Introduction to Statistics - Free Educational videos for Students in K-12

Introduction to Statistics - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson . And
00:02	today we're going to begin a very interesting topic .
00:05	Today we're talking about an introduction to statistics . Let's
00:10	get started . All right for the introduction to statistics
00:31	, let's first define what exactly statistics is . So
00:36	statistics is the science of collecting , organizing , analyzing
00:40	and interpreting data is all about data . Well ,
00:44	first you got to collect data data just doesn't appear
00:47	. You gotta collect it somehow . Maybe you do
00:50	a survey and get data that way . Maybe you
00:52	perform some experiments and you measure and record data as
00:56	you go along once you have the data . Well
00:59	then what do you do with it ? Well ,
01:00	we organize it put it in order maybe from least
01:03	to greatest . That's a common thing to do at
01:04	the start . Uh Maybe you put them in a
01:07	table . Maybe you'll make a graph . Well then
01:10	you analyze it . What is the data telling us
01:13	? We do things like find the mean median mode
01:15	or range uh to kind of get a sense of
01:19	what the data is all about and then we interpret
01:22	that data . What does it tell us now that
01:24	we know and have all this data and have tried
01:27	to analyze it somehow . How does that help answer
01:31	? Whatever questions we were looking for answers for ?
01:33	Okay , that's what statistics is all about . It's
01:37	all about collecting that data and using it to help
01:40	answer a question . So statistics is all about answering
01:44	a question . Well , first , what exactly is
01:47	a good statistical question ? Well , a statistical question
01:51	is where you expect to get a variety of answers
01:54	. That's that's really big . A variety of answers
02:00	. A whole range of answers . You're not expecting
02:01	just a couple of different options . Right ? Uh
02:05	and you are interested in the distribution and tendency of
02:08	those answers . Now , one more thing I want
02:10	to add about statistical questions . Don't get confused from
02:14	a survey question and a statistical question . For example
02:19	, if your statistical question was uh How much do
02:23	6th graders way ? Well that's your statistical question .
02:28	But when you do the survey you're not gonna ask
02:30	people , how much do sixth graders wait , you're
02:32	gonna say , how much do you weigh and you
02:35	go to the next person , how much do you
02:36	weigh and all the sixth graders you're gonna survey .
02:38	You ask them , how much do you weigh ?
02:40	That would not be a statistical question , but it's
02:43	going to help us get data to answer the statistical
02:47	question . So with that let's get to our first
02:49	example . Okay example one Let's say your science teacher
02:53	asked you to do an experiment about mice . And
02:57	she asked what is the weight of a mouse ?
03:00	Okay , well first is this a statistical question And
03:03	if so explain now if you remember from the definition
03:08	, statistical questions should be giving us a variety of
03:11	answers . Uh They should be able to show us
03:14	the distribution uh and a tendency . So we have
03:17	to think well this question , if I'm doing experiment
03:21	with mice , is he going to give me a
03:23	variety of answers ? And the answer is yes .
03:27	It will . Because you can't expect all mice to
03:31	weigh the same . They're gonna be different . Just
03:33	like humans are gonna weigh different amounts . Same with
03:36	mice . So our answer yes . Because you would
03:40	expect the weight of mice to vary . Let's try
03:43	part B . Okay , part B . So we
03:46	wait a whole bunch of mice and we collected uh
03:49	that data and have it in this little table over
03:51	here . Now what we're gonna do is display that
03:55	data in a dot plot . So it looks kind
03:57	of confusing . It's hard to tell anything about the
03:59	data , right ? We've already done that first step
04:02	collecting the data . Now we're gonna organize it .
04:05	Uh And we're gonna make a dot plot . And
04:08	then after the dot plots made identify any clusters ,
04:10	peaks or gaps . And we'll talk about what those
04:13	mean in a second . But first the dot plot
04:16	adopt plot is basically you have a number line .
04:20	Uh It could be a horizontal or vertical and then
04:23	you use dots to show them where the different data
04:26	values are . It's kind of like a little bit
04:28	like a bar graph except with dots instead of bars
04:32	. Um so we're gonna start with the number line
04:35	. Well if I look at my data I can
04:37	see that the least value is 1818g and the greatest
04:44	was 28 g . So that's where I'm gonna start
04:47	on my uh dot plot . Okay so I have
04:49	my my number line done from my dot plot all
04:53	the way from 18 to 28 . I need to
04:55	label what these values means . So these were all
04:58	weight . So I'm gonna label that over here to
05:00	the side weight . And that was in grams .
05:05	Really important to label . Don't forget that . Or
05:08	else nobody's going to know what those values represent .
