Ok. Mr. Tarrou again. You are probably watching these lessons in sequence you know that already.
Let's talk about another type of quantitative graph in statistics. These are the ones we
make the most because computers make them easily and if you have a teacher that is just
using graphing calculators, TI-83/84 and maybe the NSPIRE, these calculators make your histograms
like that. BOOM! Just put your numbers in a list, which I will be showing you later
how to do with your calculator, and it just makes them very very quickly for you. Histograms
are the graph that we use, by far, the most when you are creating graphs in statistics.
Histogram... OOH... PAUSE, COPY! Ok. Benefits of a histogram. They are great for large sets
of data. If I give you like a thousand numbers and you make a stemplot by hand, not only
is going to take you forever but it is going to be just a rain of numbers going off the
side of your paper. We don't want a Matrix looking work on our paper. So these are good
for large sets of data. Very flexible when setting up class intervals. We don't have
to worry about splitting stems up by five, two, or ten. It does not display individual
pieces of dat, it just allows us to see the shape of the distribution. One and three here
kind of go together. They are good for comparing multiple distributions when your vertical
scales are equal. You will find examples about that in your book. We are going to make just
one histogram here in the time we have allotted. If you keep your vertical scales the same,
then you can look at two side by side histograms, like two side by side bar graphs, and pretty
quickly be able to compare those distributions. Which one has the lowest mean, highest mean,
where the peaks are, and compare those graphs pretty easily. The most common way of making
these vertical scales equal when you want to compare multiple distributions is instead
of making that y axis a count, how many pieces of data fall within the class width you find,
make them percents. This standardizes the vertical scale to be a max of 100 percent.
Then if you have a thousand numbers over here in this histogram and only a couple hundred,
you are not going to get that one graph towering over the other making the comparison difficult.
You want to make those vertical scales percents or Relative Frequencies for easy comparison
if you have multiple distributions. Maybe you want to graph some kind of information
about men and over here information about women and compare them. When you make a histogram
the x axis has to be a quantitative variable, it has to be a continuous quantitative variable.
We are not going to leave any gaps for that data to fall out and through the bottom of
the graph. So when you make a histogram by hand or the calculator, there can be gaps
between the bars, but not between classes. I will show you what I am talking about. We
are going to make another, haha with these same ten numbers I have used in the last couple
of videos... These are some made up grades for a stats class and that poor kid that still
has not made up his test who still has a twenty-six. Well, let's make a histogram of this data.
You may remember that converted these numerical values into letter grades and handled these
in two ways using them as categorical data. Now we are going to keep these scores raw,
we are not going to group them into groups of ten, we are just going to use these numbers
as they sit. This is going to be grades of an AP Stats class or whatever, they are just
grades. This is going to be the score that they earn. You can either do frequencies which
is a count or relatively frequency which are percents. Me writing percent and relative
frequency in a stats class is kind of redundant, I am saying the same thing twice. We worked
through this data before so we know that we can count easily by ten. Ten percent, twenty
percent, thirty percent, and forty percent. Also be aware that when you make the graphs
with your calculator it will only will only do a frequency histogram, it can only do counts.
If you want to make a relative frequency histogram, you are going to need to do that by hand.
Our scores go from a low of twenty-six to ninety-seven. I am going to leave the twenty-six
in here to highlight that outlier. Because the range is so wide I am going to count by...
let's count by tens because I don't have very much space here. So, twenty, thirty, forty,
fifty, sixty, eighty, ninety, hundred, and just for argument sakes one more score in
here of a kid in here scoring a hundred. That is going to mess up my easy percents in my
head. So I am going to do this off the top of my head, maybe we will do a count instead
of a percent. Because I have eleven scores, I can't do like two out of eleven very easily.
One, two, three, four, and this is frequency. How many kids scored between twenty and thirty?
That was that twenty-six. Ok, so we had one kid score a twenty-six between the twenty
and thirty. We had a couple of kids, one, two, three, we had three people in the seventies.
So... BOOM! We have eighties, eighty to eighty-eighty so we have four people in the eighties. We
had a couple of nineties, ninety-three, and ninety-seven. And where does this one hundred
go? Well, if you are putting the data points on the tick marks of a histogram then we need
to talk about how read the histogram, how to read the x axis. Very very important. Your
graphing calculator will give you a hint on how to do this, actually not a hint it will
tell you how to read it if you make a histogram with your calculator. We will do this in a
video a little later. This class interval represents data that is greater than or equal
to ninety, the left side is equal to, and it us up to a hundred. Ok, so if a student
scores a hundred, if I want to represent a hundred in this histogram... Well if it is
equal to a hundred I have to go into the next class interval. So I actually have to put
in 110 and represent that one student that scored a hundred over here. This is how you
read the class intervals of a histogram. You might notice my footnote that there can be
gaps between the bars but not between the classes. When you make a bar graph all of
the bars have gaps in-between them. Well I have a big ol gap here because of the outlier,
that kid that still has not made up his test. There are three... four empty class intervals.
But the the 70 runs right into the 80 which runs right into the 90, which runs right into
100 and so on. My class intervals are jammed right into each other. That means that there
is a 99.99999 that does not get lost. Because the classes are jammed up, continuous. No
place for data to fall between. We are representing a continuous quantitative variable. Now, this
is my favorite way to label the x axis. You must have, or should have a number at each
individual tick mark at the beginning and at the end of the class. That is my favorite
way to make these and I think the easiest. However, if you are showing this to somebody
that does not understand statistics very well, they might be confused by how.... What is
this score? It looks like the kids scored over a hundred. Because these are no decimals
and relatively easy values, if you like and you will see this displayed in your textbook,
I am going to count by tens. And, I am going to just put 20 in the middle, and then 30,
and 40, and 50, 60, 70. I am writing fewer numbers because I am putting them in the middle
of each class intervals. Now 80, 90, and 100. If you are going to show this grade distribution
to somebody that doesn't completely understand histograms or statistics, putting the one
single value in the middle of the class width and not at the beginning and end will make
it a little bit easier to read. But I don't like make histograms like this usually. There
you go. Histograms. BAM!!!