Frequency Tables and Histograms - Free Educational videos for Students in K-12

Frequency Tables and Histograms - By Anywhere Math

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00:0-1	Welcome to anywhere , Math . I'm Jeff Jacobson .
00:01	And today we're gonna learn how to make a frequency
00:04	table and then from that frequency table how to turn
00:07	it into a history graham . Let's get started .
00:28	Okay , today we're gonna talk about frequency tables and
00:30	hissed A grams . We're gonna start off with frequency
00:33	tables . So a frequency table , it's just a
00:36	table . Uh that organizes your data into intervals and
00:40	intervals that are the same size . So let's look
00:43	at our first example and learn how to make a
00:45	frequency table . Okay , here's example one make a
00:48	frequency table showing the shoe sizes of the students in
00:51	the class . So here is my data for their
00:53	shoe sizes . Uh it's already in order . So
00:56	that's very nice . So let's get started on the
00:58	frequency table . Now freaks . The table is very
01:00	simple . It's just two rows . The top row
01:03	is about your data , whatever your data is about
01:05	. So in our case it's shoe sizes on the
01:08	bottom is always gonna be frequency . Second step it
01:12	to decide what you want to make your intervals .
01:15	You typically want to be around four or five intervals
01:20	unless you have a whole lot of data . And
01:22	then you can you can use you'll probably use more
01:25	intervals than that . Um But if you only break
01:28	it up into two intervals , Well that's not going
01:31	to look very good for your for your instagram .
01:34	So I'm going from four all the way up to
01:36	10 . So I think I'm gonna go for my
01:39	intervals by two . So I'm gonna go from 4
01:43	to 6 for my first interview now Your teacher or
01:50	your book might show you something like this . So
01:53	4-6 Then uh 79 , 10 - 13 . And
01:59	that can work as long as you have integers for
02:03	your data . But if you notice , Well if
02:07	I go from 46 and then 7-9 . Well what
02:09	about a 6.5 ? There's a 6.5 that would have
02:13	no place to go . So instead you would do
02:17	it like this 4-6 . This one would be 6-8
02:21	. 8 to 10 And 10 to 12 . So
02:27	notice there there are no gaps . So even if
02:30	we have decimals Uh there will be a place for
02:34	him . So now all I need to do is
02:37	find out the frequency of my data values in each
02:41	of these intervals . So I just count . Let's
02:43	see from 46 . How many students had shoe size
02:47	is between four and 6 ? Well here's one 4
02:53	, 2 , Now here's A six . Now the
02:57	question is do I put this six ? Do I
02:59	count it here or do I count it here ?
03:03	And you have to have a rule because you don't
03:06	want to count them . You don't want to count
03:08	that six twice . So the rule is you include
03:12	the value on the left . So you should probably
03:15	write this down include the left , not the right
03:26	. Yeah . And if you follow that rule you'll
03:29	be fine . So this six , I'm not going
03:33	to include it here . Right . This basically is
03:35	from four all the way up . Right . Up
03:38	to six , not including six . So 1234 There
03:42	were four for students that had a size in that
03:48	interval . Okay , now 66-8 here , I include
03:53	the value on the left . So I'm including that
03:55	six . So here's at six , there's 12 345
04:03	. I'm not including that eight . So I've got
04:05	five here . Right . You see that now here
04:08	again include the value on the left , not the
04:10	right . So I include the eight in this interview
04:12	. Not to 10 . So there's 1 2 .
04:17	Right ? I don't include the 10 and then this
04:19	10 is included here . So just one . Okay
04:22	, now always , always , always double check to
04:25	make sure you didn't miss any or or include some
04:29	numbers twice . And we can do that by just
04:31	adding . So that's 9 10 11 12 . Right
04:36	. So I should have 12 values here . 123456789
04:41	10 11 12 . And I'm good . Now for
04:45	part B we're gonna learn how to turn this into
04:48	a history Graeme . Ok . Part B . Making
04:51	instagram using the frequency table and it's pretty simple .
04:54	Uh First step draw your axes and label them .
04:58	So I'm gonna start like that and sorry , that's
05:03	not perfect . Um shoe sizes whatever you have on
05:07	top , that's always going to go on your X
05:11	axis , which means my Y axis . That is
05:13	labeled frequency . You got that label now we need
05:15	to figure out well what do I want to be
05:17	counting by ? Uh Well frequency I go from one
05:21	all the way up to five so we can easily
05:23	just count by one shoe size . We use the
05:26	exact same intervals that you have here . Okay so
05:29	there's no you don't have to think about it at
05:32	all . Um So the first one we're starting at
05:36	four , so I'm gonna put a four here and
05:38	that's going to go to six . So I put
05:40	a six there . Okay I don't need to do
05:43	this , I don't need to do 4 to 6
05:46	. Okay there are no gaps so I'm just gonna
05:48	go 46 Here would be eight . So from here
05:53	to here represents 6-8 uh 10 and finally 12 .
06:00	So I've got all that ready now I'm ready to
