Interquartile Range (IQR) | Math with Mr. J - Free Educational videos for Students in K-12

Interquartile Range (IQR) | 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 how to find the inter
00:08	quartile range of a data set . Now the inter
00:11	quartile range gives us the spread of the middle ,
00:14	50% of our data compared to just range , which
00:19	gives us the spread of the entire data set .
00:22	So let's jump into the two examples that we're going
00:25	to go through together here in order to get this
00:28	down . Now the first example , we're going to
00:30	do a data set with an odd number of numbers
00:33	and the second example will be a data set with
00:36	an even number of numbers . Let's jump into our
00:39	first example here . And the first thing we want
00:42	to always do is put our data in ascending order
00:47	, which means least two greatest In the case of
00:50	this example , we are already in order so we
00:53	can move to the next step which says find the
00:57	medium . Now , steps two and 3 are kind
00:59	of combined here . These steps involve finding the court
01:04	, als the lower quartile , the median and the
01:07	upper quartile . But the first thing we need to
01:10	do is find the median as far as finding portals
01:14	. So the median is the middle of our data
01:18	set . In the case of this example we have
01:20	seven numbers , so we will have three numbers on
01:24	the left , three numbers on the right and the
01:27	number in the middle will be our median . It's
01:30	going to be 38 . So down here where it
01:33	says Q 2/50 percentile , I'm going to write 38
01:39	. Q two stands for quartile to which is the
01:43	same as the median . So Q 2/50 percentile and
01:48	median all mean the same thing . So once we
01:51	have the median we can find the lower and upper
01:54	court tiles . Let's start with the lower . So
01:57	we'll take a look at the lower half here and
02:00	we need to find the middle of that lower half
02:03	the median of the lower half . It's going to
02:06	be this 32 here . Since we have three numbers
02:09	it's going to be the Middle one . So Q
02:11	one quartile one means lower quartile . So let's write
02:16	32 upper quartile . We will take a look at
02:21	the upper half and find the middle or median of
02:24	that upper half and that's going to be our upper
02:27	quartile . So it's going to be that 50 .
02:31	So our upper quartile is 50 . Once we have
02:36	all of that information we can find the inter quartile
02:40	range . We take our upper quartile and subtract the
02:44	lower quartile . So our upper is 50 - Our
02:50	lower which is 32 . 50 -32 gives us an
02:57	inter quartile range of 18 . So I'm going to
03:04	draw some lines within our data to help us visualize
03:07	exactly what this all means . So our median was
03:12	38 . So let's draw a line there . Now
03:15	remember when we find chortled were splitting our data into
03:20	quarters or four equal parts And our inter quartile range
03:25	is the range of that Middle 50% . So our
03:30	lower quartile is 32 . Let's draw a line there
03:34	and then our upper quartile is 50 . So you
03:39	can see that we have our quarters or four equal
03:42	parts there . What we do when we take a
03:45	look at the inter quartile range is look at this
03:49	section here Our Middle 50% . So we found the
03:54	range or difference between 50 And 32 . Our upper
04:01	quartile and lower quartile . So that gave us that
04:04	inter quartile range , Let's move on to number two
04:08	and do another example . So for our second example
04:14	we're going to have a data set with 10 numbers
04:17	. So remember the first thing we want to do
04:19	is put the data in order from least to greatest
04:24	. This data is in order as well just like
04:27	the first one . So we can move to the
04:29	second step which is find the median . Now that
04:34	means the middle . In the case of this number
04:36	we have 10 numbers in our data set so we're
04:39	going to break it in half the midpoint . So
04:42	we have five numbers on the left and five numbers
04:45	on the right . So our median is going to
04:49	be right here between eight and 11 . It's between
04:53	two numbers there . So how we find the middle
04:56	we need to find the average um of eight and
04:59	11 and that's going to be our median . So
05:02	we can do that by adding eight plus 11 And
05:08	then divide by two . So eight plus 11 is
05:12	19 and 19 divided by two is nine and 5/10
05:19	or 9.5 . So that's our median . Let's do
05:24	our lower quartile next . So we need to take
05:27	a look at the bottom half here at the bottom
05:30	five numbers . And to find the middle or median
05:34	we have five numbers so we need to on the
05:36	left and two on the right . That leaves us
05:39	with six in the middle . So that's our lower
05:43	court tile . Let's take a look at our upper
05:47	quartile now . So the upper five numbers the upper
05:51	half , Two on the left , two on the
05:53	right . That leaves us with 14 as our middle
05:58	number or media in their and that's going to be
06:00	our upper quartile . So 14 now we find the
06:05	inter quartile range so take the upper quartile and subtract
06:10	the lower quartile . So 14 minus six that gives
06:17	us an inter quartile range of eight . Now let's
06:23	break this down and draw some lines to show our
06:26	core titles within the data . To really help us
06:29	understand both chortled and inter quartile range . So the
06:34	median was the middle right here , The lower quartile
06:40	is six , so right here and the upper quartile
06:44	is going to be 14 which is right here .
06:48	So we can see that we have our four equal
06:51	parts . Now inter quartile range were taking a look
06:56	at this Middle 50% . So the range of that
07:02	the upper quartile minus the lower quartile and that gives
07:07	us that inter quartile range . So there you have
07:11	it there is how you find the inter quartile range
07:15	. If you need more help with portals I'll add
07:17	links to my other videos down in the description .
07:20	So I hope that helped . Thanks so much for
07:23	watching until next time . Peace . Mm hmm .
07:29	Yeah

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