Making a Scientific Graph The Basics.

Identifying Variables Independent Variable (manipulated variable) the thing the scientist is changing gets plotted along the x axis Dependent Variable (responding variable) the thing responding to the change gets plotted on the y axis Example: Adding Miracle*Gro to help tomato plants grow taller Amount of Miracle Gro is Indep Var (Experimenter is directly controlling this) Height of the plant is the dependent (measuring how this responds ) Write the independent & dependent variable on your paper.

Independent & Dependent Variables Your Turn Joe wants to see if adding sugar to water will affect the density of the water. He designs an experiment where he measures the density of pure water, then dissolves 5 grams of sugar in and measures the density again. Next, 5 more grams of sugar are added and the density is determined yet again. This is repeated until no more sugar dissolves. Identify the independent and dependent variable in Joe’s experiment. Answer: Mass of Sugar (Indep), Density of water (depend).

Components of a Graph Axis Labels Each variable should be clearly labeled with the type of measurement (Mass, Volume, Length, etc) The units used are put in parenthesis

Components of a Graph Title Minimum title: Y vs X Examples mass vs volume Must always include both variables Better titles are a little more descriptive The effect of (ind variable) on (dep variable) of (object) The effect of percentage sugar on density of water The effect of Mass of Miracle*Gro on the height of tomato plants “Effect” is the noun, “Affect” is the verb

Axis Labels Show example graphs here Components of a Graph Title has both variables in it. Axis Labels Show example graphs here Units are in parenthesis after label Dependent Variable is on Y axis Independent Variable is on X axis

Axis Labels Show example graphs here Can you find the 6 errors in this graph set-up? Identify as many as you can and then click the numbers at the side to see if you got them all. Axis Labels Show example graphs here Capitals should be used 1 Title only includes one variable Should be “affected” 2 3 4 No units are given in parenthesis 5 Variables on wrong axis Does not describe what was measured 6

Example: Properly Set-up Graph

Components of a Graph Scale In a Scientific Graph, the scale is zoomed in so that the graph “fills the paper” to set scale, look at the range of your data for each variable Put lowest value near bottom edge of graph and highest value near top This span should cover at least 75% of graph Scale does not have to start at 0,0 Try to make every block equal to a “nice” number 1,2,4,5 or any division of 10 of these (0.2, .05, 400. etc) Stay away from ‘ugly’ scales Every block = 3,7,9, etc

Identifying Variables - Example Let’s say we were making a graph of the relationship the between the temperature and the volume of a balloon. If we did this by changing the temperature and recording what the consequent volume was, then the __________ would be the independent variable, and the ___________ would be the dependent variable. temperature volume

What axis does the independent variable go on? What is the dependent variable? How do we show the units? What would be a good title? Notice how it fills the window & does not start at zero

Example of Poor X Axis Scale: Empty Space !!!!!

Example of Poor Y Axis Scale: Empty Space !!!!!

Example of Poor Y Axis Scale: Fills up less than half of window

Don’t actually need to do, but think about how you would set it up Set an appropriate scale for the data below and plot the points on your graph paper Trial Mass of Miracle Gro (grams) Height of plant (cm) 1 11.7 2 14.0 3 4 15.6 6 18.6 5 8 19.6 Fill out scale legend at top of graph paper Don’t actually need to do, but think about how you would set it up

Your Turn: Appropriate Scales Notice Scale does not start at 0,0.

Best-Fit Line Once points are plotted, draw the straight line that comes closest to hitting all points.

Best-Fit Line Notice that about half the points are above line and half are below. The line represents the ‘middle’ of all of the points. Above Line Below Line

Another Example of a best-fit line Another Example of a best-fit line. Notice that the line does not actually hit any of the data points.

How do you find the slope of a line? Slope is the rise over the run. Slope = ΔY ΔX Slope = Y2 – Y1 X2 – X1

Determining the Slope of a Best-Fit Line Pick any two points that are on your best-fit line Pick points that are fairly far apart These two points are NOT on your line They will give you the slope of a different line instead of your best-fit line

Determining the Slope of a Best-Fit Line Write the coordinates for those 2 points on your graph Use the coordinates to calculate the slope of best-fit line (36.8, 2.50) Slope = Y2 – Y1 X2 – X1 Slope = 2.50L – 1.50L 36.8 C – 20.0 C (20.0, 1.50) Slope = 0.0595 L/°C

Interpolating Data Volume = 1.91 L Use the graph to predict what is the volume of the balloon at 27 deg C ? Volume = 1.91 L

Interpolating Data Temp = 38.0 °C At what temperature is the balloon 2.5 liters ? Temp = 38.0 °C

Interpolating Data Temp = 38.0 °C What would the volume of the balloon be at 80 C ? Temp = 38.0 °C

solve this without using graph? Extrapolating Data What is the volume of the balloon when it is 80 °C? Volume = 4.8 L Can you think of a way to solve this without using graph? Interpolating Range

Predicted value is outside of range of tested values Extrapolating Data What is the volume of the balloon when it is 80 °C? Volume = 4.8 L Predicted value is outside of range of tested values Interpolating Range

Explain the difference between interpolating and extrapolating from your data. Compare the reliability of the two.

Your Turn: Determine the Slope of the Line

Your Turn: Determine the Slope of the Line General formula for any straight line How does this slope compare with yours? Same Answer? Sig Figs? Units?

Your Turn: Determine the Slope of the Line m = slope b = Y-intercept: Value of Y when x = 0 More on Y-intercept Equation can be made more specific: Y = m x + b = ( ) + Height 1.02 cm/g Mass 11.8cm

Which equation represents the following graph correctly? A. volume = -3g/mL (mass) + 6 B. mass = 2g/mL (volume) -3 Volume (mL) C. -3 = 6g/mL (volume) + mass D. volume = 2g/mL (mass) + 6 E. mass = 2g/mL (volume) + -3 Mass (g)

Which equation represents the following graph correctly? Volume is Dependent Variable ( on Y axis) Volume (mL) D. volume = 2g/mL (mass) + 6 Mass is Independent Variable ( on X axis) y = m (x) + b Mass (g)

Sketch a graph represented by Speed = -5mps/m (Height) + 25 Y intercept = 25 Slope = -5 mps/m Speed is Dependent Variable ( on Y axis) Height is Independent Variable ( on X axis)

Sketch a graph represented by Speed = -5mps/m (Height) + 25 What will the speed be when the height is 3 m? Can Interpolate or plug values into equation

Warm-Up: Write a specific equation for the line below (1.0,20.0) (2.0,15.0) Speed (m/s) (3.0,10.0) (4.0,5.0)

Sketch a graph represented by Speed = -5mps/m (Height) + 25 Y intercept = 25 Slope = -5 mps/m Speed is Dependent Variable ( on Y axis) Height is Independent Variable ( on X axis)

The End

Y- Intercept What is the Y-Intercept of this graph ? Y intercept = 2

Y- Intercept Y intercept = 11.8 cm What is the Y-Intercept of this graph ? Y intercept = 11.8 cm

What is the Y- Intercept? Why isn’t this the Y-Intercept?

What is the Y- Intercept? Back Y-Intercept = 0