Hi. It's Paul Andersen and this is Science and Engineering Practice 4: Analyzing
and Interpreting Data. After you've done an investigation you're going to be presented
with a lot of data and it's important that you learn how to analyze that. In science
data analysis is important because it allows us to derive meaning from the data that we've
collected. And in engineering to test solutions to problems. And so basically data analysis
is important for the following reasons. This is Charles David Keeling and he spent his
whole life collecting data on the the atmospheric carbon dioxide, how much carbon dioxide there
is in the atmosphere. And he did this on the Mauna Loa observatory in Hawaii. And this
is just a portion of the data that he collected as a scientist. Just a few years, 58, 59 and
60. And when you look at this it makes no sense to me and probably makes no sense to
you. But if we organize the data correctly and we graph it you get what's called the
Keeling Curve that shows how atmospheric carbon dioxide has increased over time. Again that's
going to account for a lot of the global warming that we're seeing. Because a lot of that carbon
is coming from us. And so it's important that we can put the data together and then present
it in a way that can make meaning from that. And so the goal in science classrooms is to
analyze data. We do that by first of all organizing and graphing it. And then interpreting the
data. Making sense of the data. Evaluating it. Laying it against our theories, laying
it against our designs. And then we can use mathematics and statistics to do a lot of
that. And so the progression in school of analyzing and interpreting data really should
start at the elementary level. And so again it's like throwing darts but getting better
and better and better through the years. And so we can break this down by school level.
In other words in at elementary school students should be using a notebook. A science notebook
and they should be collecting data and everything goes into that notebook. And that could be
drawings. It can be numbers. It can be words, but they should get into this idea that they're
collecting data and they're going to have to do something with that data. As you move
through elementary they should really get to the level of tables and organizing numbers
and organizing data in a table. And so let's say you're doing an experiment on fertilizer
and how varying the amount of fertilizer effects plant growth. And so they should get in the
idea of using a table to organize that and it's really good practice to always put the
thing that you're changing or the independent variable in the first column and then dependent
variable in the second. Graphing would be important at the elementary level. I think
it's sometimes hard for students to figure out what kind of graph should I use. And so
you could give them quite a bit of scaffolding. You could say I want you to graph it in a
certain way at elementary level. But as they move into middle school, you really want the
students to do the graphing on their own. And in my class I use four different types
of graphs I expect students to understand. And you should know this. That they're going
to collect data first and then you're going to have to figure out what type of graph to
do. And so the data comes first. And so you really have to have an understanding of what
kind of data you have before you can graph it. And so the four major types of graphs
I teach are the line graph. We're looking at change over time and your going to connect
the data points. We would use a scatter plot if we're looking at correlation of variables.
So eruption, duration and waiting time at Old Faithful, this would be a scatter plot.
We're not going to connect the dots because we're just correlating those two variables.
We would use a bar graph if we're comparing different groups. And then we'd use a pie
graph if we're looking at parts of a whole. And so you could present your students with
data and first of all have them figure out, you know, what kind of a graph am I going
to use? As you move from middle school into high school you want to make sure they understand
the difference between an independent and a dependent variable. Independent variable
remember is going to be the thing that you change in an experiment or I change in an
experiment. Dependent variable is going to be what changes as a result of that. Scatter
plots are powerful graphs when we're looking at correlations. So I could graph the data
and then you could show them how to draw a line of fit or a curve of fit. Make sure that
you start to teach the difference between causation and correlation. And so when you
look at a graph like this, it looks like the fertilizer is causing the plants to grow more.
You're not always sure remember, and this is a good example you could share with your
students. We find, scientists find that there is a definite correlation between the amount
of ice cream that people eat and the amount of crime that is done in an area. So if you
were to graph it you would find that ice cream vs crime is going to be a nice kind of a relationship
like that. It's correlation. It doesn't mean causation. Like what's really causing this.
Well the warmer temperatures in the summer are causing people to eat more ice cream and
causing people to commit more crimes in the summer. And so there'd be causation here,
correlation here. And so you want to make sure when you're evaluating your data, really
be hesitant before you jump into the idea of this is causing that. As you move to high
school you can really take a look at the mathematics and the statistics behind the data. And so
a great example would be a slope. So once we've looked at this correlation of the data
I could simply calculate the slope of that line of fit. So I could figure out the rise
over the run and I could figure out a y value .4 centimeters per gram. And so slope is incredibly
important especially in a line graph when we're looking at change over time. Another
thing that students don't usually understand in my class is what's called the correlation
value or the r value. Correlation value, and you can do this in spreadsheets or on a TI
calculator. Basically an r value is going to tell you how good your data fits to a line.
If you do a regression. And so if in a linear regression you can have r values, like an
r value of 0.0 means that there's no correlation between the two data sets. 0.6 means there's
some. 1.0 means it's perfect. And we can also have negative correlation values as well.
And so if you were to look up here, what is the correlation value? Maybe 0.7, something
like that. And so students can actually start to look at their data and say how close is
it to a line? How good is it? They're starting then to evaluate the data. You could move
into the area of statistics then starting with, let's say this is our data set here,
some simple statistics that I think are pretty powerful are the sample size, mean, median
and range. And so right here the sample size would be one, two, three, four, five, six,
seven. So there are seven data points. That would be my sample size. My mean or average
is going to be 5. Add them up and divide by the total number. And then my median, to figure
out median, would be right here. It's going to be in the middle. And if we were to have
an even number it would be 5.5. You'll find that students are really good at this. Math
teachers do a pretty good job at that. And my range right here would be eleven. As you
get more and more into statistics, you can move into the idea of normal distributions.
I think standard deviation and standard error are incredibly powerful . I'll put links to
two other videos I made on those. If you can get students to collect data and then look
at, how good is this data? Then you're really not just displaying the data, you're really
starting to evaluate it. And I hope that's helpful.