Hi. It's Mr. Andersen and this
is A Beginner's Guide to Graphing Data. I
continue to be surprised by the simple mistakes
that are made by students in my high school
science class when they try to display their
data in a graph. And I think the reason why
is that we spend a lot of time in elementary
school on graphing. But as students move from
middle school to high school and on to college
we don't spend very much time on graphing.
It's just like reading. We assume that they
know how to do it. And so I've put this video
together to show you the importance of graphs,
the different types of graphs and even give
you some practice graphing some data. And
so first of all let's start with the term
graph. The term graph and the term chart can
be used interchangeably. They mean eventually
the same thing. And so you'll hear me go back
and forth between chart, graph, plot. They're
basically ways that we can take data and display
it visually. And so why do we use them? Well
let me give you an example. This right here
is Charles David Keeling. He spent years and
years and years on top of Mauna Loa in Hawaii
collecting data on the levels of carbon dioxide
in the atmosphere. And let me show you less
than one percent of the data that he collected.
It's almost incomprehensible to us. When we
get a huge list of numbers we can't make sense
of it. We can't find patterns. But if I were
to show you all of the data that Mr. Keeling
collected we would find the Keeling curve.
And this is one of the most famous graphs
in all of science. It's basically showing
increasing levels of carbon dioxide. You see
annual cycling of carbon dioxide and this
is very important because it's tied to global
warming. And so when we can see the data,
we can make sense of the data. And so there
are five major types of graphs that I'm going
to talk about in this video. They are line,
scatter, bar, histogram and pie graph. And
so I want to start with a little pre-quiz
and see what you know. And so could you right
now point to the line graph on the right?
Let me show you if you're right. Line graph
is going to be that one. Could you point to
the scatter plot now? And what about a bar
graph? Could you point to the bar graph? And
the histogram? And hopefully you can point
to then the pie graph. Okay. So how did you
do? Did you get all of those right? Hopefully.
The ones that are confusing, obviously, a
line graph is going to be dots connected with
a line. Even though we have a best fit line
here the scatter plot is not going to connect
the dots at all. It's going to show correlation
between number sets. Did you get screwed up
on the bar graph? How we tell the different
between a bar graph and a histogram? Bar graph
we're going to have space between the different
columns and histogram they're going to touch.
And so the reason it's important that you
know and can identify the different graph
types is that as a scientist you're going
to collect data and then you're going to have
to choose what graph you're going to use.
In other words the data always comes first
and then you've got to figure out what graph
you're going to use. And so let's talk about
five different types of graphs. First one
is going to be a line graph. We're going to
use a line graph if we are looking a change
over time. And so in this one we're looking
at US trade in goods and services. And so
you can see the dates are going to be along
the x-axis and then the moneys are going to
be along the y-axis. And so in science maybe
we're collecting data on an individual worm
and how much oxygen it respires over time
or consumes over time, then a line graph would
be a great example. Let's say we're looking
at a scatter plot. We're going to use that
when we're correlating two number sets or
two sets of data. So it's a correlation of
variables. And so this scatter plot right
here, they're looking at the eruption of Old
Faithful, how long that eruption takes and
then the time between the eruptions. And you
can see that there's a relationship between
those two. Scatter plots are really important
in a science classroom. For ever varying one
variable, we call that the independent variable,
then measuring how that effects another variable
we call that the dependent variable, then
a scatter plot is going to be the graph of
choice. And so when you're doing that, make
sure you put the independent variable on the
x-axis. And so let's say that this plant right
here, I'm doing an experiment where I vary
the amount of fertilizer and then I measure
how much that plant grows over time. Well
since I'm varying the independent variable,
I'm going to put that on the x, the amount
of fertilizer and then we put plant growth
on the y and we look at a correlation between
those two. So scatter plots are incredibly
important in a science room. What about a
bar graph? We us a bar graph if we're comparing
two groups together, or more that two groups.
And so in this bar graph we're looking at
worldwide incarceration rates and we're comparing
different countries. Let's say in the lab
we're measuring how different colors of light
effect the rate of photosynthesis. Then we
could put the rate of photosynthesis on the
y-axis and then we'd represent each of those
different colors of light using a different
bar. Lots of times a bar graphs, that bar
is going to represent the average or the mean
of all the data we collected. What about a
histogram then? Histogram is when we're looking
at the distribution of data. So let's look
at this histogram here. We're looking at height
of black cherry trees. We have different heights
along the bottom and then we just have the
number of trees on the side. And so for example,
how many of these cherry trees are going to
be between the height of 70 and 75 feet? Well
we'd look here and we'd find that that's going
to be eight. So let's say we're graphing humans
height along the bottom and then we're looking
at the frequency, that would be a histogram.