06:02	draw my bars and the bars of my hissed a
06:06	gram . The height Is whatever you had for the
06:09	frequency . Right ? So from 4 to 6 that
06:13	interval I had a frequency of four . So from
06:18	here to here all the way up to four draw
06:23	bar the difference with his diagrams and bar graphs .
06:27	It looks very similar to a bar graph , but
06:29	there should be no gaps . Okay so now here
06:33	6-8 , The frequency was five , so 6-8 ,
06:37	It's up to five just like that notice they're touching
06:43	, that's what it should look like for a history
06:45	Graham . 8 to 10 , frequency of 8 to
06:48	10 had a frequency of two . So that is
06:52	right about there . and finally from 10 to 12
06:57	the frequency was only one and that's gonna be just
07:02	like that . Okay . Um finally I'll add a
07:06	little uh title at the top . You don't need
07:10	a key for instagram , so I'll just say for
07:14	the title students shoe size , here's one to try
07:21	on your own . Okay , example to instead of
07:31	making it instagram , we're gonna learn how to use
07:33	one to answer three questions . So here is our
07:36	history Graham , it's about the winning speeds at the
07:39	Daytona 500 . So first question A Which interval contains
07:45	the most data values ? So if you look at
07:48	our history graham here , Remember the most amount of
07:52	data values will be the bar that is the highest
07:54	, the tallest . So if you look over here
07:57	, which one is it ? Well , you can
07:58	see that it is the interval of 150-159 mph .
08:05	Most of the winning speeds for the Daytona 500 were
08:09	within that interval . Okay . And part b how
08:13	many of the winning speeds are less than 100 and
08:15	40 MPH . So if we look , let's see
08:19	for 120 to 100 and 29 MPH in that interval
08:25	there was only one winning speed , It was in
08:27	that it's pretty slow for the Daytona 500 . Uh
08:31	And then let's see from 100 and 30 to 139
08:37	in that interval , let's see there were 44 winning
08:41	speeds in that interval , and let's see one plus
08:45	four , that would give us for five total Winning
08:49	speeds that were less than 140 mph . And finally
08:54	part see how many of the winning speeds are at
08:56	least 160 mph . So let's look well from At
09:01	least means 160 or greater . Right , so at
09:06	160 to 169 that interval there were seven , seven
09:13	speeds in that interval . Seven winning speeds in that
09:15	interval . And then from 100 and 70 to 100
09:18	and 79 MPH , there were five . So we
09:24	have those up , seven and five would give us
09:26	12 . So there were 12 total speeds that were
09:30	at least 160 mph , that won the Daytona 500
09:35	. Now , before you get to the , on
09:37	your own , if you notice this history graham ,
09:39	you'll notice It's not like the one we did an
09:42	example one . Right , we go from 150 to
09:48	150 , - 169 . Uh they're not exactly the
09:51	same number . And that's because all our values were
09:55	whole numbers . They were all integers . Okay .
09:57	We didn't have any like 159.5 mph because if we
10:02	did then would we be kind of stuck ? We
10:05	would fall in between those two intervals . So if
10:08	you have all whole numbers then this type of history
10:11	game will work fine . But if not like shoe
10:14	sizes , if you got decimals , you gotta be
10:16	careful and do what we did . An example one
10:19	. Okay , here's one to try on your own
10:28	. Finally , an example three , we're talking about
10:30	the shapes of distributions now . We use this when
10:33	we have doc plots or hissed a grams . We
10:36	can describe the shape that the history grammar dot plot
10:40	makes . Um So I've got four examples . This
10:44	first one . If you notice you have most of
10:46	your data here on the right side and it's kind
10:51	of going down to the left . So we call
10:54	that skewed left . Okay . We would describe the
10:59	shape of this distribution skewed left . It's going down
11:02	to the left down here . We call that detail
11:07	of the distribution . Okay , So when you're thinking
11:11	of it , you look where is most of my
11:12	data ? And where is very few of my data
11:16	. And that's the direction you're going towards . Where
11:19	there's a few uh where there's a little few amount
11:23	of data values . Okay , The next one .
11:26	Well , here you notice it's pretty even right left
11:32	side and the right side very uh similar . We
11:36	call this this is symmetric , It's got symmetry .
11:42	So the name of that distribution symmetric . Okay .
11:45	And this last one , well , if this was
11:47	skewed left , you notice here here , we have
11:50	most of our data on the left side and it's
11:52	going down to the right side , which means it
11:56	is skewed . Right ? Okay . We would call
12:00	that distribution skewed , right ? And finally , well
12:03	, what if you have one word ? Pretty much
12:06	flat ? Um , This we would call it's uniform
12:11	, or you can also just call it flat flat
12:14	distribution . Okay , So those are the shapes of
12:17	distributions . Here's one to try on your own .
12:27	Thanks for watching . And if you like this video
12:30	, please subscribe .

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