Hello again. I'm Mr. Tarrou. Today, I'm going to start the very first set of notes for one of the other class that I teach,
Ap statistics.
Ap statistics is a study of,
data, data analysis.
Think of computers and
all the mountains of information that we store now.
Presidential elections, um
medical studies.
Anything that collects data.
We have to analyze it
somehow.
And get conclusions out of that data.
That's what we tend to do
in statistics.
The first step that of ... I don't know why I put two up (chuckles).
The first step of data analysis is
drawing a graph, looking to see what your
picture, your distribution of data
looks like.
and the first two types
graphs, we're going to look at
Is really gonna be for
something that we don't do a whole lot of
math two in statistics or
at least in an intro to statistics.
And that is the categorical
variable or we're going to look at the
two categorical graphs.
The first type is a pie chart.
Those are the circles you see in the newspaper maybe
or on the internet. Um. We're all
you know maybe not comfortable making them but
we've seen them a lot.
Well pie charts are good
but without the help of a
computer. They're a little bit
awkward to make by hand.
We must contain
all the categories of a whole
within that pie chart and
we only use these when we want to emphasize
each category's relation to a whole.
So I've got two sets of numbers here.
I'm only going to work with one set.
But if I want to compare my grades and
these are not my grades but from
say one period of statistics
to the second period of statistics.
That would not be really all that great to attempt
to do with the use of a pie graph.
So but let's take the
first row here and see what we have as
far as letter grades. Now these are all
numbers and
but we must not forget that we're looking at
categorical graphs.
So we got a couple of people here
with A's.
We have a few people here with B's.
We've got three people with
a C. And...
One person. Let's say that they
you know haven't made up a test yet with an F.
Now we do a ten point grading scale. In case
that looks a little bit weird for you.
I want to represent this with a pie chart.
Ok, well first of all
you know your grades, I don't have anyone with D's.
But you know your grades are
parts of a whole. You know there's
four, five grades that we give. Five grades.
And you know I'm going to represent
all of those possibilities.
So, we're going to have
um you know
a certain section for A's.
A certain section for B's.
We got a section for C's.
Uh.. we're running out of colors here. D's.
And then finally F's. And we're going to represent
that in a pie chart. Well, pie
charts start with a circle.
And within
that circle you're representing
percents of data that are in
that category. Not counts.
So just because there's two people that have an A
You can't show that in a
pie chart. You must do that with percents.
So this is ten people total
and if two people have A out of ten,
two divided by ten is twenty percent.
So I need to try and estimate as close as I can.
This is the awkward part.
What twenty percent of a circle
looks like. Well that's not quite
twenty five. So let's say it's right here.
So this is my A's
and you would not write this in a pie chart
but that's twenty percent of the
data. Now we have B.
There's four people that have a B.
Well, four out of ten
is forty percent. So..
That's a little bit less than half.
So I'm not going to go half the circle. But a little bit
less.And again I'm trying to estimate
these values and that's again where the awkwardness
comes in when you're doing this by hand.
My B's represent
forty percent of my class.
And again I'm just doing this for teaching. You do
not put these percents inside of a
pie chart.
Uh.. we have C's are three out of ten
or thirty percent or hmm well almost
one third of a circle
that is uh an orange here.
So let's say that
it's about...
here.
So I've got some kids making C's.
That represents three out of my
ten students.
And I can see why I pick ten people like I can do my math easy.
That's thirty percent of the data.
There's no D's and my F's
are
ten percent.
So I'm just trying to represent
my.. all my categories of the
whole inside of one's circle.
All of my categories
of my whole must contain all the categories of a whole
are represented in that circle.
Now here's the disadvantage of a pie chart
that you can....
...it doesn't have very much flexibility.
...... If for some reason
like let's say you know c'mon we are talking
Ap stats right? No one's going to make a
twenty six percent left something weird going on.
Well, it's a test and it's not been made up yet.
So what if I wanted
to not represent that value
with an F and just use
A,B, and C just represent
sum of my categories
of the whole. No way.
Can't do it. So pie chart
cannot show this data
if I'd only leave out that F.
So offer to make is restrictive
in the fact that you have to use all the
categories of the whole and you cannot ignore one
if you like to and not
great for side by side
comparisons. Only if you want to represent
each category
in relation to the entire whole.
And again I got to fill that back again cause
you can't just have part of a circle. You gotta have it all.
YOU GOTTA HAVE IT ALL MAN!
So that means we will look at bar
graphs. So copy that down.
And I will write some new notes while you do.
Ok, did you get all those notes down?
Take a second, pause. And
maybe copy these notes down if you like.
Ok, so bar graphs.
We're back!
All right, bar graphs the second type
of um categorical graph
that we have. Much more flexible
much more common
and we make these much more often in statistics.
Here are some benefits. I will have to add some more
in the minute.
There are easier to make and read.
They can compare any set of quantities that are measured in the same of unit of measure.
In other words all of your categories have to come from the same one singular whole.
We can make side by side bar graphs for easy comparison. We are going to do that
in a second.
You don't have to use all the categories of a whole.
Now I am going to. That means like if don't want to include this
person that got an F just because they did not make up
a test, I don't have to.