And then you're probably familiar with a pie
chart. We use that if we're ever looking a
parts of the whole. And so these are all the
different families of rodents and then we
can see what percent each of those are of
each of the different families. So muridae
is going to be most popular. Those are going
to be the rats and the mice. Okay. So once
we've got that, which graph we're going to
use, then we can actually get to the graphing.
And so let's play with that for a second.
Let's say I've got data from a pretend ice
cream store that I have here in Bozeman. And
on this data right here I've got the average
high temperature in Bozeman and then I've
got the number of ice cream cones that I was
able to sell during these different months.
And so let's say I wanted to display for example
all the different months and then the percentage
of the whole of which I sold ice cream. So
I'd be looking at a pie chart. So I'd have
all the different months as a different section
of that whole pie. Let's say I just want overtime
to look at the average temperatures. The average
high temperatures in Bozeman and what would
I use? That would be a line graph. Let's say
I want to look at three specific months, three
groups and compare the ice cream sales in
all months that start with the letter J, well
then a bar graph would be great. So let's
get to a real graph and show you all the elements
of a graph. So let's say I want to look at
the correlation of ice cream sales and average
high temperatures at my ice cream sale, or
my ice cream store. And I would use a scatter
plot. So let me show you all the important
parts of a scatter plot. First thing you want
to do is you want to figure out where your
axis are gong to be. And so I'm going to put
along the x-axis, I'm going to put the temperature
and then I'm going to put my ice cream sales
on the y. Next thing I want to do is I want
to have a title for each of those. And so
I'm going to put average high temperature
along the bottom. Notice I put in parenthesis
the units that I'm measuring it in. Then I'm
going to put ice cream sales on the y-axis
and I'm going to put the units that I measure
that on as well. What's next on the graph?
Next is going to be the title. The title should
tell you everything contained on the graph.
In other words I'm going to look at the correlation
of ice cream sales and average high temperature.
I'm going to tell you where it is and I'm
going to give you the date for that. Lot's
of times the titles are too simplistic. You'll
have a title that's just simply ice cream.
You have to have way more information in the
title. In fact I should be able to look at
the title and it should be the story of everything
contained within that graph. What's next,
well on a scatter plot, we're going to have
the data. And then finally we should have
a best fit line. A best fit line is going
to be like an average of the data. If you're
putting this in free hand, basically half
of the dots on your scatter plot should be
above it and then half of them should be below.
A good best fit line should never extend past
your data. I should't put like an arrow on
the end of it, because really I can only put
a best fit line within my data. I can only
interpolate within that graph. So these are
all the elements of a graph. Good title, label
the axis, make sure you have linear numbers
so it's going, you can see here that there's
15, 15, 15 between each of those major grid
lines and we're going to have the same thing
here on the y. You've got your data points
and then you have a best fit line. So those
are all the elements of a good graph. Another
important thing that students tend to do is
they want to include the number zero here.
You don't have to have a number zero. If your
data doesn't have the 0 in it, then it shouldn't
be on your graph. So let's look at a bad graph.
Let's say I'm collecting data where I'm looking
at the amount of fertilizer and how that effects
plant growth. And let's say that a student
gives you this graph. Can you find all the
errors in the graph? I can find at least,
you know, 10 probably. Number 1. Let's start
with the title. It's got a title, but the
title isn't very descriptive. The title should
show me what's going to be on my x and what's
going to be on my y axis. So like the relationship
or the relation of fertilizer to plant height.
Next thing, I've got plant height here, but
since I'm varying the amount of fertilizer,
my independent variable should be down here.
So we would want the fertilizer to be down
here and then we'd want plant height to be
on the side. We also want to make sure that
we put units in parenthesis that we measure
it in. So we would have plant height over
here then fertilizer down here. This is a
scatter plot so you should never connect the
dots in a scatter plot. Other things that
we have is we have non-linear scaling. So
down here you see it goes 5 7 11 15 17 19.
The distance between each of these should
be equal. And then this number here 12.5 doesn't
tell me anything. I couldn't measure anything
else on here because I'm just given one number.
So you have to have at least 2 numbers on
your gridline. You can also see that the best
fit line is extending past the data. And so
this is a bad scatter plot. So we're having
quite a few errors on that so you want to
try to remedy that when you're making a scatter
plot of your own. And so let's get to that.
So basically I've got two videos that I've
made. One is on graphing data by hand. And
if you want to watch that you can click on
that box right here. And the other one is
going to show you how to use a scatter plot
graphing that by spreadsheet. So the next
steps, if you want to do some graphing is
click on one of those. And if you just wanted
to learn about the good elements of graphs
then I hope that was helpful.
