Box-and-Whisker Plots - Free Educational videos for Students in K-12

Box-and-Whisker Plots - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson . And
00:02	today we're gonna learn how to make Box and Whisker
00:06	plots . Let's get started . All right . So
00:26	today we're talking about box and Whisker plots . Now
00:29	in a second you'll see exactly why they're called box
00:32	and whisker plots . But before we do that ,
00:35	it's important to know what is the whole point of
00:39	a box and Whisker plot . Why would you ever
00:41	make one ? What does it tell you about the
00:43	data ? So a box and Whisker plot shows the
00:47	variability of a data set . Now , if you
00:51	haven't learned about measures of variation , go back and
00:56	check out this video here that I made a little
00:58	bit ago about measures of variation . Box and Whisker
01:02	plot uses those same measures . But we just take
01:05	it take those measures and make it a lot easier
01:08	to look at um than just looking at the numbers
01:11	. And to make a box and Whisker plot ,
01:13	you need something called a five number summary . The
01:16	five number summary is all five measures are values that
01:20	you need to have to be able to make that
01:22	box and whisker plot . So first you need to
01:25	know the least value . That's one you need the
01:31	greatest value as well . Uh You also need the
01:37	first quartile , I'll call that Q . One .
01:40	You also need the third quartile Q . Three and
01:43	finally you need the median . Those are the five
01:51	the five numbers that you will need to know before
01:54	you can start to construct your box and Whisker plot
01:56	. So let's get started with our first example .
01:59	Alright example one make a box and whisker plot for
02:02	the following ages in years . So here is my
02:04	data set as always . The very first step is
02:08	to put it in order from least to greatest .
02:10	Okay and then as always you want to double check
02:14	. I really can't stress that enough because if you
02:16	forget a number , everything could be wrong . So
02:19	make sure you check . So let's see . 12
02:22	11 12 123 and 10 11 12 . Good .
02:25	So I'm happy now I need to know those five
02:29	numbers . I need to know my least Value ,
02:32	my greatest value . Q one , Q 3 .
02:35	And my median . So first my least 14 .
02:40	That's easy . My greatest . 38 . Now let's
02:44	find the median . So right in the middle there
02:48	30 is my median . Now I find the median
02:53	of my lower half for Q one . So halfway
02:57	between 20 and 26 is going to be 23 .
03:02	That's my cue one which would be 34 . That's
03:06	my cue three . So I've got my five number
03:10	summary , least value Q . One , median Q
03:14	. Three and my greatest value . Now I'm ready
03:17	to do uh the box and whisker plot first .
03:21	You're going to make a number line and your number
03:23	line Does't need to start at zero . You start
03:26	wherever your least value is . So my least value
03:30	is 14 . So that's where I'm gonna start .
03:32	I need to go all the way up to 38
03:34	. So I think I'm gonna count by twos .
03:36	I don't want to count by one because that's gonna
03:38	take too long . So I've got my number line
03:40	that's ready to go now it's time to make the
03:43	box and Whisker plot . So at your least value
03:48	you're gonna put a dot and we're gonna put it
03:50	you're you're used to put in the points on the
03:53	number line . This is slightly different , you put
03:55	everything above it . So that's easy to see the
03:58	numbers so there's a point . Um And then at
04:03	Q . One I'm not going to put a point
04:05	, I'm going to draw a vertical line directly above
04:09	that value . So my Q . One is that
04:12	23 ? So 23 would be here . I'm gonna
04:16	draw a vertical line . Okay . Just kind of
04:20	like what we did there , vertical line there .