05:11	Uh and then we just look at the data and
05:13	put that . So at 18 . How many mice
05:17	weighed ? 18 g . Well , if I look
05:19	at my data , I can count too . So
05:22	I put one To just two dots right above that
05:28	number 18 . And I keep going . So 19
05:30	if I looked there were three . So I'm gonna
05:33	do one two three Like that . And we'll keep
05:39	going . Um at this point you'll notice there were
05:46	no 24 is no 25 , 26 is so I'm
05:49	gonna put nothing there . Uh and then I get
05:51	to 27 and keep going . So there are two
05:53	of those And then finally 1 28 . Um One
06:01	good thing to do before you're finished is just double
06:04	check to make sure you counted all of the data
06:08	values . So just count your dots and make sure
06:10	it matches the values over there . So I've got
06:13	12345 15 18 1920 . And if you look at
06:19	that little chart , I have 20 values there .
06:21	So I'm happy with that now the pot is done
06:24	. Let's go to the next part . Identify any
06:26	clusters , peaks or gaps . Well , let's look
06:29	at the clusters . First . A cluster is where
06:31	a lot of data values are kind of bunched together
06:35	. So if you look over here you'll notice ,
06:39	well It looks like there's a whole bunch of data
06:42	values right there , you're just gonna pick kind of
06:46	what's in the middle , where they're kind of all
06:48	seem to kind of be drawn to . So that
06:49	would be 20 . Uh So that's a cluster you
06:52	might be asking , is it possible to have two
06:54	clusters ? Sure , if you've got a big bunch
06:57	here and another big bunch here , it's possible to
07:00	have more than one cluster . That's okay , peaks
07:03	. Well , hopefully you can kind of guess what
07:05	that is . That's just are there any things where
07:08	it's the tallest ? So right here again , 20
07:11	, there is a peak at 20 and same thing
07:13	. It's possible to have more than one peak .
07:15	If for example 21 also went up to six ,
07:22	Then we would say there's a peak at 20 and
07:25	21 , but as of right now there's only one
07:29	piece because that is the tallest and finally gaps .
07:32	Hopefully that's obvious again what that is , where there's
07:35	spaces in between the data values and that obviously is
07:39	right here . Uh So there is a gap between
07:45	Mhm . 23 and 27 . Okay , so that's
07:52	just kind of helping to uh explain our data a
07:56	little bit more . Okay . Finally part c use
08:00	the distribution to answer what is the weight of a
08:03	mouse ? Our original statistical question . Well , looking
08:07	at that data , looking at our dot plot and
08:10	seeing those clusters and the peaks , we can say
08:12	that most my way About 20 grants right ? Our
08:25	cluster was around 20 , our peak was at 20
08:28	. Uh so that's how he would answer that question
08:31	. Here's one to try on your own . Alright
08:39	, I was able to , The dot plot shows
08:41	the heights of sixth graders in my math class .
08:45	So here is the dot plot . You can see
08:48	uh These are all heights in centimeters not inches .
08:51	Um And part A says how many students are in
08:54	my class ? Well , if you remember all of
08:58	these dots represent a data value . So in this
09:01	place these dots represent one students hype . So to
09:05	figure out how many students , I just count the
09:08	dots . So let's see . We got 1234 2021
09:14	22 . So there are 22 students in my class
09:22	. Okay , let's try part B . Ok .
09:24	Part B . How can you collect these data ?
09:27	Well , to figure out heights , we're probably gonna
09:31	use a measuring tape . Right ? And make sure
09:34	that you're measuring in centimeters , right ? Because that's
09:39	what the data was . Let's try part C .
09:42	Okay . Finally , part C write a statistical question
09:45	you can answer using the dot plot and then answer
09:48	that question . So we're writing a statistical question .
09:52	Uh It has to be about the dot plot .
09:54	Remember this was about height of students in my class
09:58	. So maybe our question could be , I'll call
10:01	our 6th graders and Mr Jacobson's Math class . That
10:04	is a question that we could answer using this top
10:07	plot . So that's great . There's our statistical question
10:09	and let's answer it . Well , how tall are
10:12	most ex creators in my math class ? If you
10:14	look , we have two peaks right here . There's
10:18	56 57 . By the way , you may have
10:22	noticed , I didn't label every single uh every single
10:25	dash , but if you noticed , I'm going by
10:28	the same amount . So 1 52 that would be
10:31	1 53 . 1 54 55 56 . 1 57
10:35	. 1 58 . That's fine . You can do
10:37	it that way . Just be consistent . Um So
10:40	we've got a peek peek here at 1 56 and
10:42	1 57 . That's also kind of where we have
10:45	a cluster , so we would say um Most of
10:52	the students , oh Are what ? About 156 cm
11:02	probably . Are about 156 cm tall . Hopefully you
11:11	can see all of that . Uh That's it .
11:14	For example , to here's wanted to try on your
11:16	own as always . Thank you so much for watching
11:24	. And if you like this video , please subscribe
00:0-1	.

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