But, I am going to just for teaching purposes.
When you set up a bar graph
your variable of interest of interest is along the x axis.
always.
The vertical axis has to two types of names.
Or, you can put two types of variables there.
Sort of.
How you count.
It can be a frequency, or simply a count.
Like I have got two people with an A.
I have got 4 people with a B. Now these are not just counts.
These are... sort of like. 10, 20, 30, 40....
That is not 2, 4, 3, and 1, no.
You can do frequencies which are counts,
or you can do percents which I might run out of room to write
but it is called Relative Frequency.
That is what we call percents in AP Statistics.
So we are going to do a relative frequency bar graph.
And we are going to display these two sets of data side by side.
So.
Here is how you make a, or one way, to make a side by side bar graph.
I can make a bar for one period, bar graph, and another bar graph for another period.
But, bar graphs are allowed to have spaces in-between their catagories
and because of that, if we are going to make a side by side bar graph
they are often just crammed in the same picture to make comparisons even easier.
So we got 20 percent with A's in period... let's say it is already in blue so
period one.
We have got 20 percent with A's.
We have got 40% with B's
We have got 30% with C's.
And that one kid that got the F because they have not made up their test.
Now let's do period 2.
in green. Now you see I am kind of making a key with my graph. That is to let somebody else know
how to read it.
Well in this class I have 3 out of 10, or 30%
with A's since I am doing a relative frequency on the y axis.
I have got my B's... I have got 1, 2, 3, 4. So the same 40%.
I hope you can see these colors on the computer.
I will shade that in a second.
We have two people in 70's. Now if you are doing a 10 point grading scale like my school
that is 20% with C's.
And we have a 65, so there is one person with a D.
So incase you cannot see the colors here, we have the unfilled bars for period one
And the filled in bars for period 2.
Now you can just really quickly glance at them and say
that the B's are the same,
Period two has more A's, fewer C's, so overall the trend is that the second period class is a little bit stronger
in grades right now.
And there is still a couple of people doing poorly in each one, but overall second period has more A's
at 30% compared to 20%.
The B's are the same.
Second period has less people with C's at 20% as opposed to 30% for period one.
And D's and F's, I have got one person with a D. The lowest grade in period one is an F.
Now I just compared and contrasted those two classes. That is also something we do
a lot in Stastics.
Analyze what we see, and I just gave you numerical values in my conclusion to say
that right now second period is doing stronger.
I did not say they were doing better just because I said so.
Ok.
Now..
One thing I would like to talk about is
with this graph that we are looking at...
We have to be careful when we look at data and we are trying to determine if it is quantitative...
You will see me write that word a little later. That means that my data is numbers and I am going to work
with it as raw numerical data.
Or is it categorical.
I am going to keep these grades up here and we are going to look at just period one.
Eh, we will look at this other column of numbers instead.
And..
We are going to say... ok... well...
These are all numbers.
You know, when you get a grade
that is a number. Well there is going to be two types of variables we study.
Quantitative and Categorical.
Right now I am going over categorical variables.
Well.
We have numbers, now see I erased the A, B, C, D, and F.
So, it seems like the letters have gone, the categories have gone.
Well, below here I am going to make something that is later you might think looks like I am setting up
something called a histogram.
But here I am going to put that this is scores of 100 to 90.
And here in this area I am going to put scores of 90 to... excuse me...
89 to 80.
And then I have got scores here of 79-70.
I have got
69 to 60.
And then I have got below 60.
It seems like I am going to make something later called a histogram.
It seems like I have got my x axis representing numerical values.
But I have got it in groups of numbers. Are you in this group of 100-90?
Are you in this group of 89 to 80?
And then going down to just simply this last group which I am no longer counting by 10 which is really the big
give away.
I have just said 60 or below, or below 60.
So 59 or lower.
I mean there are sixty values included in there.
That is the F.
So I am using the numerical grade to put you still into a category, which kind of makes a bit of a gray line there
between making something called a histogram which is for quantitative data and a bar graph for categorical.
So even though I am going to drop the A, B, C, and D's, I am going to handle these numbers as still
being categorical and put it into a group based on that.
So 100 to 90, well that is 3 people out of... you know what...
Let's do... let's do a frequency on the y axis.
instead of percents.
So 1, 2, 3, 4,
I have got
3 people in the 90's to 100
I have got 1, 2, 3, 4, people in the 80's
I have got 79 and 71.
[school announcement]
So I have got 79 and 71 again, my two people in the 70's.
I have got one person with 65.
So one person in the 60's. And nobody below 60.
I am putting the gaps in-between these categories to really emphasize again that I am taking your numerical
grade to put you into a group, or a category.
Later when we study something called histograms, where we are using the numbers in their raw state
and not assign a category or a letter grade, then these are going to run together and all touch.
But bar graphs also always have gaps between the bars, or between the categories.
So there is the two types of categorical graphs.
Don't think that you can just get away with doing your homework. There is still going to be issues when you
get into those problems.
You try and set them up, they will be a little bit harder than yo think even though this all looks
maybe rather familiar.
Have a good day:) BAM!