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

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


Introduction to Statistics - By Anywhere Math



Transcript
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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