Making histograms, boxplots,and timeplots with a graphing calculator

Making histograms, boxplots,and timeplots with a graphing calculator


I am going to put this data in the calculator
and that means when I turn it on I’m going to hit the stat button to put some statistics
stuff in, and hit edit to start putting in some numbers. The calculator should have six lists in it. If you should accidentally delete the list
by going and hitting L1 and delete. Now you only have five lists because L1 is
gone. How do you get that back? Well if there were numbers in that list they
actually would not be gone you’d get that back by going to second quit get back to your
home screen, hit stat. Do select 5 which is set up editor. Nothing has happened yet, you just selected
that command out of your calculator, and hit enter done. Now I want to go to stat edit. The one I just deleted a second ago ..is back. Okay so let’s put our numbers back into
the calculator 1-9. 1 enter 2 enter, 3, 4, 5,6,7,8, 9 okay. We are not going to be using those numbers
a lot during this little presentation… but we will a near the end. What we’re interested in is this data value. Again some two digit values, you can think
of them as test scores if you want, or any random value. You have 87 16, 16, 71, 96, 72, 83, 65, 99,
and 78 hmm. Something happened…I should have the same
number of data in each column. Well if I scroll back up here it wasn’t
by accident, I put 16 in here twice. I really didn’t mean to do that. So If I want to take a number out of a list
I accidentally typed in twice I hit delete…And Oh crud. I didn’t want to delete both of the 16s. I’m later going to use those counting values
as a sequence of the tests and I want to make a time plot. So I want to put that 16 back where it belonged
not at the end. Which sometimes is okay oops I went too far. I want to put that 16 back. So if you miss a number when putting data
in to the calculator I wanted 16 to show up again between 87 and 71 so I put my cursor
on 71 and above the delete button which I used to get rid of the 16s, It says insert
so I do second insert it gives me a zero back there where I want the 16 to be. Alright enter…and we are good to go. I want to show you how to make a boxplot and
a histogram at the moment with your graphing calculator. Okay so I want to stop putting data into the
graphing calculator. So I’m going to do 2nd quit and get back
to the home screen. Hit clear to not distract you with anything. Stat plot how do I make a stat plot, scatter
plot box plot or histogram? Well that is a type of statistical plot, that
will be in yellow or blue depending on your calculator. Hit second stat plot, unless you have a TI
inspire, and then you wouldn’t be watching this video. All my plots are off that is important if
you are just learning to use a graphing calculator. I don’t want any mistakes to show up. So I am going to choose 1. Oh if some of them are on you can hit 4 to
turn all your plots off at once, there are other ways to do that as well, which you’ll
see. Okay I want to go to stat plot 1 and I want
it to turn it on by hitting enter. Down here you can make a scatter plot. A scatter plot with dots attached with lines
for the histogram. I’d like to focus on that right now. So Histogram enter, you see how that just
changed. A minute ago it was asking me for both X and
Y’s but a histogram and all the graphs we talked about, histogram, stem plot, boxplot…which
we haven’t actually talked about yet. But those are univariate data graphs, so I
only need one list of numbers. So that first list of numbers we are not going
to deal with right now. So let’s make a histogram and see what that
looks like. Zoom…I’ve gotta clear that out. Lets try that again, Zoom if I scroll down
to 9 you’ll see me do that later. Zoom 9 is setting up your window for a statistical
plot. So zoom is standard. Oops I left some junk in my calculator that
shouldn’t be there that looks like a parabola. So I’m going to hit y=, my regular y=,
not second y=, and yes I have some stuff in there. I’m going to clear that out and go back
to zoom graph. So I have a flat looking histogram here. It isn’t left or right skewed it looks pretty
flat across the top it looks symmetric. If I hit trace, I’ve got oops. No wonder it is so flat I used the wrong list. Remember we put data into list one and list
two. So I want to make a histogram with my actual
data. So how do you do that? So second step plot go back to choice 1. Oh that’s right I put the actual data I
want to use in list two. The first column was these numbers list two
was these numbers. I gotta come down to X list. And above your 1,2,3,4,5,6 L1 , L2 these are
your lists these are where you put your data value. So I put my value into list two. So I’m going to do second list two over
the x list value and now zoom 9 wup clear Zoom 9 zoom stat,Wow that’s not much, but
it shouldn’t be after only putting in nine numbers. It’s not a very good picture. I do have the minimal of five class intervals
but not a great picture. Let’s hit trace and see what we see. 16 to 36.75. That calculator is telling you how to read
the histogram. That class is for X’s greater than or equal
to 16, but less than 36.75. Carrying over we had some decimals in our
intervals and yet our data had no decimals. So what we normally do when we make graphing
histograms with a graphing calculator is we have to go back and change the scale ourselves. And you do that by hitting window and scrolling
down the min, the x min is the minimum value of 16, I’m going to change that to 15. And our x scale is a decimal when none of
our data has decimals, that doesn’t make sense. So I’m going to change that to 15 and just
let itself count up to its maximum value. You won’t have problem with that x max there. It will refigure as you go through the histogram. I’m going to change the x scale to something
more reasonable, and by changing that from 20 something to 15 I’m going to get more
bars, more class intervals and possibly see some better distribution. Instead of doing zoom 9, I’m just going
to hit graph. We still kind of see not such a great histogram
