In this video I'm going to show you how to graph data by hand. We're going
to be making a scatter plot of some data. Graphing by hand is somewhat tedious. Especially
when you're setting up your axis. But it's important when you're learning how to graph.
It's probably the best place to start. And so let's say I give you the following data.
Let's say I do a lab where I vary the amount of fertilizer that I'm giving plants and then
I measure how high those plants grow. And so the independent variable in this case is
going to be the fertilizer and the dependent variable is going to be the growth of the
plants. And so you could pause the video if you want to right now. You could try to make
the graph of this data and then you could come back and look at the important parts
of a graph and how I set it up. Or you could just watch me and then when you're done try
a graph of your own. And so the first thing you want to do is figure out what kind of
a graph you are going to use. In this case I'm going to use a scatter plot because I'm
looking at the correlation between two number sets. Next thing I want to do is I want to
make sure I set up my axis in the right way. Since I'm varying the amount of fertilizer,
I want that to be on the x-axis and I want plant growth to be on the y-axis. The thing
you change will be here and the thing you measure will be here. Notice that I've also
put what I'm measuring and then the units that I measure it in. So fertilizer is going
to be measured in grams and I put that in parenthesis. Just likewise, plant growth is
going to be on the y-axis and then I put that measuring in centimeters. Next thing I want
to include is a good title. And so I could look at the relation of fertilizer to plant
growth. If I knew more about this lab, like the type of plant or the time period when
it was done, I would include that in my title as well. Make sure that you can look at the
title and you should be able to label the axis just based on the that. You shouldn't
have the title that's, for example, just "Plant Growth". You want to have as much information
in that title as you can. Next thing I want to do is I want to put numbers and I want
to put tick marks or major gridlines on both the x and the y-axis. This is hard to do.
And so let's say you're doing a test and you're given this amount of graph paper, you want
to make sure you use all of the graph paper. And that's going to give us a better graph
and it's going to allow us to look at patterns in the data. And so this is sometimes difficult.
First thing I want to do is count the number of squares. And so I count the total number
of squares, and it's 21 squares and then I look at the range. And so you can see here
that my fertilizer values go from 2 to 12 and so I have a spread of 10 grams that I
want to make sure I'm able to graph. Now students have a tendency to want to put the number
0 here. But since 0 is not in my data set, I don't want to include 0 on my graph. I want
to use all of the graph paper. And so a quick way to do this, if I divide the number of
grams by the total number of squares, that tells me basically how many grams per square.
And so I can start here, this being 2, this being 2.47 and then just move across like
that. But you can see it's going to be really unwieldily. It's going to be a bunch of decimal
values. It would end exactly at 12 but it's not going to look that nice. And so since
I'm less than .5, I could simply round up to .5. And so I could label it across the
bottom as 2, 2.5, 3, 3.5, and 4. And so I've labelled all of those whole numbers across
the bottom. I didn't have to put all of those there but I at least have to have two or three
numbers so you can figure out what the scale is going to be. Now let's go and try to do
the y-axis or plant growth. I count fifteen squares here on my graph paper and I've got
a range of 80 cm of plant growth. So likewise I could divide that 80 centimeters by the
number of squares and that's going to give me 5.33 cm/square. So if I were to round down
5 I wouldn't have enough room to put my data here on the side. And so what I can do is
I can round up and I can say that maybe everyone of these gridlines is going to be 6 centimeters.
And now I put my, label my axis on here. I want to make sure that I can go from all the
way from 18 up to 98. So each of these is then going to be 6 centimeters and so I can
show all of my data. So every two is going to be 12. And so you want to make sure that
it's a linear labeling of the x and the y axis. Next thing I want to do is I want to
graph my data. Well what's my first data point? Fertilizer of 12, so I'm going to go all the
way over here to 12 and then I'm going to have plant growth of 98. Well if this is 92
that means this is 98 so my first data point should be right there. And so now I'm going
to put all the other data points from my graph. So I'm going to fill those in with dots. Now
you can see that there were sometimes when I had same amount of fertilizer but two different
types of plant growth and that's fine. One thing I don't want to do right now if I'm
doing a scatter plot is I never want to connect these lines because those are different plants
and so that would make any sense. I'm almost done though. What's the last thing that I'm
missing right here on my graph is going to be a line of fit. And so a line of fit is
going to be a line that represents the average of my data. It doesn't always have to be a
straight line. You can see in this case that as I increase the amount of fertilizer it
starts to stabilize up here at the end. And so that's going to be my line of fit. We don't
want to extend it past my last data point. We don't really know what might happen out
here. It would only be just a guess. And so that's kind of hand graphing. What's your
next step? Well if you already know how to do graphing by spreadsheet then I wouldn't
watch this. You could subscribe to this video. That would be great or subscribe to this channel.
But if you want to see how to graph this data using a spreadsheet, I'm going to use Excel,
just click on this box right here. That's graphing by hand and I hope that was helpful.