This video shows highlights from a lesson in AP Statistics in which a teacher uses a variety of technology tools to support students' learning. Also included is a ...
Hollylynne: Let's watch as an AP Statistics
teacher uses a variety of technologies to
support a lesson on introducing the concept
of sampling distribution.
Mr. Roberts: So tonight I think your homework
is just going to be to look at the PowerPoint
for today and take notes on it, um, because
it's a lot of definitions so I'd rather us
do stuff than go over definitions.
Cause so we're going to talk about it today
but I want you guys to write it down, um,
Okay, so today we're starting something new,
You guys haven't seen it before it which is
kind of nice um let's do this.
Okay so we have to keep in mind what statistics
is about right.
So the whole point of statistics is that we're
going to take a sample of something, look
at it infer from it okay.
We're going to go from the population we're
going to take a sample out of it okay.
We're going to collect data, um, and then
we're going to infer from it about the population
So two things that you kind of need to know
right now are these guys right here and we
actually - I need you to write these down
A parameter and a statistic.
Well we're going to switch gears okay.
I don't want to look at the population anymore
what we're going to do is that we're going
to find where, when we sample where our sample
lies among other samples.
So what I did is that I recorded a bunch of
people's heights okay.
Specifically I recorded four hundred and thirty,
I recorded 430 height, okay.
Do you know what's a mean of this is?
No, I don't know what the average of this.
Do you know how much it varies?
Okay you don't know anything about this okay
but what we're going to do is that we're going
to sample from it and see what we can do with
our samples okay.
Um, so what I'm going to do is I'm going to
ask half of you pretty much, I'm going to
number you guys off, I want you guys to take
samples of ten and I'm going to ask you to
record four numbers okay.
I want you to record the range, the mean,
the standard deviation and the median okay.
And then I'm going to the other half of you
guys are going to use a sample size of 20
and do the same exact thing.
Alright so are you telling me that we assigned
Alright and then what you do?
Where is that in your calculator?
Let's see if you remember where that is real
Students: Math, probability random?
Mr. Roberts: Okay do we want to do random?
Student: Random integer.
Mr. Roberts: Random integer . We want to do
the random integer.
Okay so when you guys hit rand int it says
lower/upper what does that mean?
Okay so lower is the lowest that you want
to select from the upper is the where?
The highest okay and what does N mean?
Student: The number of, uh, integers you want
Mr. Roberts: The number that you want to select
So what happens if you repeat?
Okay if you guys cleared your calculators
let's, um let's seed your calculator real
quick one more time so that you're not getting
the same sample as someone else.
Alright, in your calculator, okay.
The very first thing that you kind of want
to do is that you just want to type in some
Don't tell your friends!
It's your own number don't look at mine!
Just literally just make up numbers.
Student: (Mumbled question)
Mr. Roberts: Sure it could be one digit, two
digit, three digit, mine's a lot of digits.
Okay so then you're going to hit the store
button which is right here above the on button
Okay, it's an arrow and then hit math, and
slide over to probability okay?
And you'll see the number right - the first
ones called Rand and you hit enter.
Okay so now hopefully you guys won't get the
same numbers from your algorithms as everybody
Okay because really we can debate this whole
word random right?
With your calculators, but if they're seeded
we all should be getting different numbers.
Hollylynne: Students use large whiteboards
to plot the data from their samples.
Mr. Roberts: Yeah, hey for those that are
waiting to plot, um, I sent you guys through
a remind text, um, I sent you guys a form
for you to fill out, um, it's asking you for
the mean, the range, the standard deviation
and the median of your samples okay.
And next to each question it says the mean
N equals 10, the mean n equals 20.
If you're a 10-person put it in the N equals
10, if you're a 20 sample put it in the N
equals 20 okay?
This, when we graph it, I mean this is literally
why we like looking at graphs right?
Why we like looking at histograms and dot
plots because now I can see what the data
is doing correct?
So, when I look at the heights you guys can
tell me about what the range is right?
I did max minus min.
It's about 12.
You guys know what the mean is.
Okay so when we have software , specifically
when we have a graph you guys can tell me
a lot about it now alright.
And then when we have software that can crunch
big data 'so to speak' like big for us alright.
We can easily pull out some numbers to describe
the height of whatever they're talking about.
I'm going to collect - how many kids are in
Okay let's say that all 30 of you guys did
a sample of ten okay?
So look what I just got here okay.
So this thing just did this okay let me see
if I can pull this guide to the right okay.
So I took out IQR I don't want to do it.
Delete attribute okay.
So what this did, okay, is this literally
represents every single one of you okay?
