47	other topics involving data . So an understanding of this
00:51	will help you moving forward . We have two examples
00:54	that we're going to work through . One example will
00:57	have an odd number of numbers in the data set
01:00	and the other will have an even number of numbers
01:03	in the data set . Let's jump into our first
01:06	example and in this example we're going to work with
01:09	the data set with an odd number of numbers .
01:12	So let's jump into it . And we need to
01:14	start by ordering our data from least to greatest .
01:18	So ascending order . Now in this example the data
01:22	is already in order . But if you're working with
01:25	the data set that's not in order , make sure
01:28	least two greatest or ascending order is the first thing
01:33	you do . The next step we need to find
01:36	the median also referred to as Q2 , which means
01:41	chortled to or the 50th%ile . So this is going
01:45	to be the middle of our data . Now for
01:49	this example we have nine numbers in our data set
01:53	. So the middle is going to be the fifth
01:56	number . That's going to give us four numbers on
01:59	the left and four numbers on the right . So
02:02	the fifth number is this eight right here , that's
02:06	going to be our median . So let's put 84
02:12	quartile two or the 50th percentile or the median .
02:17	Now that's the middle point . So what we need
02:20	to do now , we need to find the median
02:22	of the lower half and the median of the upper
02:26	half . The median or middle of the lower half
02:29	is going to give us the lower quartile and the
02:33	median of the upper half or middle of the upper
02:35	half is going to be the upper quartile . So
02:39	let's take a look at the lower half first and
02:42	we have four numbers here . So we need to
02:44	find the middle . So we have an even number
02:48	of numbers within that lower half . We have four
02:51	numbers , so we don't have a specific number sitting
02:55	directly in the middle . So we're going to have
02:57	to take a look at the middle two numbers the
03:00	two and the four right here . Now we need
03:04	to find what's directly in between that two and 4
03:09	. Now we can think this through and we know
03:12	three is in between two and four but sometimes it's
03:16	not going to be that easy to figure out .
03:19	So we need to do it mathematically , I'll show
03:21	you how to do that as well and we'll see
03:23	if we still get three . So what we need
03:26	to do if we need the median in between two
03:29	numbers , we find the average , so we need
03:32	to add then divide by two . So we have
03:35	two plus four And then divide by two . That's
03:40	going to give us our average . So two plus
03:44	4 is six and six divided by two gives us
03:50	three . So we still got three , so three
03:53	is our Quartile one or lower quartile eight is our
04:00	cue to to recap so our median . And now
04:03	we need to end with finding our upper quartile .
04:07	So we'll take a look at the upper half and
04:12	we have four numbers here . So an even number
04:14	of numbers , so we need to take a look
04:16	at the midpoint Were middle of our two middle numbers
04:21	here , so what's going to be in between 10
04:25	and 14 ? So let's find the average between those
04:28	two numbers and that's going to give us the median
04:31	of that upper half . So we do 10 plus
04:36	14 And we divide by two to find the average
04:41	. So 10 plus 14 is 24 In 24 divided
04:46	by two is going to give us 12 , So
04:51	12 is going to be our upper quartile . So
04:55	let's split this data set into quarters or four equal
05:00	pieces to give you a visual of splitting this up
05:04	. So we know our 25th%ile or lower quartile is
05:09	at three which is right in between two and 4
05:12	. So I'm going to draw a line , Our
05:15	median or 50th%ile is this eight right here ? So
05:20	let's draw a line And then our upper quartile or
05:25	75th%ile is in between the 10 and 14 at 12
05:31	. So you can see that we have one ,
05:36	two , three and four equal pieces . That's what
05:42	portals are . We split our data set into four
05:46	equal pieces now that we know how to find the
05:50	lower quartile median and upper quartile of a data set
05:54	with an odd number of numbers . We're going to
05:56	take a look at a data set with an even
05:59	number of numbers . So let's jump into it .