as far as shape in that histogram, we only put 9 numbers in, so I’m doing this more
for you just knowing how to use your calculator and not really analyzing distribution so much. If we hit trace we can see that we have nice
whole number values since our data doesn’t have any decimals and scrolling over no data
in these class intervals. We have three pieces of data between 65 and
75. Again x was greater than 60 and less than
75. We have three pieces of data between x is
greater than or equal to 75 and less than 90 and two pieces of data in our last interval. So we have a histogram with the use of our
calculator…Awesome. Okay let’s make a box plot. You see that outlier there, there is a small
body of data and clearly the outlier of 16 is showing up as a bar that is way off by
itself. This is not going to be a great picture since
we have such a small set of data. But you can hit window and change that x scale
to an even smaller number and hit graph, now we can see the big gap which is starting to
develop between the 16 and the other values which is starting to actually show a distribution
that is showing very slightly right skewed. Very slightly because there are so few pieces
of data that it’s hard to make a shape discussion off of that. Let’s make a box plot, go back to second
stat plot, and hit 1 so we are going to make a modified box plot and a regular box plot. A regular box plot is going to be well let’s
see what it looks like. Enter on the second icon on the third row. Hit zoom 9 every time you want to make a new
stat plot. We have this graph that looks very, very left
skewed with a very long whisker. That is not actually left skewed, these three
intervals each of these by the way, getting ahead of my notes, hold 25 percent of your
data So these three quarters are about the same width, it varies a little bit there. Then boom! A really long whisker. The really long whisker without the growing
interval as you go to the left is the indicator of an outlier. Lets check that with something called a modified
box plot. So second stat plot 1 and now I am going to
go down with the right arrow to the modified dot box plot. That’s got a couple of dots in it. We are going over modified dot box plots in
the next video or so maybe in the section 1.2. And hit enter zoom 9. Now that modified box plot what it has done
for you is an IQR test for you automatically. That is when you take q3 –q1 find a value
multiply that by 1.5 and you add it to q3 and subtract it from q1 to make this interval
to help identify outliers that has not been in my video yet as notes, it will be in your
textbooks. I am sure by now if you are using these as
references you go through texts, you probably have already heard about an IQR test. But we’ll speak of that tomorrow as well. There’s you outlier! That really long whisker we had a second ago
is nice and short. This is somewhat symmetric. Your intervals are going a bit to the right
so that tiny body of data is a little bit right skewed. But with only 9 numbers again that is not
a good description. You won’t get a good shape for that small
set of data. Here it is your outlier of 16 being highlighted
by your calculator doing the IQR test for you. You can’t just throw outliers willy-nilly. You have to have a good reason to throw them
out and one way of identifying the cause of outliers is with something called a time plot. Now in your textbook, if you are just starting
your textbooks you haven’t actually talked about scatter plots or bivariate data graphs,
but you have probably seen a time plot it is actually a form of a scatter plot which
is a form of a bivariate graph. Whenever you have time we are going to use
the sequence of scores as our variable of time. If you remember I put these numbers in and
said we wouldn’t use themfor a few minutes. Stat, edit and here we have list one as being
in the sequence of when these grades were taken and data was collected and we have the
outlier, clearly we can see that the outlier happened earlier in the data collection process. Which is probably because of user error testing
purposes, maybe not knowing what to expect on tests, or maybe it was an experiment. Maybe user error, the wrong calibration of
tools or something like that. We are going to identify this outlier with
a time plot using our calculator. You know they only have nine pieces of data. I don’t want to type in a bunch of stuff
while I show you how to use your graphing calculator. I want to display the L1and L2 lists at the
same time. I want to make a scatter plot where the time
is the X axis and the data is the Y axis. So second stat plot, I am going to go back
to stat plot 1 to turn on the scatter plot option which is the first one in the first
row. Now see what it is doing it saying where is
the X’s and where are the Y’s? My X list is going to be list 1 that was the
sequence of events. Right now it isn’t set up correctly so second
L1 and for the y list it would be second aL2. My time is going to be 1 or X list and my
data is list 2. Okay zoom 9 let’s see what happens. Okay try that again zoom 9 let’s see what
happens there is my time plot. If I hit trace. I can trace along and it will show me the
coordinates of each one of the points. Again the X coordinate was a sequence of when
the data was collected, and our outlier is showing up very early in the data collection
process. Could be no good reason to get rid of that
piece of data, but it could be learning to use a new piece of machinery, maybe it was
mis-calibration, or user error. Maybe we have a reason to throw out that outlier
through the process of making this time plot. Okay I think I may have just a minute left. If I do stat, edit. Let’s do something neat let’s display
this data in both a histogram and a box plot at the same time, to see the comparison between
the two. So second stat plot, 1. I am going to have one be a histogram and
remember my data was in list two and not list one. Okay I am going to arrow up to plot 2 and
hit enter. I am going to turn it on and below it below
the histogram I just asked for I am going to put a box plot underneath the histogram
and zoom 9 and there you go!