You pulled ten numbers from your population
you randomly selected right in an SRS okay
with your calculator, some number generator
and then what you guys did is that from every
sample you collected a number correct.
So this was a distribution of what?
Mr. Roberts: All the population of all the
heights okay it's literally that sheet of
It's this thing.
Distribution - this is your population of
What is this guy?
Distribution of your sample okay now from
all the distribution of your samples to every
all 30 of you collected four statistics that
I asked you guys to collect right?
Now the new thing that you guys are going
to learn is this thing called a sampling distribution
It is literally a distribution of statistics.
D you guys hear the difference?
Did I say heights?
I said of a statistic right?
So I'm going to take all thirty means alright?
I only have like three up there but I'm going
to take every single mean that you guys got
and I'm gonna plot it okay.
This is now a sampling distribution, a very
limited one, but a sampling distribution so
what does this dot right here represent?
Let's just say at 69 what does that dot represent?
What is 69?
Mr. Roberts: The mean of what?
Of the sample right.
This is like the cool part about this.
Well I think it's cool.
I'm going to do this 500 times okay.
(To do do do) Awesome.
So I took 500 samples out of this population
Of size what?
Do you remember the size that we did?
10 okay everybody did a sample size of 10.
500 people sampled and all 500 of them filled
out a Google Form and gave it to me.
There it is.
So if I only grabbed 10 of you guys I don't
know as much if I grab 30 of you.
I'm going to take 500 samples of size 30.
We cool with that?
So let's just say that like there's 500 of
ya'll in here, aww man, you know.
Every single one of you took a sample of 30
all right and found these four statistics.
Look at it go.
So every single one of these is a sample right?
Every single one of those is a mean of a sample
Are we okay with that?
So, okay so let's kind of go through these
questions because this is what I wanted to
hit I don't know if I hit them all or not.
So let's just make sure.
Do we know what a sampling distribution is
that word sampling distribution?
Okay, distribution of samples, okay or distribution
Okay so it's our distribution of means, our
ranges , our medians, our mins our maxes,
our standard deviations okay.
Alright you guys rock.
Hollylynne: Let's hear from the teacher on
how he decided to use technology to support
Mr.Roberts: I think that they did, with the
use of Fathom, I think it did come home pretty
Mr. Roberts: And ultimately like this was
nice I wanted to get them up and moving, but
I really wanted to sample themselves.
Hollylynne: -Right, and I think they had,
they had that experience.
Mr. Roberts: Exactly and they got to use a
number generator to pull numbers and they
got to fight in their heads this idea of what
a sample is versus statistics cause they ask
me like hey doing this and then people go
up and do in the sample themselves helped
out a ton when it came to doing the sampling
distribution in Fathom.
Mr. Roberts: Um, especially when I said this
is all 30 of you and these are all the four
numbers that each of you got, so let's plot
those and then doing - okay well let's say
there's 500 of y'all and plotting those and
Hollylynne: Right, right.
Mr. Roberts: Um, and when they go over that
PowerPoint tonight hopefully they'll connect
things that we do in class with the PowerPoint.
Hollylynne: So you use a lot of different
technology tools today.
Mr. Roberts: Yeah when I think about it I
did, didn't I?
Hollylynne: You did!
So how did you kind of decide and choose-
I mean they were using the graphing calculators,
they, um, you were using Fathom, you use the
Mr. Roberts: Yep
Hollylynne: You know in the Google Form - How
did you kind of think about how to pull that
Mr. Roberts: Yeah, so I guess it just kind
of went through my head of like what can I
use to model the data.
Um, what can I use to gather information and
when you teach statistics the calculator is
your go to.
I know to use the random integer function,
um, and then through just like using Google
I know that I can gather information quickly
and that's what I wanted to do today is gather
information quickly from them.
Mr. Roberts: So just blast it out, fill out
a form, get all the information.
Everything is nice and like I know who did
ten, who did twenty, so I know I can compare
Mr. Roberts: And then the Fathom like that's
just that's just for me.
I've actually, liked, taken time out to learn
that and so that's just nice just to have
a really quick way to model data which is
awesome because I've used it for some of the
past chapters, especially in descriptive statistics
that's amazing for.
Because you just throw data up on a, on a-
Hollylynne: Em-hmm, em-hmm
Mr. Roberts: Histogram, boxplot, dotplot,
you can, you can go like this (snapping fingers)
and you can really challenge them and say
okay which one is better?
And they have to justify their response.
Or which, what does this give you like, what
So we've done it before using Fathom.
Mr. Roberts: So entering in the sampling distribution
and that's talking about describing sampling
distributions it just kind of flows so.
Mr. Roberts: Yeah.
Preparing to Teach Mathematics with Technology