06:02	In this example we're going to work with a data
06:05	set with an even number of numbers and we need
06:08	to start by ordering our data from least to greatest
06:12	. So ascending order in this example we are already
06:17	in order . But if you're working with some numbers
06:19	that are out of order make sure you start with
06:22	ordering those numbers from least to greatest . So let's
06:27	move on to step two which is find the median
06:30	. Now we have eight numbers within this data set
06:33	, so we're going to have four on the left
06:36	and four on the right . That's going to give
06:38	us our middle . It's going to be in between
06:42	the 21 and the 28 . So we need to
06:45	find the middle between those two numbers . And we
06:49	can do that by finding the average . So let's
06:52	come down to where it says Q2 which stands for
06:55	quartile to which is the same thing as the median
06:58	, it's the 50th%ile . So to find the average
07:02	, we need to add those numbers 21 plus 28
07:07	And then divide by two . So 21 plus 28
07:12	gives us 49 And 49 divided by two is going
07:18	to give us 24 and 5/10 or 24 a half
07:24	. That's going to be our median , that's the
07:27	middle point of our data set there . So once
07:32	we have our median we need to find the median
07:35	of the lower half and median of the upper half
07:38	. The median or middle of the lower half is
07:41	going to be the lower quartile and then the median
07:44	or middle of the upper half is going to be
07:46	the upper quartile . So let's do the lower half
07:51	first . So the lower four numbers , we need
07:54	to find the middle of those lower four numbers .
07:58	And since we have an even number of numbers there
08:00	, we don't have a number sitting directly in the
08:04	middle . So we're going to need to take a
08:05	look at the two numbers in the middle and find
08:10	what's in between . That's going to give us our
08:13	median again because we don't have one specific number sitting
08:17	in the middle there . So we need to take
08:19	a look at the two in the middle and find
08:22	what's in between and just like the median , we
08:24	can do that by finding the average Or in the
08:27	case of this one we can probably think it through
08:30	and we know that 16.5 is in between 16 and
08:34	17 . But let's solve it mathematically as well .
08:38	So again average add 16 Plus 17 and then divide
08:44	by two . So 16 plus 17 is going to
08:49	give us 33 divided by two and we get 16
08:55	and 5/10 or 16.5 . That's going to give us
08:59	our lower quartile . So that's the 25% mark within
09:05	our data set there . The 25th%ile . So once
09:09	we have that we can do the upper court tile
09:12	. So let's take a look at the upper half
09:16	and find the middle or median of that upper half
09:19	. Now we have four numbers again , an even
09:22	number of numbers , so we're not going to have
09:24	one specific numbers sitting in the middle . We're going
09:27	to take a look at the two middle numbers which
09:30	31 and 39 find the midpoint between those two .
09:36	That's going to give us our median of that upper
09:39	half and we can do that by finding the average
09:42	. So add 31 plus 39 divided by two .
09:50	31-plus 39 is going to give us 70 , yeah
09:56	, 70 divided by two , gives us 35 .
10:00	So 35 is going to be the upper quartile ,
10:04	it's the 75% mark within our data . The 75th%ile
10:11	. So those are our core titles . The lower
10:14	quartile is 16.5 . That's the 25th percentile . Then
10:19	we have the median which is 24 a half .
10:22	That's the 50th percentile , the middle of our data
10:26	set and then for our upper quartile we have 35
10:31	. So that's the 75th percentile . I'm going to
10:34	draw some lines within our data set there so we
10:37	can visualize where these quartile are and how it breaks
10:41	our data into four equal parts . So 16.5 is
10:46	going to be right here , Right in between that
10:49	16 and 17 that we talked about earlier , The
10:53	median , which is the middle point is right here
10:57	in between the 21 and 28 , like we talked
11:00	about earlier and then we have our upper quartile In
11:04	between the 31 and the 39 . So you can
11:08	see that we have one , two , three and
11:15	four equal pieces . This line right here represents the
11:20	25th%ile . This line is the 50th And then this
11:25	is the 75th . So there you have it .
11:29	There is how you find the lower quartile , the
11:31	median and the upper quartile . I hope that helped
11:35	. Thanks so much for watching until next time .
11:39	Peace . Mhm .

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