24 thoughts to “Making histograms, boxplots,and timeplots with a graphing calculator”

  1. Thank you so much Rob 🙂 by the way, what AP stats book do you use? Title? Author? and what practice prep books would you recommend? Thank you again

  2. i think u should compile all your notes and keep it at a specific location. That way we can print your notes and wont have to copy them during every video.You would also be able to make additional income by charging some small price like 5 to 10$.Also u should use other graphing calculators like a casio one.That way u will be able to reel in more students

  3. I've been following up with these videos throughout my AP Statistics course and now I'm watching them again in review for the AP exam. Your work is incredible and so helpful. Please, never stop doing what your'e doing!

  4. The king of calculators
    I have to say, by comparison to other types of calculators that I have used; Texas Instruments are not very user friendly, when it comes to certain graphing procedures like your's in this video your showing us. You had to do a lot of adjustments for displaying that data, that should be automatic (and usually are automatic on most other calculators). Texas Instruments is a good calculator in a lot of ways, but I am thinking that Casio is probably the best; although most Casio's are more simple, I think you can get complex Casio calculators. Casio's are also really really tough, and do not easily break. Of course, although it is not a pocket calculator; nothing beats the power of Mathematica if you know how to use it (and Wolfram Alpha on-line which is partially free and simple, could do the sort of things you are doing here very easily); Wolfram Research are the king of calculators! I have Mathematica installed on my computer!!! See for yourself https://www.wolframalpha.com

  5. BAM!!! I love the beginning. I wish I saw this before so I won’t waste so much time.(at least I won’t be wasting much time from now :)) love those mistakes and fixes
    I’m going to learn through this whole course before my college stats class. This is going to rock! BAM!!

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