04:22	Same thing at the median media is 30 a vertical
04:26	line above vertical line . Q . Three . The
04:29	exact same thing . 30 for vertical line . And
04:32	then finally my greatest value . I do the same
04:35	thing as my lease . And I put a point
04:37	between your first quartile or Q . One and your
04:41	third quartile . That's where the box from . Box
04:45	and whisker plot is . So you basically just connect
04:49	these lines . So that's my box . Then you
04:52	can probably guess here is where we draw the whiskers
04:56	. So just a line coming out from the middle
05:01	, not from the bottom , not from the top
05:03	, just right in the middle . So these are
05:05	the whiskers right ? They look kind of like cat
05:08	whiskers I guess . And this is the box and
05:11	that is your box and Whisker plot . Here's one
05:14	to try on your own . Alright , before we
05:21	move on to the next example , I want to
05:23	kind of tell you what the whole point of the
05:26	box and whisker plot is . If you remember at
05:28	the beginning of the video we said it it shows
05:30	the variability , how the data is spread out the
05:33	distribution . If you remember this line right here represents
05:38	the first quartile and when you think of portals ,
05:41	you think of quarters or 1/4 . And that's important
05:46	to realize because this whisker right here from the least
05:51	value to my first quarter mile represents about 1/4 of
05:59	the data . This other whiskers same thing about 1/4
06:07	of the data . Every whisker is always going to
06:10	represent about 1/4 of the data . It's not always
06:12	going to be exactly 1/4 but it's going to usually
06:15	be pretty close to 1/4 of the data . Now
06:18	the box here is my first quartile here is my
06:22	third quarter . Tell if you remember inter quartile range
06:26	, we're talking about the middle half . So the
06:29	box yeah Is about 1/2 of the data . And
06:38	if you want to break it down even more from
06:41	the median to the first quartile here . This little
06:44	section that's 1/4 in this little section here is 1/4
06:50	. So put them together . That's what makes the
06:52	whole box one half . So keep that in mind
06:55	. I would put this in your notes . That's
06:56	going to help you hopefully understand the next example are
07:01	an example to the box . And whisker plot over
07:03	on the right here shows the body mass index or
07:07	B . M . I . Of 1/6 grade class
07:10	. So part a . Is asking what fraction of
07:13	the students have a bmi of at least 22 .
07:17	So if we look over at the box and whisker
07:19	plot you'll see 22 is right at that third quartile
07:24	. And at least that's the key word there at
07:28	least . Or key phrase At least means 22 or
07:32	greater . Well greater 22 or greater is talking about
07:37	that . Right . Whisker . That upper whisker .
07:40	And remember we just said those whiskers always represent about
07:46	1/4 of the data . So that's our answer .
07:49	What fraction the students have a Bmi of at least
07:51	20 to about 1/4 of the students . Let's look
08:01	at B . Are the data more spread out ?
08:04	Below the first quartile or above the third quartile ?
08:09	So below the first quarter's out . Well that's that
08:12	left whisker that lower whisker and above the third .
08:16	Well that's the right whisker . So How can we
08:20	tell which 1 uh that where the data is more
08:24	spread out ? Well if you look the length of
08:28	those whiskers are not the same . The left one
08:31	is much shorter than the right Whisker . The right
08:34	whiskers a lot longer . Which would tell you that
08:38	that data is much more spread out . So the
08:43	answer to be are the data more spread out below
08:46	the first quarter L . Or above the 3rd 3rd
08:49	quartile . So the answer is going to be above
08:52	the third quartile because that right whisker is longer .
08:56	Let's try part C . Okay part see find and
08:58	interpret the I . Q . R . Or inter
09:01	quartile range . If you remember from measures of variation
09:04	. Inter quartile range . We get that from taking
09:07	the third quartile and subtracting the first quartile . So
09:11	it's the range of that middle half of our data
09:14	. Or in a box . And whisker plot .
09:16	It's the range of the box . So third quartile
09:21	. That was 22 minus the first quartet which is
09:25	19 . So our I . Q . R .
09:30	Is equal to three . Okay . And let's uh
09:35	let's interpret that . So we would say the middle
09:38	half of students . Bmi is varied by no more
09:42	than three . Here's one to try on your own
09:49	. Okay . Lastly we're going to talk about the
09:51	shapes of box and whisker plots . The first one
09:53	is called skewed left . And if you notice the
09:57	whisker on the left is longer than the whisker on
10:00	the right and more of the data is on the
10:03	right side . We call that skewed left . It's
10:07	the exact same thing as how we describe hissed a
10:11	grams . The shape of history grams . So if
10:13	you've already seen that video , this should look very
10:15	familiar . Um If the two whiskers are about the
10:20	same length and the box , the media is kind
10:23	of right in the middle . The data is not
10:26	more to one side or the other . We call
10:29	that symmetric . Um And then finally the last one
10:32	skewed right . If that whisker is longer on the
10:35	right , um than the one on the left and
10:39	more of the data is towards the left than we
10:42	call that skewed right . Here's one to try on
10:45	your own as always . Thank you so much for
10:52	watching . And if you like this video , please
10:53	subscribe .

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