so far we've taken a look at various parts of the scientific method we've taken a look at a lot of data collection on how to measure we've taken a look at how to analyze that data in terms of doing mathematics taking a look at how to round off answers to math problems for example but another excellent way of doing analysis is through graphing if you have a whole lot of data points it makes sense to sort of put it into some sort of pictorial representation in other words to make a picture out of your data a picture that you can make some sense of in order to make a proper graph you need to have first of all an xais and a y AIS and you have to put some very specific things on these axes you see you as an experimentor have control over one of the variables and that variable called the indep dependent variable will go on the x axis that's the variable that you the experimenter have control over the other variable is what changes depending on the variable that you've just controlled temperature for example over time we're going to let an experiment go over a certain period of time time will be the independent variable and the temperature will depend on how long we let that reaction sit for so the temperature is dependent on time so the Y AIS will have the dependent variable the variable that changes as a result of the experimenter changing the independent variable all other variables should remain constant to avoid contaminating your results when you put your data points down you want to make sure that they're put down properly so your axis should have increasing regular interval divisions 0 10 20 30 40 50 60 70 80 90 on this axis 0 50 100 150 200 250 300 regularly increasing then the data points can be placed on the graph and circles put around them these circles are called Point protectors the purpose of a point protector is twofold one it shows that the data point was the result of a measurement and as you remember when you take a measurement that last digit is an estimate so to show the uncertainty with the measurement you put a circle around it to say it's in this ballpark the other reason you put a point protector is so that when you draw your line or curve or whatever you're going to draw if you cover up the data point the circle will still give away the data Point's location to say hey wait there's a data point buried underneath this line you just drew over it so a point protector is necessary when drawing a proper graph in addition to that you need to make sure that you have a title the title will always be the same thing you don't have to come up with any kind of creative title Y versus X whatever's on the Y AIS versus whatever's on the x axis temperature versus time that's it that's all you have to put for your title temperature versus time Y versus X dependent versus independent variable left versus right if you want to look at it that way also notice that each of the variables has a unit after it so we know exactly what these numbers are representing there's many different ways of measuring temperature you can have degrees Celsius you can have degrees Fahrenheit you can have Kelvin there's even a scale called the Ranken scale this tells us that we're using Kelvin as our scale so make sure that you have units after each of your axis labels the last thing you want to have is a line or a curve that best represents the best fit of your data the simplest kind of graph of course will be from linear data you know y = mx plus b where your data Falls roughly along a straight line in that case you're going to need to draw what's called a best fit line to go through your data points in such a way that there's rough ly the same number of data points above as below and the distances of the data points to the line are roughly equal on both sides I'll draw you one so you can see what that looks like okay so here we have a series of data points that falls roughly on a linear kind of scale you don't start at 0 0 you don't start at the origin because the equation is y = mx + b m of course being the slope B being where the line intersects the Y AIS and if we always started at 0 0 the equation would be y = mx + 0 and we wouldn't even need to put it in there so you're not going to start at 0 0 we can start with the first data point and we can swivel this line back and forth with a ruler until we have roughly the same number of points above and below low and when you add the distances of the points to the line on either side they add up to roughly the same thing there are computer programs that will do this for you it's called linear regression but in the case of a lab eyeballing it will generally be good enough for doing most of what you need to do and that would be a line of best fit you can also have curves of best fit but most of the data you're going to plot in lab is going to be linear data once you've drawn your graph now now you're going to use your graph to draw some sort of conclusion about the data that you just collected there are a couple different kinds of relationships you can have a direct relationship where changing one variable causes the other variable to change in exactly the same manner for example increasing this variable causes this variable to increase as well or decreasing this variable will cause a decrease in that variable an IND direct or inverse relationship is where as one variable increases the other one decreases increasing X causes a decrease in y and vice versa so that's an indirect or inverse relationship a graph can also be used to get information that was not obtained during the experiment to make predictions for example we know exactly what's going on with these data points but what if we want to find out information that's not one of those data points well it's easy we can either use interpolation where we get information between our data points or extrapolation where we get data beyond our data points this is going to be very handy when using the reference tables in interpolation you know what x is and you want to find out what Y is so you start at the x-axis you go up to the best fit line and shoot over to the Y AIS and read whatever ever it says there reading in between data points to get information that's interpolation if you want to find information that's beyond your collected data points you extend your line you make it extend a little extra extra extrapolation again you know what x is you want to find out what Y is start at X shoot up to the line of best fit and over to the Y AIS you can also do the same thing if you know what Y is you can shoot over to the line and drop down to the x- axis to get information off of that this is how you will be making use of many of your reference tables interpreting graphs through interpolation or extrapolation this is reference table h on the New York State chemistry reference tables this reference table will plot the vapor pressure of four different gases at different temperatures what vapor pressure is doesn't matter right now but here's how you use the data if you know what the temperature is you can find the vapor pressure very easily let's say we want to find the vapor pressure of propanone at 50° C so we start at 50° C we go up to the propanone line and then we shoot across and read the information off of the Y AIS let's say we want to know at what temperature will ethanol have a vapor pressure of 50 kilopascals so we start at 50 kilopascals we go across to the ethanol line and we drop down and read the temperature off of the graph that is interpolation using information you have to get information that you might need so graphs are an excellent way to represent your data to make it more understandable and easier to reach a conclusion about whether you're hypoth hthis is supported and maybe just maybe you will have solved your problem thanks to the magic of graphs